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Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE NORMALISATION ISO/IEC JTC1/SC2/WG2 Universal Multiple-Octet Coded Character Set (UCS) ISO/IEC JTC1/SC2/WG2 N2191 Date: 2000-03-14 Title: Proposal for Encoding Additional Mathematical Symbols in the BMP Source: U.S. National Body Status: Working Document of JTC1/SC2/WG2 (and Summary Proposal Form) Action: For review and comment by JTC1/SC2/WG2 Distribution: Members of JTC1/SC2/WG2 Introduction This document constitutes the consolidated proposal for completion of the set of mathematical symbols encoded in ISO/IEC 10646. Additional alphanumeric symbols were added to the CD for 10646-2, and have been under ballot. This proposal provides for the complementary set – those math symbols, operators, and delimiters that are currently missing from the repertoire of math symbols encoded in the BMP of 10646-1. This proposal is the culmination of a several-year process of collation and review of mathematical symbols, with close cooperation between the Unicode Technical Committee and the STIX Project, involving extensive expertise from the mathematical, scientific, and technical publishing industry. In our opinion, this proposal is now quite mature, having passed the technical scrutiny of the mathematicians and technical publishing experts of the STIX Project, and the character encoding scrutiny of the UTC. It is now ready for review and comment by WG2. We urge consideration for a new subdivision of work for an Amendment to 10646-1 to add this repertoire to the UCS, to meet the expressed needs of the international mathematical, scientific, and technical publishing industry for the representation of mathematics using the ISO/IEC 10646 character encoding. The document we present here is divided into six parts: Introduction, background, rationale, and references Annex 1: Proposal summary form Annex 2: Draft charts and names list, enumerating the proposed repertoire Annex 3: Relevant excerpts from L2/00-002, to illustrate glyphs currently missing from Annex 2 Annex 4: Symbol variants defined using a Variation Selector (VS) Annex 5: Letters of support from major mathematical organizations Background This proposal originated as the work of the STIX Project (Scientific and Technical Information eXchange), a working group reporting to STIPUB, a consortium of publishers of mathematical, scientific, and technical books and journals. The ultimate product of the STIX group will be the creation of one comprehensive set of fonts for scientific and technical publishing. This set of fonts should be adopted and supported by all major STM (scientific, technical, and mathematics) publishers internationally. It will also be made available for general use under license but free of charge, with the explicit aim to ease and foster the uninhibited flow, exchange, and linking of scientific information worldwide.
Transcript
Page 1: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

1

ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION

ORGANISATION INTERNATIONALE DE NORMALISATION

ISOIEC JTC1SC2WG2 Universal Multiple-Octet Coded Character Set (UCS)

ISOIEC JTC1SC2WG2 N2191

Date 2000-03-14 Title Proposal for Encoding Additional Mathematical Symbols in the BMP Source US National Body Status Working Document of JTC1SC2WG2 (and Summary Proposal Form) Action For review and comment by JTC1SC2WG2 Distribution Members of JTC1SC2WG2

Introduction This document constitutes the consolidated proposal for completion of the set of mathematical symbols encoded in ISOIEC 10646 Additional alphanumeric symbols were added to the CD for 10646-2 and have been under ballot This proposal provides for the complementary set ndash those math symbols operators and delimiters that are currently missing from the repertoire of math symbols encoded in the BMP of 10646-1 This proposal is the culmination of a several-year process of collation and review of mathematical symbols with close cooperation between the Unicode Technical Committee and the STIX Project involving extensive expertise from the mathematical scientific and technical publishing industry In our opinion this proposal is now quite mature having passed the technical scrutiny of the mathematicians and technical publishing experts of the STIX Project and the character encoding scrutiny of the UTC It is now ready for review and comment by WG2 We urge consideration for a new subdivision of work for an Amendment to 10646-1 to add this repertoire to the UCS to meet the expressed needs of the international mathematical scientific and technical publishing industry for the representation of mathematics using the ISOIEC 10646 character encoding The document we present here is divided into six parts

bull Introduction background rationale and references bull Annex 1 Proposal summary form bull Annex 2 Draft charts and names list enumerating the proposed repertoire bull Annex 3 Relevant excerpts from L200-002 to illustrate glyphs currently missing from Annex 2 bull Annex 4 Symbol variants defined using a Variation Selector (VS) bull Annex 5 Letters of support from major mathematical organizations

Background This proposal originated as the work of the STIX Project (Scientific and Technical Information eXchange) a working group reporting to STIPUB a consortium of publishers of mathematical scientific and technical books and journals The ultimate product of the STIX group will be the creation of one comprehensive set of fonts for scientific and technical publishing This set of fonts should be adopted and supported by all major STM (scientific technical and mathematics) publishers internationally It will also be made available for general use under license but free of charge with the explicit aim to ease and foster the uninhibited flow exchange and linking of scientific information worldwide

Math Symbols 2000-03-14

2

The symbol complement of the STIX font set will be based on the symbols in this proposal along with many other symbols already encoded in ISOIEC 10646 as well as variant forms not included here (because they are required by publishing house styles without different meaning from symbols included above) Additional technical symbols from areas other than mathematics will also be included in the font definitions More information about the STIX Project can be found at the STIX web site hosted by the American Mathematical Society (AMS) httpwwwamsorgSTIX The Unicode Technical Committee worked closely with the STIX Project over the past two years to refine the proposal into a character encoding proposal suitable for addition to ISOIEC 10646 During this process duplicates have been identified and removed and clarification of distinctions between characters glyphs and variants has been made The original proposal was divided into two large portions a proposal for the addition of alphanumeric symbols (under ballot for the CD for 10646-2) and this proposal for the addition of other mathematical symbols As this proposal has developed it has been connected to other standardization efforts which are now interdependent on the completion of mathematical symbol encoding in ISOIEC 10646 In particular the special problems of handling technical texts have been examined in detail by the W3C HTML Math Working Group their MathML proposal which is interdependent with this proposed repertoire of math symbols for ISOIEC 10646 was accepted as a W3C Recommendation on 7 April 1998 [see httpwwww3corgMath ]The work of the HTML Math Working Group is also related to the work of the OpenMath Consortium Major vendors of mathematical formatting software are also dependent on the resolution of the encoding of additional mathematical symbols in ISOIEC 10646-1

Rationale Scientific communication and publication via the World Wide Web are currently hindered by the absence both of suitable symbol fonts and of recognized methods of indicating particular symbols and their relationships to one another The availability of a complete UCS character encoding of mathematical symbols and of a correlated universal font set for their rendering will benefit scientific and technical publishing in several ways bull Elimination of certain legal problems with distributing PDF files and publishing on the World Wide Web bull Ease of exchange of documents from different publishers bull Simpler and more robust re-use of archived material The STIX Project group has agreed that the basis for the organization of such a font set should be ISOIEC 10646Unicode ISOIEC 10646 is the reference character set for XML and therefore for MathML as well It is the character set of the programming language Java and underlies all current Windows operating systems as well as many others In XML documents and most importantly for use in MathML one must be able to identify all notation either by numerical character reference or by entity reference But numerical character references are ISOIEC 10646 numbers since that is the character set underlying XML If entity names are used they must still be mapped to something that applications will be able to handle and render All of these considerations argue very strongly that the set of mathematical symbols encoded in the UCS should be completed so as to enable the representation and presentation of mathematics and other technical materials dependent on mathematics ndash both for the World Wide Web and for data interchange dependent on XML In the charts and lists shown in the Annexes we have included only what we believe to be unique symbols not currently covered by the repertoire of ISOIEC 10646 The language of mathematics is fluid and symbols are defined in context to represent particular mathematical concepts The tool set of an active mathematician ideally consists of several alphabets whose members can be distinguished from one another to represent various classes of variables and constants and a fairly extensive collection of similarly-sized shapes to represent various operations or delimitation of expressions There are of course many fully standardized shapes that are now used almost exclusively to represent particular operations and relations but even these are sometimes adopted in fields where they are not already in use and redefined to have some other particular meaning For this reason the names suggested for the symbols listed here are in some cases not functionally precise where multiple varying meanings are possible or a single precise meaning is not available the name simply describes the shape of the proposed character

Math Symbols 2000-03-14

3

Variants Many math symbols occur in two or more variant forms with the same or similar meanings usually but not always attached to both In order to accommodate the sometimes strong preferences of authors and publishers a single Variation Selector (VS) is recommended to be applied to a fixed list of symbols with predetermined results The Variation Selector follows the symbol whose variant it specifies As a character by itself the Variation Selector has no independent appearance it only functions to choose a particular variant for the character it follows Only combinations defined by the standard should be meaningful In any other context the Variation Selector character should be ignored The Variation Selector (VS) in this proposal is completely analogous to the Mongolian Free Variation Selector (MVS) characters already in ISOIEC 10646 The difference is merely that the MVS characters are only meaningful in combination with other Mongolian characters to select variants of those characters The VS is separately proposed for use in combination with mathematical symbol characters to select variants of those characters The exact list of variants currently known to be required for mathematical scientific and technical publishing is shown in Annex 4

Letter-like Symbols For a mathematician or other scientist alphabets provide the symbols to represent ad hoc variables as well as a number of more well-defined concepts Different styles of alphabets have different meanings some of which have been formally standardized in some disciplines but many of which follow only the strength of custom or even current necessity The CD for ISOIEC 10646-2 includes sets of mathematical alphanumeric symbols that are regularly used in mathematical and technical literature those alphabets and digits will not be further dealt with here There remain however some individual letters from or related to these alphabets that are routinely used in a turned or inverted orientation as well as a few symbols in the style of a particular math alphabet but not part of its normal alphabetic complement These are considered distinct letter-like symbols and are therefore candidates for code assignments They are included in this proposal along with the larger collection of general mathematical symbols and operators

Brace Parts A small collection of brace and bracket parts has also been included in this proposal These characters are intended to complete the coverage of the PostScript symbol set as well as some character-like entities used by TeX and other technical typesetting systems These brace parts are explicitly intended as compatibility characters to match those preexisting repertoires Their inclusion facilitates the interconversion of data from such systems with systems using the ISOIEC 10646 character encoding

Explanation of Conventions in the Annexes In Annex 3 four data elements are given for each symbol bull an arbitrary reference ID indicating location in the corresponding chart bull an asterisk () if there is an existing symbol in Unicode or another symbol in this collection that appears to be

similar bull a one-letter code indicating the class of the symbol bull a proposed name for the symbol (usually based on form occasionally based on meaning if dominant) Note the proposed name shown in Annex 3 may have been superseded by the name shown in Annex 2 In all cases the name shown in Annex 2 should take precedence for this proposal Annex 3 is only attached because of the difficulty of completing a high-quality font for Annex 2 in time to meet the deadline for consideration at the Beijing WG2 meeting The one-letter codes indicating the class of the symbol are as follows

N normal or ordinary eg symbol used as a variable A alphabetic subclass of ordinary D diacritic or combining symbol

Math Symbols 2000-03-14

4

P punctuation B binary operator eg ltmathgta + bltmathgt R relation eg ltmathgta = bltmathgt L large operator eg sum product O opening delimiter (assuming left-to-right presentation) C closing delimiter (assuming left-to-right presentation) F nondirectional delimiter (fence post)

In Annex 3 the two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form a size-graded sequence with the present ISOIEC 10646 squares 25A0 25A1 25AA and 25AB Ideally the largest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest just a bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used ad hoc to define various operations with different sizes often indicating the degree of conformity to a particular notion (Several different geometric shapes are used in this manner the most common being squares and circles)

References International Organization for Standardization ISO 31XI-1992 Mathematical signs and symbols for use in the physical sciences and technology 2nd edition 1992 (by ref in ANSIIEEE P1324) American Society of Mechanical Engineers ANSI Y1020-1975 Mathematical signs and symbols for use in physical sciences and technology 1975 Institute of Electrical and Electronics Engineers ANSIIEEE P1324 (draft revision of Y1020) Draft standard mathematical signs and symbols for use in physical sciences and technology 1992 ISOIEC 88791986 Information Processing --- Text and Office Systems --- Standard Generalized Markup Language (SGML) Annex D Public text ISOIEC 9573-13 Information Technology --- SGML Support Facilities --- Techniques for Using SGML --- Part 13 Public entity sets for mathematics and science Stepney Susan (editor) Proposal to add the ISO Standard Z character set to UnicodeISO-IEC 10646 SC2 N3393 Committee Draft ISOIEC CD 10646-2 L298-405 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L298-406 Proposal to encode mathematical variant tags L299-045 Proposal to encode mathematical alphanumeric symbols L299-049 Addendum to L298-405 Request for assignment of codes to mathematical and technical symbols L299-159 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (revised) L299-160 Proposal to encode mathematical variant tags L299-195 Proposal to encode mathematical alphanumeric symbols L299-199 Mathematical Alphabets (for L299-195)

Math Symbols 2000-03-14

5

L299-244R Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L299-346 Mathematical brace pieces L200-002 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (supersedes L299-244R)

ISOIEC JTC 1SC 2WG 2 PROPOSAL SUMMARY FORM TO

ACCOMPANY SUBMISSIONS FOR ADDITIONS TO THE REPERTOIRE

OF ISOIEC 10646

Please fill Sections A B and C below Section D will be filled by SC 2WG 2

For instructions and guidance for filling in the form please see the document Principles and Procedures for Allocation of New Characters and Scripts (httpwwwdkuugdkJTC1SC2WG2prot)

A Administrative

1 Title Proposal for Encoding Additional Mathematical Symbols in the BMP

2 Requesters name US

3 Requester type (Member bodyLiaisonIndividual contribution) Member body

4 Submission date 2000-03-14

5 Requesters reference (if applicable) WG2 N2191

6 This is a complete proposal

B Technical - General

1 (Choose one of the following)

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

038F

0390

0391

0392

0393

0394

0395

0396

0397

0398

0399

039A

039B

039C

039D

039E

039F

03A0

03A1

03A3

03A4

03A5

03A6

03A7

03A8

03A9

03AA

03AB

03AC

03AD

03AE

03AF

03B0

03B1

03B2

03B3

03B4

03B5

03B6

03B7

03B8

03B9

03BA

03BB

03BC

03BD

03BE

03BF

03C0

03C1

03C2

03C3

03C4

03C5

03C6

03C7

03C8

03C9

03CA

03CB

03CC

03CD

03CE

03D8

03D9

03F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

x

y

z

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

200A

200B

200C

200D

200E

200F

2011

2013

2014

2015

2017

2018

2019

201A

201B

201C

201D

201E

2020

2021

2022

2026

2028

2029

202A

202B

202C

202D

202E

202F

2030

2032

2033

2039

203A

203C

203E

2044

204E

204F

2050

2051

2052

2053

2054

2055

2056

2057

205F

2061

2062

2063

206A

206B

206C

206D

206E

206F

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

2147

2148

2149

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

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prod

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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cent

pound

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 2: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

2

The symbol complement of the STIX font set will be based on the symbols in this proposal along with many other symbols already encoded in ISOIEC 10646 as well as variant forms not included here (because they are required by publishing house styles without different meaning from symbols included above) Additional technical symbols from areas other than mathematics will also be included in the font definitions More information about the STIX Project can be found at the STIX web site hosted by the American Mathematical Society (AMS) httpwwwamsorgSTIX The Unicode Technical Committee worked closely with the STIX Project over the past two years to refine the proposal into a character encoding proposal suitable for addition to ISOIEC 10646 During this process duplicates have been identified and removed and clarification of distinctions between characters glyphs and variants has been made The original proposal was divided into two large portions a proposal for the addition of alphanumeric symbols (under ballot for the CD for 10646-2) and this proposal for the addition of other mathematical symbols As this proposal has developed it has been connected to other standardization efforts which are now interdependent on the completion of mathematical symbol encoding in ISOIEC 10646 In particular the special problems of handling technical texts have been examined in detail by the W3C HTML Math Working Group their MathML proposal which is interdependent with this proposed repertoire of math symbols for ISOIEC 10646 was accepted as a W3C Recommendation on 7 April 1998 [see httpwwww3corgMath ]The work of the HTML Math Working Group is also related to the work of the OpenMath Consortium Major vendors of mathematical formatting software are also dependent on the resolution of the encoding of additional mathematical symbols in ISOIEC 10646-1

Rationale Scientific communication and publication via the World Wide Web are currently hindered by the absence both of suitable symbol fonts and of recognized methods of indicating particular symbols and their relationships to one another The availability of a complete UCS character encoding of mathematical symbols and of a correlated universal font set for their rendering will benefit scientific and technical publishing in several ways bull Elimination of certain legal problems with distributing PDF files and publishing on the World Wide Web bull Ease of exchange of documents from different publishers bull Simpler and more robust re-use of archived material The STIX Project group has agreed that the basis for the organization of such a font set should be ISOIEC 10646Unicode ISOIEC 10646 is the reference character set for XML and therefore for MathML as well It is the character set of the programming language Java and underlies all current Windows operating systems as well as many others In XML documents and most importantly for use in MathML one must be able to identify all notation either by numerical character reference or by entity reference But numerical character references are ISOIEC 10646 numbers since that is the character set underlying XML If entity names are used they must still be mapped to something that applications will be able to handle and render All of these considerations argue very strongly that the set of mathematical symbols encoded in the UCS should be completed so as to enable the representation and presentation of mathematics and other technical materials dependent on mathematics ndash both for the World Wide Web and for data interchange dependent on XML In the charts and lists shown in the Annexes we have included only what we believe to be unique symbols not currently covered by the repertoire of ISOIEC 10646 The language of mathematics is fluid and symbols are defined in context to represent particular mathematical concepts The tool set of an active mathematician ideally consists of several alphabets whose members can be distinguished from one another to represent various classes of variables and constants and a fairly extensive collection of similarly-sized shapes to represent various operations or delimitation of expressions There are of course many fully standardized shapes that are now used almost exclusively to represent particular operations and relations but even these are sometimes adopted in fields where they are not already in use and redefined to have some other particular meaning For this reason the names suggested for the symbols listed here are in some cases not functionally precise where multiple varying meanings are possible or a single precise meaning is not available the name simply describes the shape of the proposed character

Math Symbols 2000-03-14

3

Variants Many math symbols occur in two or more variant forms with the same or similar meanings usually but not always attached to both In order to accommodate the sometimes strong preferences of authors and publishers a single Variation Selector (VS) is recommended to be applied to a fixed list of symbols with predetermined results The Variation Selector follows the symbol whose variant it specifies As a character by itself the Variation Selector has no independent appearance it only functions to choose a particular variant for the character it follows Only combinations defined by the standard should be meaningful In any other context the Variation Selector character should be ignored The Variation Selector (VS) in this proposal is completely analogous to the Mongolian Free Variation Selector (MVS) characters already in ISOIEC 10646 The difference is merely that the MVS characters are only meaningful in combination with other Mongolian characters to select variants of those characters The VS is separately proposed for use in combination with mathematical symbol characters to select variants of those characters The exact list of variants currently known to be required for mathematical scientific and technical publishing is shown in Annex 4

Letter-like Symbols For a mathematician or other scientist alphabets provide the symbols to represent ad hoc variables as well as a number of more well-defined concepts Different styles of alphabets have different meanings some of which have been formally standardized in some disciplines but many of which follow only the strength of custom or even current necessity The CD for ISOIEC 10646-2 includes sets of mathematical alphanumeric symbols that are regularly used in mathematical and technical literature those alphabets and digits will not be further dealt with here There remain however some individual letters from or related to these alphabets that are routinely used in a turned or inverted orientation as well as a few symbols in the style of a particular math alphabet but not part of its normal alphabetic complement These are considered distinct letter-like symbols and are therefore candidates for code assignments They are included in this proposal along with the larger collection of general mathematical symbols and operators

Brace Parts A small collection of brace and bracket parts has also been included in this proposal These characters are intended to complete the coverage of the PostScript symbol set as well as some character-like entities used by TeX and other technical typesetting systems These brace parts are explicitly intended as compatibility characters to match those preexisting repertoires Their inclusion facilitates the interconversion of data from such systems with systems using the ISOIEC 10646 character encoding

Explanation of Conventions in the Annexes In Annex 3 four data elements are given for each symbol bull an arbitrary reference ID indicating location in the corresponding chart bull an asterisk () if there is an existing symbol in Unicode or another symbol in this collection that appears to be

similar bull a one-letter code indicating the class of the symbol bull a proposed name for the symbol (usually based on form occasionally based on meaning if dominant) Note the proposed name shown in Annex 3 may have been superseded by the name shown in Annex 2 In all cases the name shown in Annex 2 should take precedence for this proposal Annex 3 is only attached because of the difficulty of completing a high-quality font for Annex 2 in time to meet the deadline for consideration at the Beijing WG2 meeting The one-letter codes indicating the class of the symbol are as follows

N normal or ordinary eg symbol used as a variable A alphabetic subclass of ordinary D diacritic or combining symbol

Math Symbols 2000-03-14

4

P punctuation B binary operator eg ltmathgta + bltmathgt R relation eg ltmathgta = bltmathgt L large operator eg sum product O opening delimiter (assuming left-to-right presentation) C closing delimiter (assuming left-to-right presentation) F nondirectional delimiter (fence post)

In Annex 3 the two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form a size-graded sequence with the present ISOIEC 10646 squares 25A0 25A1 25AA and 25AB Ideally the largest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest just a bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used ad hoc to define various operations with different sizes often indicating the degree of conformity to a particular notion (Several different geometric shapes are used in this manner the most common being squares and circles)

References International Organization for Standardization ISO 31XI-1992 Mathematical signs and symbols for use in the physical sciences and technology 2nd edition 1992 (by ref in ANSIIEEE P1324) American Society of Mechanical Engineers ANSI Y1020-1975 Mathematical signs and symbols for use in physical sciences and technology 1975 Institute of Electrical and Electronics Engineers ANSIIEEE P1324 (draft revision of Y1020) Draft standard mathematical signs and symbols for use in physical sciences and technology 1992 ISOIEC 88791986 Information Processing --- Text and Office Systems --- Standard Generalized Markup Language (SGML) Annex D Public text ISOIEC 9573-13 Information Technology --- SGML Support Facilities --- Techniques for Using SGML --- Part 13 Public entity sets for mathematics and science Stepney Susan (editor) Proposal to add the ISO Standard Z character set to UnicodeISO-IEC 10646 SC2 N3393 Committee Draft ISOIEC CD 10646-2 L298-405 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L298-406 Proposal to encode mathematical variant tags L299-045 Proposal to encode mathematical alphanumeric symbols L299-049 Addendum to L298-405 Request for assignment of codes to mathematical and technical symbols L299-159 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (revised) L299-160 Proposal to encode mathematical variant tags L299-195 Proposal to encode mathematical alphanumeric symbols L299-199 Mathematical Alphabets (for L299-195)

Math Symbols 2000-03-14

5

L299-244R Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L299-346 Mathematical brace pieces L200-002 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (supersedes L299-244R)

ISOIEC JTC 1SC 2WG 2 PROPOSAL SUMMARY FORM TO

ACCOMPANY SUBMISSIONS FOR ADDITIONS TO THE REPERTOIRE

OF ISOIEC 10646

Please fill Sections A B and C below Section D will be filled by SC 2WG 2

For instructions and guidance for filling in the form please see the document Principles and Procedures for Allocation of New Characters and Scripts (httpwwwdkuugdkJTC1SC2WG2prot)

A Administrative

1 Title Proposal for Encoding Additional Mathematical Symbols in the BMP

2 Requesters name US

3 Requester type (Member bodyLiaisonIndividual contribution) Member body

4 Submission date 2000-03-14

5 Requesters reference (if applicable) WG2 N2191

6 This is a complete proposal

B Technical - General

1 (Choose one of the following)

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

038F

0390

0391

0392

0393

0394

0395

0396

0397

0398

0399

039A

039B

039C

039D

039E

039F

03A0

03A1

03A3

03A4

03A5

03A6

03A7

03A8

03A9

03AA

03AB

03AC

03AD

03AE

03AF

03B0

03B1

03B2

03B3

03B4

03B5

03B6

03B7

03B8

03B9

03BA

03BB

03BC

03BD

03BE

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03C0

03C1

03C2

03C3

03C4

03C5

03C6

03C7

03C8

03C9

03CA

03CB

03CC

03CD

03CE

03D8

03D9

03F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

x

y

z

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

200A

200B

200C

200D

200E

200F

2011

2013

2014

2015

2017

2018

2019

201A

201B

201C

201D

201E

2020

2021

2022

2026

2028

2029

202A

202B

202C

202D

202E

202F

2030

2032

2033

2039

203A

203C

203E

2044

204E

204F

2050

2051

2052

2053

2054

2055

2056

2057

205F

2061

2062

2063

206A

206B

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206E

206F

0

1

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3

4

5

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7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

0

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F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

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2149

0

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A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

21F6

21F7

21F8

21F9

21FA

21FB

21FC

21FD

21FE

21FF

0

1

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8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

2

3

4

5

6

7

8

9

lt

=

gt

22F2

22F3

22F4

22F5

22F6

22F7

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22F9

22FA

22FB

22FC

22FD

22FE

22FF

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

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237C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

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25A1

25AA

25AB

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25C4

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

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iexcl

cent

pound

curren

yen

13

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

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=

gt

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2980

2981

2982

2983

2984

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2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

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2992

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2996

2997

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2999

299A

299B

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 3: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

3

Variants Many math symbols occur in two or more variant forms with the same or similar meanings usually but not always attached to both In order to accommodate the sometimes strong preferences of authors and publishers a single Variation Selector (VS) is recommended to be applied to a fixed list of symbols with predetermined results The Variation Selector follows the symbol whose variant it specifies As a character by itself the Variation Selector has no independent appearance it only functions to choose a particular variant for the character it follows Only combinations defined by the standard should be meaningful In any other context the Variation Selector character should be ignored The Variation Selector (VS) in this proposal is completely analogous to the Mongolian Free Variation Selector (MVS) characters already in ISOIEC 10646 The difference is merely that the MVS characters are only meaningful in combination with other Mongolian characters to select variants of those characters The VS is separately proposed for use in combination with mathematical symbol characters to select variants of those characters The exact list of variants currently known to be required for mathematical scientific and technical publishing is shown in Annex 4

Letter-like Symbols For a mathematician or other scientist alphabets provide the symbols to represent ad hoc variables as well as a number of more well-defined concepts Different styles of alphabets have different meanings some of which have been formally standardized in some disciplines but many of which follow only the strength of custom or even current necessity The CD for ISOIEC 10646-2 includes sets of mathematical alphanumeric symbols that are regularly used in mathematical and technical literature those alphabets and digits will not be further dealt with here There remain however some individual letters from or related to these alphabets that are routinely used in a turned or inverted orientation as well as a few symbols in the style of a particular math alphabet but not part of its normal alphabetic complement These are considered distinct letter-like symbols and are therefore candidates for code assignments They are included in this proposal along with the larger collection of general mathematical symbols and operators

Brace Parts A small collection of brace and bracket parts has also been included in this proposal These characters are intended to complete the coverage of the PostScript symbol set as well as some character-like entities used by TeX and other technical typesetting systems These brace parts are explicitly intended as compatibility characters to match those preexisting repertoires Their inclusion facilitates the interconversion of data from such systems with systems using the ISOIEC 10646 character encoding

Explanation of Conventions in the Annexes In Annex 3 four data elements are given for each symbol bull an arbitrary reference ID indicating location in the corresponding chart bull an asterisk () if there is an existing symbol in Unicode or another symbol in this collection that appears to be

similar bull a one-letter code indicating the class of the symbol bull a proposed name for the symbol (usually based on form occasionally based on meaning if dominant) Note the proposed name shown in Annex 3 may have been superseded by the name shown in Annex 2 In all cases the name shown in Annex 2 should take precedence for this proposal Annex 3 is only attached because of the difficulty of completing a high-quality font for Annex 2 in time to meet the deadline for consideration at the Beijing WG2 meeting The one-letter codes indicating the class of the symbol are as follows

N normal or ordinary eg symbol used as a variable A alphabetic subclass of ordinary D diacritic or combining symbol

Math Symbols 2000-03-14

4

P punctuation B binary operator eg ltmathgta + bltmathgt R relation eg ltmathgta = bltmathgt L large operator eg sum product O opening delimiter (assuming left-to-right presentation) C closing delimiter (assuming left-to-right presentation) F nondirectional delimiter (fence post)

In Annex 3 the two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form a size-graded sequence with the present ISOIEC 10646 squares 25A0 25A1 25AA and 25AB Ideally the largest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest just a bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used ad hoc to define various operations with different sizes often indicating the degree of conformity to a particular notion (Several different geometric shapes are used in this manner the most common being squares and circles)

References International Organization for Standardization ISO 31XI-1992 Mathematical signs and symbols for use in the physical sciences and technology 2nd edition 1992 (by ref in ANSIIEEE P1324) American Society of Mechanical Engineers ANSI Y1020-1975 Mathematical signs and symbols for use in physical sciences and technology 1975 Institute of Electrical and Electronics Engineers ANSIIEEE P1324 (draft revision of Y1020) Draft standard mathematical signs and symbols for use in physical sciences and technology 1992 ISOIEC 88791986 Information Processing --- Text and Office Systems --- Standard Generalized Markup Language (SGML) Annex D Public text ISOIEC 9573-13 Information Technology --- SGML Support Facilities --- Techniques for Using SGML --- Part 13 Public entity sets for mathematics and science Stepney Susan (editor) Proposal to add the ISO Standard Z character set to UnicodeISO-IEC 10646 SC2 N3393 Committee Draft ISOIEC CD 10646-2 L298-405 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L298-406 Proposal to encode mathematical variant tags L299-045 Proposal to encode mathematical alphanumeric symbols L299-049 Addendum to L298-405 Request for assignment of codes to mathematical and technical symbols L299-159 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (revised) L299-160 Proposal to encode mathematical variant tags L299-195 Proposal to encode mathematical alphanumeric symbols L299-199 Mathematical Alphabets (for L299-195)

Math Symbols 2000-03-14

5

L299-244R Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L299-346 Mathematical brace pieces L200-002 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (supersedes L299-244R)

ISOIEC JTC 1SC 2WG 2 PROPOSAL SUMMARY FORM TO

ACCOMPANY SUBMISSIONS FOR ADDITIONS TO THE REPERTOIRE

OF ISOIEC 10646

Please fill Sections A B and C below Section D will be filled by SC 2WG 2

For instructions and guidance for filling in the form please see the document Principles and Procedures for Allocation of New Characters and Scripts (httpwwwdkuugdkJTC1SC2WG2prot)

A Administrative

1 Title Proposal for Encoding Additional Mathematical Symbols in the BMP

2 Requesters name US

3 Requester type (Member bodyLiaisonIndividual contribution) Member body

4 Submission date 2000-03-14

5 Requesters reference (if applicable) WG2 N2191

6 This is a complete proposal

B Technical - General

1 (Choose one of the following)

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

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ΐ

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

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trade

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

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cap

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

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Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

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Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

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Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 4: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

4

P punctuation B binary operator eg ltmathgta + bltmathgt R relation eg ltmathgta = bltmathgt L large operator eg sum product O opening delimiter (assuming left-to-right presentation) C closing delimiter (assuming left-to-right presentation) F nondirectional delimiter (fence post)

In Annex 3 the two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form a size-graded sequence with the present ISOIEC 10646 squares 25A0 25A1 25AA and 25AB Ideally the largest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest just a bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used ad hoc to define various operations with different sizes often indicating the degree of conformity to a particular notion (Several different geometric shapes are used in this manner the most common being squares and circles)

References International Organization for Standardization ISO 31XI-1992 Mathematical signs and symbols for use in the physical sciences and technology 2nd edition 1992 (by ref in ANSIIEEE P1324) American Society of Mechanical Engineers ANSI Y1020-1975 Mathematical signs and symbols for use in physical sciences and technology 1975 Institute of Electrical and Electronics Engineers ANSIIEEE P1324 (draft revision of Y1020) Draft standard mathematical signs and symbols for use in physical sciences and technology 1992 ISOIEC 88791986 Information Processing --- Text and Office Systems --- Standard Generalized Markup Language (SGML) Annex D Public text ISOIEC 9573-13 Information Technology --- SGML Support Facilities --- Techniques for Using SGML --- Part 13 Public entity sets for mathematics and science Stepney Susan (editor) Proposal to add the ISO Standard Z character set to UnicodeISO-IEC 10646 SC2 N3393 Committee Draft ISOIEC CD 10646-2 L298-405 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L298-406 Proposal to encode mathematical variant tags L299-045 Proposal to encode mathematical alphanumeric symbols L299-049 Addendum to L298-405 Request for assignment of codes to mathematical and technical symbols L299-159 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (revised) L299-160 Proposal to encode mathematical variant tags L299-195 Proposal to encode mathematical alphanumeric symbols L299-199 Mathematical Alphabets (for L299-195)

Math Symbols 2000-03-14

5

L299-244R Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L299-346 Mathematical brace pieces L200-002 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (supersedes L299-244R)

ISOIEC JTC 1SC 2WG 2 PROPOSAL SUMMARY FORM TO

ACCOMPANY SUBMISSIONS FOR ADDITIONS TO THE REPERTOIRE

OF ISOIEC 10646

Please fill Sections A B and C below Section D will be filled by SC 2WG 2

For instructions and guidance for filling in the form please see the document Principles and Procedures for Allocation of New Characters and Scripts (httpwwwdkuugdkJTC1SC2WG2prot)

A Administrative

1 Title Proposal for Encoding Additional Mathematical Symbols in the BMP

2 Requesters name US

3 Requester type (Member bodyLiaisonIndividual contribution) Member body

4 Submission date 2000-03-14

5 Requesters reference (if applicable) WG2 N2191

6 This is a complete proposal

B Technical - General

1 (Choose one of the following)

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

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bull

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permil

prime

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lsaquo

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206F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

2147

2148

2149

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

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21F7

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21FF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

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8

9

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B

C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

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6

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8

9

lt

=

gt

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

2321

237C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

A

B

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239C

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239E

239F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

25A0

25A1

25AA

25AB

25AC

25B2

25BA

25BC

25C4

25CA

25CB

25CF

25D8

25D9

25E6

25F8

25F9

25FA

25FB

25FC

25FD

25FE

25FF

0

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5

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8

9

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B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

iexcl

cent

pound

curren

yen

13

2900

2901

2902

2903

2904

2906

2907

2908

2909

290A

290B

290C

290D

290E

290F

2910

2911

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2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

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2930

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293B

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2940

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294A

294B

294C

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2950

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295A

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2960

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2970

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297A

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

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9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

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W

X

Y

Z

[

]

^

_

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a

b

c

d

e

f

g

h

i

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k

l

m

n

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q

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|

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2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

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29A0

29A1

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29AB

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29B0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 5: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

5

L299-244R Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 L299-346 Mathematical brace pieces L200-002 Request for assignment of codes to mathematical and technical symbols that do not appear in Unicode 20 or ISOIEC 10646 (supersedes L299-244R)

ISOIEC JTC 1SC 2WG 2 PROPOSAL SUMMARY FORM TO

ACCOMPANY SUBMISSIONS FOR ADDITIONS TO THE REPERTOIRE

OF ISOIEC 10646

Please fill Sections A B and C below Section D will be filled by SC 2WG 2

For instructions and guidance for filling in the form please see the document Principles and Procedures for Allocation of New Characters and Scripts (httpwwwdkuugdkJTC1SC2WG2prot)

A Administrative

1 Title Proposal for Encoding Additional Mathematical Symbols in the BMP

2 Requesters name US

3 Requester type (Member bodyLiaisonIndividual contribution) Member body

4 Submission date 2000-03-14

5 Requesters reference (if applicable) WG2 N2191

6 This is a complete proposal

B Technical - General

1 (Choose one of the following)

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

038F

0390

0391

0392

0393

0394

0395

0396

0397

0398

0399

039A

039B

039C

039D

039E

039F

03A0

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03AA

03AB

03AC

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03F4

0

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8

9

A

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E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

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y

z

2000

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2015

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2020

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

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2140

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

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21F9

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

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2229

222B

2248

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

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lt

=

gt

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

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237C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

25A0

25A1

25AA

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

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[

]

^

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`

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iexcl

cent

pound

curren

yen

13

2900

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290A

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290D

290E

290F

2910

2911

2912

2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

292D

292E

292F

2930

2931

2932

2933

2934

2935

2936

2937

2938

2939

293A

293B

293C

293D

293E

2940

2941

2942

2943

2944

2945

2946

2947

2948

2949

294A

294B

294C

294D

294E

294F

2950

2951

2952

2953

2954

2955

2956

2957

2958

2959

295A

295B

295C

295D

295E

295F

2960

2961

2962

2963

2964

2965

2966

2967

2968

2969

296A

296B

296C

296D

296E

296F

2970

2971

2972

2973

2974

2975

2976

2977

2978

2979

297A

297B

297C

297D

297E

297F

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 6: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

ISOIEC JTC 1SC 2WG 2 PROPOSAL SUMMARY FORM TO

ACCOMPANY SUBMISSIONS FOR ADDITIONS TO THE REPERTOIRE

OF ISOIEC 10646

Please fill Sections A B and C below Section D will be filled by SC 2WG 2

For instructions and guidance for filling in the form please see the document Principles and Procedures for Allocation of New Characters and Scripts (httpwwwdkuugdkJTC1SC2WG2prot)

A Administrative

1 Title Proposal for Encoding Additional Mathematical Symbols in the BMP

2 Requesters name US

3 Requester type (Member bodyLiaisonIndividual contribution) Member body

4 Submission date 2000-03-14

5 Requesters reference (if applicable) WG2 N2191

6 This is a complete proposal

B Technical - General

1 (Choose one of the following)

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

038F

0390

0391

0392

0393

0394

0395

0396

0397

0398

0399

039A

039B

039C

039D

039E

039F

03A0

03A1

03A3

03A4

03A5

03A6

03A7

03A8

03A9

03AA

03AB

03AC

03AD

03AE

03AF

03B0

03B1

03B2

03B3

03B4

03B5

03B6

03B7

03B8

03B9

03BA

03BB

03BC

03BD

03BE

03BF

03C0

03C1

03C2

03C3

03C4

03C5

03C6

03C7

03C8

03C9

03CA

03CB

03CC

03CD

03CE

03D8

03D9

03F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

x

y

z

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

200A

200B

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2011

2013

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

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2149

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

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21FF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

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5

6

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8

9

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B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

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3

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6

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8

9

lt

=

gt

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

2321

237C

0

1

2

3

4

5

6

7

8

9

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B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

A

B

239B

239C

239D

239E

239F

23A0

23A1

23A2

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

25A0

25A1

25AA

25AB

25AC

25B2

25BA

25BC

25C4

25CA

25CB

25CF

25D8

25D9

25E6

25F8

25F9

25FA

25FB

25FC

25FD

25FE

25FF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

iexcl

cent

pound

curren

yen

13

2900

2901

2902

2903

2904

2906

2907

2908

2909

290A

290B

290C

290D

290E

290F

2910

2911

2912

2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

292D

292E

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2930

2931

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2935

2936

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2938

2939

293A

293B

293C

293D

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2940

2941

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294A

294B

294C

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2950

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2960

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

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9

lt

=

gt

A

B

C

D

E

F

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H

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K

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O

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Q

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[

]

^

_

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k

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2980

2981

2982

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2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

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2992

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2999

299A

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29A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 7: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

b The proposal is for addition of character(s) to an existing block

Name of the existing block

Greek and Coptic (3) General Punctuation (14) Combining Diacritical Marks for Symbols (4) Letterlike Symbols (15) Arrows (12) Mathematical Operators (14) Miscellaneous Technical (29) Geometric Shapes (8) Supplemental Arrows [New block 2900297F] (128) Miscellaneous Math Symbols [New block 298029FF] (117) Supplemental Math Operators [New block 2A002AFF] (247)

Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical Operators blocks and do not constitute new scripts

2 Number of characters in proposal 951

3 Proposed category (see section II Character Categories)

4 Proposed Level of Implementation (see clause 15 ISOIEC 10646-1) Level 3

Is a rationale provided for the choice Yes

If Yes reference

The repertoire includes 4 combining characters which can be used in free combinations with other existing 10646 characters Many relational operators are intended to be usable with overlaid combining marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL LINE OVERLAY to productively indicate negation Finally the mathematical repertoire in general is intended for complex rendering with the productive application of other combining marks to indicate derivatives vectors and many other concepts

Limited subsets of the mathematical symbols can of course be used for Level 1 implementations but the repertoire addressed by this proposal is aimed at full and complete mathematical rendering and interchange (Note that this proposal encompasses the symbols needed for mathematical content but is not intended to cover mathematical markup languages or layout controls)

5 Is a repertoire including character names provided Yes See Annex 2

a If YES are the names in accordance with the character naming guidelines in Annex K of ISOIEC 10646-1 Yes

b Are the character shapes attached in a reviewable form Yes See Annexes 2 and 3

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

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Ε

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Κ

Λ

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Π

Ρ

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Φ

Χ

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Ϊ

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ά

έ

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θ

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micro

ν

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ο

π

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ω

ϊ

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ό

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ώ

037E

0384

0385

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

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sbquo

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dagger

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bull

hellip

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permil

prime

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lsaquo

rsaquo

frasl

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

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22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

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23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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t

u

v

w

x

y

z

|

~

iexcl

cent

pound

curren

yen

13

2900

2901

2902

2903

2904

2906

2907

2908

2909

290A

290B

290C

290D

290E

290F

2910

2911

2912

2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

292D

292E

292F

2930

2931

2932

2933

2934

2935

2936

2937

2938

2939

293A

293B

293C

293D

293E

2940

2941

2942

2943

2944

2945

2946

2947

2948

2949

294A

294B

294C

294D

294E

294F

2950

2951

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2953

2954

2955

2956

2957

2958

2959

295A

295B

295C

295D

295E

295F

2960

2961

2962

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2964

2965

2966

2967

2968

2969

296A

296B

296C

296D

296E

296F

2970

2971

2972

2973

2974

2975

2976

2977

2978

2979

297A

297B

297C

297D

297E

297F

0

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2

3

4

5

6

7

8

9

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

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29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

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29E7

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29EA

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29EC

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29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 8: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

6 Who will provide the appropriate computerized font (ordered preference True Type PostScript or 96x96 bit-mapped format) for publishing the standard

The Unicode Consortium working in collaboration with STIPUB and various professional font vendors

If available now identify source(s) for the font (include address e-mail ftp-site etc) and indicate the tools used

7 References

a Are references (to other character sets dictionaries descriptive texts etc) provided Yes

c Are published examples (such as samples from newspapers magazines or other sources) of use of proposed characters attached

No not in WG2 N2191 However a very large collection of source citations has been collected by the STIX Project group of STIPUB That group constitutes a consortium of mathematical scientific and technical publishers who have refined this repertoire on the basis of their publication requirements for symbol usage

8 Special encoding issues

Use of a VARIATION SELECTOR The use of this character is described in the proposal

Does the proposal address other aspects of character data processing (if applicable) such as input presentation sorting searching indexing transliteration etc (if yes please enclose information) Yes

There are no new input or presentation issues not already present for the existing repertoire of math symbols Sorting indexing and transliteration are generally not an issue for math symbols Some special letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematical concepts in text documents

C Technical - Justification

1 Has this proposal for addition of character(s) been submitted before No (with a few exceptions) If YES explain

Note that a few individual characters among the repertoire of 951 may appear in other proposals before WG2 For example the Q-shaped koppa letters have independently been requested Several arrow characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included The vast majority of the 951 characters in this proposal are requested here for the first time

2 Has contact been made to members of the user community (for example National Body user groups of the script or characters other experts etc) Yes

If YES with whom

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

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037E

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

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bdquo

dagger

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bull

hellip

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[

permil

prime

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lsaquo

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frasl

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

0

1

2

3

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5

6

7

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B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

2147

2148

2149

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

21F6

21F7

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21F9

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21FF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

0

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3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

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3

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6

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8

9

lt

=

gt

22F2

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

2321

237C

0

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6

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

A

B

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239C

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239E

239F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

25A0

25A1

25AA

25AB

25AC

25B2

25BA

25BC

25C4

25CA

25CB

25CF

25D8

25D9

25E6

25F8

25F9

25FA

25FB

25FC

25FD

25FE

25FF

0

1

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4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

iexcl

cent

pound

curren

yen

13

2900

2901

2902

2903

2904

2906

2907

2908

2909

290A

290B

290C

290D

290E

290F

2910

2911

2912

2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

292D

292E

292F

2930

2931

2932

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2934

2935

2936

2937

2938

2939

293A

293B

293C

293D

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2940

2941

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2946

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2949

294A

294B

294C

294D

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2950

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2959

295A

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295C

295D

295E

295F

2960

2961

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2964

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296A

296B

296C

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296F

2970

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297A

297B

297C

297D

297E

297F

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

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k

l

m

n

o

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q

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y

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|

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2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

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29AA

29AB

29AC

29AD

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29B0

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29BB

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 9: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

STIPUB (Scientific and Technical Information Publishing Consortium) representing mathematical and other major technical publishing interests American Mathematical Society International Mathematical Union major mathematical software vendors W3C MathML participants

If YES available relevant documents See the references and appended approval letters in the proposal

3 Information on the user community for the proposed characters (for example size demographics information technology use or publishing use) is included

The repertoire is intended for all international mathematical information technology use and for mathematical scientific and technical publishing worldwide It is intended to complete the base symbol set for MathML It is also intended as the underlying symbol encoding for all major mathematical layout software programs

Reference

4 The context of use for the proposed characters (type of use common or rare)

Common to rare depending on the particular subfield of mathematics involved

Reference

5 Are the proposed characters in current use by the user community Yes

If YES where

Books journals articles online documents Reference STIPUB can provide voluminous references This constitutes the complete world community of mathematical users all books journals magazines and other publications in mathematics and scientific and technical disciplines that make use of mathematics worldwide

6 After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP Yes

If YES is a rationale provided Yes

If YES reference See WG2 N2191

7 Should the proposed characters be kept together in a contiguous range (rather than being scattered) Yes and No

Exact details of the proposed distribution of the characters into existing and new blocks of 10646 are provided in Annex 2

8 Can any of the proposed characters be considered a presentation form of an existing character or character

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

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0390

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

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k

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o

p

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ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

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U

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[

permil

prime

Prime

lsaquo

rsaquo

frasl

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

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2126

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

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2248

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

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lt

=

gt

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

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2310 2320

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

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G

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J

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 10: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

sequence Yes (a few)

If YES is a rationale for its inclusion provided No

In these instances the precedents are already clearly established in the standard For example a quadruple integral character is requested the double and triple integral are already encoded as characters

If YES reference

9 Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing character Yes

If YES is a rationale for its inclusion provided No not in detail

There are numerous instances among mathematical symbols where one symbols is generically similar to another in appearance but where it is well understood in mathematical practice to not be the same symbol Annex 2 provides a number of cross-references where there might be confusions regarding the distinctiveness of a particular character either with respect to existing encoded characters in 10646 or with respect to other characters in this proposal Mathematical symbols are also replete with examples where the same function can be represented by different symbols Multiplication for example can already be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR However it can also be represented by a zero-width operator such as in xy where this expression represents the variable x multiplied by the variable y Multiple symbols corresponding to the same abstract mathematical functions are requested for encoding as separate characters when their form is distinct in different mathematical traditions or subfields

If YES reference

WG2 2191 does provide a detailed rationale for the request for two additional sets of squares as geometric shape characters

10 Does the proposal include use of combining characters andor use of composite sequences (see clause 411 and 413 in ISOIEC 10646-1) Yes

If YES is a rationale for such use provided Yes

If YES reference See B4 above

Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided No

Such a list would be unmanageably long since combining marks are intended for productive use in mathematics

If YES reference

11 Does the proposal contain characters with any special properties such as control function or similar semantics Yes

If YES describe in detail (include attachment if necessary)

The VARIATION SELECTOR is described in WG2 N2191 and the list of variants it selects is detailed in

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

038F

0390

0391

0392

0393

0394

0395

0396

0397

0398

0399

039A

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039C

039D

039E

039F

03A0

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03AA

03AB

03AC

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

x

y

z

2000

2001

2002

2003

2004

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2006

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200A

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2011

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2015

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2020

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202A

202B

202C

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2030

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2033

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203A

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203E

2044

204E

204F

2050

2051

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205F

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206A

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

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2147

2148

2149

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

21F6

21F7

21F8

21F9

21FA

21FB

21FC

21FD

21FE

21FF

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

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2265

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

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brvbar

sect

uml

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laquo

not

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plusmn

sup2

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acute

micro

para

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cedil

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13

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

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A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

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4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

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5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

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2

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7

8

9

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B

C

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E

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 11: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Annex 4

D SC 2WG 2 Administrative (To be completed by SC 2WG 2)

1 Relevant SC 2WG 2 document numbers

2 Status (list of meeting number and corresponding action or disposition)

3 Additional contact to user communities liaison organizations etc

4 Assigned category and assigned prioritytime frame

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

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ά

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

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ndash

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rsquo

sbquo

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dagger

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bull

hellip

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[

permil

prime

Prime

lsaquo

rsaquo

frasl

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201B

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201D

201E

2020

2021

2022

2026

2028

2029

202A

202B

202C

202D

202E

202F

2030

2032

2033

2039

203A

203C

203E

2044

204E

204F

2050

2051

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2053

2054

2055

2056

2057

205F

2061

2062

2063

206A

206B

206C

206D

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206F

0

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5

6

7

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E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

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C

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F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

2147

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2149

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

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21FF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

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5

6

7

8

9

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B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

2

3

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6

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8

9

lt

=

gt

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

2321

237C

0

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3

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6

7

8

9

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F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

A

B

239B

239C

239D

239E

239F

23A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

25A0

25A1

25AA

25AB

25AC

25B2

25BA

25BC

25C4

25CA

25CB

25CF

25D8

25D9

25E6

25F8

25F9

25FA

25FB

25FC

25FD

25FE

25FF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

iexcl

cent

pound

curren

yen

13

2900

2901

2902

2903

2904

2906

2907

2908

2909

290A

290B

290C

290D

290E

290F

2910

2911

2912

2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

292D

292E

292F

2930

2931

2932

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2934

2935

2936

2937

2938

2939

293A

293B

293C

293D

293E

2940

2941

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2943

2944

2945

2946

2947

2948

2949

294A

294B

294C

294D

294E

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2950

2951

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2953

2954

2955

2956

2957

2958

2959

295A

295B

295C

295D

295E

295F

2960

2961

2962

2963

2964

2965

2966

2967

2968

2969

296A

296B

296C

296D

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296F

2970

2971

2972

2973

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2975

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2978

2979

297A

297B

297C

297D

297E

297F

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

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9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

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Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

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k

l

m

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o

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q

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|

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2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

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299D

299E

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29A0

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29B0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 12: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols ProposalFirst Draft MTHM000307lstCreated from L200-033R and L200-002

File StatisticsTotal Characters 591Lines in file 746+ Generated 86Name lines 677

Characters 591Reserved 0Unassigned 86

Secondary lines 102Aliases 33Comments 14Cross Refs 41Can Decomps 0Compatibility 14Ignored 0

Header Lines 53Blocks 11Subheaders 40Notices 0Title lines 1Subtitles 1Page breaks 0

Empty lines 0Iso Comments 0AnnexP Notes 0

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

΄

΅

Ά

Έ

Ή

Ί

Ό

Ύ

Ώ

ΐ

Α

Β

Γ

Ε

Ζ

Η

Θ

Ι

Κ

Λ

Μ

Ν

Ξ

Ο

Π

Ρ

Σ

Τ

Υ

Φ

Χ

Ψ

Ω

Ϊ

Ϋ

ά

έ

ή

ί

ΰ

α

β

γ

δ

ε

ζ

η

θ

ι

κ

λ

micro

ν

ξ

ο

π

ρ

ς

σ

τ

υ

φ

χ

ψ

ω

ϊ

ϋ

ό

ύ

ώ

037E

0384

0385

0386

0387

0388

0389

038A

038C

038E

038F

0390

0391

0392

0393

0394

0395

0396

0397

0398

0399

039A

039B

039C

039D

039E

039F

03A0

03A1

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03A5

03A6

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03A9

03AA

03AB

03AC

03AD

03AE

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03B0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

x

y

z

2000

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

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2140

2141

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

21F6

21F7

21F8

21F9

21FA

21FB

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

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221A

221E

221F

2229

222B

2248

2260

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

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9

lt

=

gt

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

2321

237C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

A

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

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F

G

H

I

J

25A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

R

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T

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Z

[

]

^

_

`

a

b

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g

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i

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k

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m

n

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p

q

r

s

t

u

v

w

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z

|

~

iexcl

cent

pound

curren

yen

13

2900

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 13: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 2

03FFGreek and Coptic0370

037 038 039 03A 03B 03C 03D 03E 03F

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03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

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206FGeneral Punctuation2000

200 201 202 203 204 205 206

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hellip

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permil

prime

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lsaquo

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2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

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20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

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214FLetterlike Symbols2100

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trade

Ω

$

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2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

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21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

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+

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

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cap

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equiv

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22FFMathematical Operators2280

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22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

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23FFMiscellaneous Technical2380

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23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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loz

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

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=

gt

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2980

2981

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2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

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2999

299A

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

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2A0A

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2A20

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2A3A

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2A40

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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8

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B

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E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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2

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6

7

8

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B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 14: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 3

03F4Greek and Coptic03D8

Archaic Greek Letters03D8 GREEK LETTER Q-KOPPA03D9 GREEK SMALL LETTER Q-KOPPA

Greek symbol03F4 GREEK THETA SYMBOL WITH STRAIGHT

BARrarr 0472 cyrillic capital letter fitaasymp 03B8 θ

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

206FGeneral Punctuation2000

200 201 202 203 204 205 206

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

S

ndash

mdash

lsquo

rsquo

sbquo

ldquo

rdquo

bdquo

dagger

Dagger

bull

hellip

T

U

V

W

X

Y

Z

[

permil

prime

Prime

lsaquo

rsaquo

frasl

13

v

w

x

y

z

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

200A

200B

200C

200D

200E

200F

2011

2013

2014

2015

2017

2018

2019

201A

201B

201C

201D

201E

2020

2021

2022

2026

2028

2029

202A

202B

202C

202D

202E

202F

2030

2032

2033

2039

203A

203C

203E

2044

204E

204F

2050

2051

2052

2053

2054

2055

2056

2057

205F

2061

2062

2063

206A

206B

206C

206D

206E

206F

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 5

2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 6

20FFCombining Diacritical Marks for Symbols20D0

20D 20E 20F

20E5

20E6

20E7

20E8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

2147

2148

2149

0

1

2

3

4

5

6

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8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

21F6

21F7

21F8

21F9

21FA

21FB

21FC

21FD

21FE

21FF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

0

1

2

3

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8

9

A

B

C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

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brvbar

sect

uml

copy

ordf

laquo

not

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reg

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plusmn

sup2

sup3

acute

micro

para

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cedil

sup1

ordm

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13

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2A00

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

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5

6

7

8

9

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 15: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 4

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prime

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2063General Punctuation2000

2039 ltreservedgt203A ltreservedgt203B ltreservedgt203C ltreservedgt203D ltreservedgt203E ltreservedgt203F ltreservedgt2040 ltreservedgt2041 ltreservedgt2042 ltreservedgt2043 ltreservedgt2044 ltreservedgt2045 ltreservedgt2046 ltreservedgt2047 ltreservedgt2048 ltreservedgt2049 ltreservedgt204A ltreservedgt204B ltreservedgt204C ltreservedgt204D ltreservedgt204E LOW ASTERISK204F REVERSED SEMICOLON2050 EM LEADER2051 TWO ASTERISKS ALIGNED VERTICALLY2052 SOLIDUS OVERBAR2053 REVERSE SOLIDUS WITH HORIZONTAL

STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

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20FFCombining Diacritical Marks for Symbols20D0

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F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

2105

2113

2116

2122

2126

212E

213B

213C

213D

213E

213F

2140

2141

2142

2143

2144

2145

2146

2147

2148

2149

0

1

2

3

4

5

6

7

8

9

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B

C

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E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

(

)

+

-

0

2190

2191

2192

2193

2194

2195

21A8

21F4

21F5

21F6

21F7

21F8

21F9

21FA

21FB

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21FD

21FE

21FF

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4

5

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C

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E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

radic

infin

cap

int

asymp

ne

equiv

le

ge

2202

2206

220F

2211

2212

2215

2219

221A

221E

221F

2229

222B

2248

2260

2261

2264

2265

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 13

22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

1

2

3

4

5

6

7

8

9

lt

=

gt

22F2

22F3

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

2302

2310 2320

2321

237C

0

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3

4

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6

7

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9

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B

C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

238 239 23A 23B 23C 23D 23E 23F

A

B

239B

239C

239D

239E

239F

23A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

C

D

E

F

G

H

I

J

25A0

25A1

25AA

25AB

25AC

25B2

25BA

25BC

25C4

25CA

25CB

25CF

25D8

25D9

25E6

25F8

25F9

25FA

25FB

25FC

25FD

25FE

25FF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

iexcl

cent

pound

curren

yen

13

2900

2901

2902

2903

2904

2906

2907

2908

2909

290A

290B

290C

290D

290E

290F

2910

2911

2912

2913

2914

2915

2916

2917

2918

2919

291A

291B

291C

291D

291E

291F

2920

2921

2922

2923

2924

2925

2926

2927

2928

2929

292A

292B

292C

292D

292E

292F

2930

2931

2932

2933

2934

2935

2936

2937

2938

2939

293A

293B

293C

293D

293E

2940

2941

2942

2943

2944

2945

2946

2947

2948

2949

294A

294B

294C

294D

294E

294F

2950

2951

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2953

2954

2955

2956

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2959

295A

295B

295C

295D

295E

295F

2960

2961

2962

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2964

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296A

296B

296C

296D

296E

296F

2970

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2972

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297A

297B

297C

297D

297E

297F

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

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s

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y

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|

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2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

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29AA

29AB

29AC

29AD

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29AF

29B0

29B1

29B2

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29BB

29BC

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29BF

29C0

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29CA

29CB

29CC

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 16: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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2063General Punctuation2000

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STROKE2054 BIG SOLIDUS2055 BIG REVERSE SOLIDUS

= z notation schema hiding2056 TURNED AMPERSAND2057 13 QUADRUPLE PRIME

asymp 2035 2035 20352058 ltreservedgt2059 ltreservedgt205A ltreservedgt205B ltreservedgt205C ltreservedgt205D ltreservedgt205E ltreservedgt205F MEDIUM MATH SPACE

bull four-eighteenths of an emasymp 0020P

2060 ltreservedgt2061 FUNCTION APPLICATION

bull contiguity operator indicating application of afunction

2062 INVISIBLE TIMESbull contiguity operator indicating multiplication

2063 VARIATION SELECTORbull in conjunction with preceding character indicatesvariant choice

2000 ltreservedgt2001 ltreservedgt2002 ltreservedgt2003 ltreservedgt2004 ltreservedgt2005 ltreservedgt2006 ltreservedgt2007 ltreservedgt2008 ltreservedgt2009 ltreservedgt200A ltreservedgt200B ltreservedgt200C ltreservedgt200D ltreservedgt200E ltreservedgt200F ltreservedgt2010 ltreservedgt2011 ltreservedgt2012 ltreservedgt2013 ltreservedgt2014 ltreservedgt2015 ltreservedgt2016 ltreservedgt2017 ltreservedgt2018 ltreservedgt2019 ltreservedgt201A ltreservedgt201B ltreservedgt201C ltreservedgt201D ltreservedgt201E ltreservedgt201F ltreservedgt2020 ltreservedgt2021 ltreservedgt2022 ltreservedgt2023 ltreservedgt2024 ltreservedgt2025 ltreservedgt2026 ltreservedgt2027 ltreservedgt2028 ltreservedgt2029 ltreservedgt202A ltreservedgt202B ltreservedgt202C ltreservedgt202D ltreservedgt202E ltreservedgt202F ltreservedgt2030 ltreservedgt2031 ltreservedgt2032 ltreservedgt2033 ltreservedgt2034 ltreservedgt2035 ltreservedgt2036 ltreservedgt2037 ltreservedgt2038 ltreservedgt

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20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

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2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

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21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

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22FFMathematical Operators22F2

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STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

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ARROW

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SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

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25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

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29FFMiscellaneous Math Symbols2980

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 17: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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20FFCombining Diacritical Marks for Symbols20D0

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20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

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2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

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21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

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prod

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22FFMathematical Operators2280

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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[

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iexcl

cent

pound

curren

yen

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

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29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 18: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 7

20E8Combining Diacritical Marks for Symbols20E5

Combining Symbols20E5 COMBINING REVERSE SOLIDUS OVERLAY20E6 COMBINING DOUBLE VERTICAL STROKE

OVERLAY= z notation finite function

20E7 ANNUITY SYMBOL= actuarial bend

20E8 TRIPLE UNDERDOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

210 211 212 213 214

trade

Ω

$

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2126

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213B

213C

213D

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

larr

uarr

rarr

darr

harr

amp

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)

+

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

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prod

sum

minus

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int

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22FFMathematical Operators2280

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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[

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iexcl

cent

pound

curren

yen

13

2900

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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amp

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 19: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 8

214FLetterlike Symbols2100

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

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21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

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22FFMathematical Operators2280

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22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 20: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 9

2149Letterlike Symbols213B

Letterlike symbols213B GREEK SYMBOL STRAIGHT EPSILON

asymp ltfontgt 03B5 ε213C GREEK SYMBOL REVERSED STRAIGHT

EPSILON213D OPEN-FACE GREEK SMALL LETTER GAMMA

asymp ltfontgt 03B3 γ213E OPEN-FACE GREEK CAPITAL GAMMA

asymp ltfontgt 0393 Γ213F OPEN-FACE GREEK CAPITAL PI

asymp ltfontgt 03A0 Π2140 OPEN-FACE SUM

asymp ltfontgt 03A3 Σ2141 TURNED SANS SERIF CAPITAL G

= game2142 TURNED SANS SERIF CAPITAL L2143 REVERSED SANS SERIF CAPITAL L2144 INVERTED SANS SERIF CAPITAL Y2145 CAPITAL DIFFERENTIAL D

asymp ltfontgt 0044 D2146 DIFFERENTIAL D

asymp ltfontgt 0064 d2147 EXPONENTIAL E

asymp ltfontgt 0065 e2148 IMAGINARY I

asymp ltfontgt 0069 i2149 $ IMAGINARY J

asymp ltfontgt 006A j

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 10

21FFArrows2190

219 21A 21B 21C 21D 21E 21F

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uarr

rarr

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harr

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

part

prod

sum

minus

frasl

middot

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infin

cap

int

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22FFMathematical Operators2280

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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loz

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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[

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iexcl

cent

pound

curren

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 21: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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21FFArrows2190

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21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

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prod

sum

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22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 22: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 11

21FFArrows21F4

Arrows21F4 DOWNWARDS WHITE ARROW WITH CORNER

LEFTWARDS= return

21F5 amp DOWNWARDS ARROW LEFTWARDS OFUPWARDS ARROW

21F6 THREE RIGHTWARDS ARROWS21F7 ( LEFTWARDS ARROW WITH VERTICAL

STROKE21F8 ) RIGHTWARDS ARROW WITH VERTICAL

STROKE= z notation partial function

21F9 LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation

21FA + LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE

21FB RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function

21FC - LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation

21FD LEFTWARDS OPEN-HEADED ARROW21FE RIGHTWARDS OPEN-HEADED ARROW21FF 0 LEFT RIGHT OPEN-HEADED ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 12

227FMathematical Operators2200

220 221 222 223 224 225 226 227

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prod

sum

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22FFMathematical Operators2280

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 14

22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 15

237FMiscellaneous Technical2300

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 16

23FFMiscellaneous Technical2380

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 17

23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

K

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[

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iexcl

cent

pound

curren

yen

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

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2999

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 23: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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22FFMathematical Operators22F2

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STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

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23B6Miscellaneous Technical237C

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SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

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25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

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297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

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29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

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8

9

A

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D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 24: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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22FFMathematical Operators2280

228 229 22A 22B 22C 22D 22E 22F

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22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

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237FMiscellaneous Technical2300

230 231 232 233 234 235 236 237

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23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

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2A00

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 25: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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22FFMathematical Operators22F2

Mathematical operators22F2 1 ELEMENT OF WITH LONG HORIZONTAL

STROKE22F3 2 ELEMENT OF WITH VERTICAL BAR AT END

OF HORIZONTAL STROKE22F4 3 SMALL ELEMENT OF WITH VERTICAL BAR

AT END OF HORIZONTAL STROKE22F5 4 ELEMENT OF WITH DOT ABOVE22F6 5 ELEMENT OF WITH OVERBAR22F7 6 SMALL ELEMENT OF WITH OVERBAR22F8 7 ELEMENT OF WITH UNDERBAR22F9 8 ELEMENT OF WITH TWO HORIZONTAL

STROKES22FA 9 CONTAINS WITH LONG HORIZONTAL

STROKE22FB CONTAINS WITH VERTICAL BAR AT END OF

HORIZONTAL STROKE22FC SMALL CONTAINS WITH VERTICAL BAR AT

END OF HORIZONTAL STROKE22FD lt CONTAINS WITH OVERBAR22FE = SMALL CONTAINS WITH OVERBAR22FF gt Z NOTATION BAG MEMBERSHIP

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237FMiscellaneous Technical2300

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Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

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SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

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25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

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Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 26: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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237FMiscellaneous Technical2300

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23FFMiscellaneous Technical2380

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23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

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25FFGeometric Shapes25A0

25A 25B 25C 25D 25E 25F

loz

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

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297FSupplemental Arrows2900

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2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 27: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

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SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

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25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

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297FSupplemental Arrows2900

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2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

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2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

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0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

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B

C

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 28: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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23B6Miscellaneous Technical237C

Miscellaneous technical237C RIGHT ANGLE WITH DOWNWARDS ZIGZAG

ARROW

Brace pieces239B LEFT PARENTHESIS UPPER HOOK239C LEFT PARENTHESIS EXTENSION239D LEFT PARENTHESIS LOWER HOOK239E RIGHT PARENTHESIS UPPER HOOK239F RIGHT PARENTHESIS EXTENSION23A0 RIGHT PARENTHESIS LOWER HOOK23A1 LEFT BRACKET UPPER CORNER23A2 LEFT BRACKET EXTENSION23A3 LEFT BRACKET LOWER CORNER23A4 RIGHT BRACKET UPPER CORNER23A5 RIGHT BRACKET EXTENSION23A6 RIGHT BRACKET LOWER CORNER23A7 LEFT CURLY BRACE UPPER HOOK23A8 LEFT CURLY BRACE MIDDLE PIECE23A9 LEFT CURLY BRACE LOWER HOOK23AA CURLY BRACE EXTENSION23AB RIGHT CURLY BRACE UPPER HOOK23AC RIGHT CURLY BRACE MIDDLE PIECE23AD RIGHT CURLY BRACE LOWER HOOK23AE INTEGRAL EXTENSION23AF HORIZONTAL LINE EXTENSION23B0 UPPER LEFT OR LOWER RIGHT BRACE

SECTION23B1 UPPER RIGHT OR LOWER LEFT BRACE

SECTION

Summation sign parts23B2 SUMMATION SYMBOL TOP23B3 SUMMATION SYMBOL BOTTOM

Vertical brackets23B4 TOP SQUARE BRACKET23B5 A BOTTOM SQUARE BRACKET23B6 B BOTTOM ABOVE TOP SQUARE BRACKET

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 18

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 29: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

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2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

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297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

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29FFMiscellaneous Math Symbols2980

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29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

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iexcl

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not

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micro

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2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 30: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 19

25FFGeometric Shapes25F8

Geometric shapes25F8 C UPPER LEFT TRIANGLE25F9 D UPPER RIGHT TRIANGLE25FA E LOWER LEFT TRIANGLE25FB F WHITE MEDIUM SQUARE25FC G BLACK MEDIUM SQUARE25FD H WHITE VERY SMALL SQUARE25FE I BLACK VERY SMALL SQUARE25FF J WHITE DIAMOND WITH CENTERED DOT

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 20

297FSupplemental Arrows2900

290 291 292 293 294 295 296 297

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 31: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

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2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

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29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 32: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 21

2946Supplemental Arrows2900

2921 K NORTH WEST-SOUTH EAST ARROW2922 L NORTH EAST-SOUTH WEST ARROW2923 M NORTH WEST ARROW WITH HOOK2924 N NORTH EAST ARROW WITH HOOK2925 O SOUTH EAST ARROW WITH HOOK2926 P SOUTH WEST ARROW WITH HOOK2927 Q NORTH WEST AND NORTH EAST ARROWS2928 R NORTH EAST AND SOUTH EAST ARROWS2929 S SOUTH EAST AND SOUTH WEST ARROWS292A T SOUTH WEST AND NORTH WEST ARROWS292B U RISING DIAGONAL CROSSING FALLING

DIAGONAL292C V FALLING DIAGONAL CROSSING RISING

DIAGONAL292D W SOUTH EAST ARROW CROSSING NORTH

EAST ARROW292E X NORTH EAST ARROW CROSSING SOUTH

EAST ARROW292F Y FALLING DIAGONAL CROSSING NORTH

EAST ARROW2930 Z RISING DIAGONAL CROSSING SOUTH EAST

ARROW2931 [ NORTH EAST ARROW CROSSING NORTH

WEST ARROW2932 NORTH WEST ARROW CROSSING NORTH

EAST ARROW2933 ] WAVE ARROW POINTING DIRECTLY TO THE

RIGHTrarr 219D rightwards wave arrow

2934 ^ ARROW POINTING RIGHTWARDS THENCURVING UPWARDS

2935 _ ARROW POINTING RIGHTWARDS THENCURVING DOWNWARDS

2936 ` ARROW POINTING DOWNWARDS THENCURVING LEFTWARDS

2937 a ARROW POINTING DOWNWARDS THENCURVING RIGHTWARDS

2938 b RIGHT-SIDE ARC CLOCKWISE ARROW2939 c LEFT-SIDE ARC ANTICLOCKWISE ARROW293A d TOP ARC ANTICLOCKWISE ARROW293B e BOTTOM ARC ANTICLOCKWISE ARROW293C f TOP ARC CLOCKWISE ARROW WITH MINUS293D g TOP ARC ANTICLOCKWISE ARROW WITH

PLUS293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE

ARROW293F LOWER LEFT SEMICIRCULAR

ANTICLOCKWISE ARROW2940 i ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlay2941 j CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlay2942 k RIGHTWARDS ARROW ABOVE SHORT

LEFTWARDS ARROW2943 l LEFTWARDS ARROW ABOVE SHORT

RIGHTWARDS ARROW2944 m SHORT RIGHTWARDS ARROW ABOVE

LEFTWARDS ARROW2945 n RIGHTWARDS ARROW WITH PLUS BELOW2946 o LEFTWARDS ARROW WITH PLUS BELOW

Supplemental arrows2900 p RIGHTWARDS TWO-HEADED ARROW WITH

VERTICAL STROKE= z notation partial surjection

2901 q RIGHTWARDS TWO-HEADED ARROW WITHDOUBLE VERTICAL STROKE= z notation finite surjection

2902 r LEFTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2903 s RIGHTWARDS DOUBLE ARROW WITHVERTICAL STROKE

2904 t LEFT RIGHT DOUBLE ARROW WITHVERTICAL STROKE

2905 RIGHTWARDS TWO-HEADED ARROW FROMBAR= maps to

2906 u LEFTWARDS DOUBLE ARROW FROM BAR= maps from

2907 v RIGHTWARDS DOUBLE ARROW FROM BAR= maps to

2908 w DOWNWARDS ARROW WITH HORIZONTALSTROKE

2909 x UPWARDS ARROW WITH HORIZONTALSTROKE

290A y UPWARDS TRIPLE ARROW290B z DOWNWARDS TRIPLE ARROW290C LEFTWARDS BROKEN ARROW290D | RIGHTWARDS BROKEN ARROW290E LEFTWARDS DOUBLY BROKEN ARROW290F ~ RIGHTWARDS DOUBLY BROKEN ARROW2910 RIGHTWARDS TWO-HEADED BROKEN

ARROW2911 RIGHTWARDS ARROW WITH DOTTED STEM2912 UPWARDS ARROW TO BAR2913 DOWNWARDS ARROW TO BAR2914 RIGHTWARDS ARROW WITH TAIL WITH

VERTICAL STROKE= z notation partial injection

2915 RIGHTWARDS ARROW WITH TAIL WITHDOUBLE VERTICAL STROKE= z notation finite injection

2916 RIGHTWARDS TWO-HEADED ARROW WITHTAIL= bijective mapping

2917 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH VERTICAL STROKE= z notation surjective injection

2918 RIGHTWARDS TWO-HEADED ARROW WITHTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection

2919 LEFTWARDS ARROW-TAIL291A RIGHTWARDS ARROW-TAIL291B LEFTWARDS DOUBLE ARROW-TAIL291C RIGHTWARDS DOUBLE ARROW-TAIL291D LEFTWARDS ARROW TO FILLED DIAMOND291E RIGHTWARDS ARROW TO FILLED DIAMOND291F LEFTWARDS ARROW FROM BAR TO FILLED

DIAMOND2920 RIGHTWARDS ARROW FROM BAR TO FILLED

DIAMOND

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 33: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 22

297FSupplemental Arrows2947

2971 EQUAL ABOVE RIGHTWARDS ARROW2972 TILDE OPERATOR ABOVE RIGHTWARDS

ARROW2973 LEFTWARDS ARROW ABOVE TILDE

OPERATOR2974 RIGHTWARDS ARROW ABOVE TILDE

OPERATOR2975 RIGHTWARDS ARROW ABOVE DOUBLE

TILDE OPERATOR2976 LESS THAN ABOVE LEFTWARDS ARROW2977 LEFTWARDS ARROW THROUGH LESS-THAN2978 GREATER-THAN ABOVE RIGHTWARDS

ARROW2979 SUBSET ABOVE RIGHTWARDS ARROW297A LEFTWARDS ARROW THROUGH SUBSET297B SUPERSET ABOVE LEFTWARDS ARROW297C LEFT FISH TAIL297D 13 RIGHT FISH TAIL297E UP FISH TAIL297F DOWN FISH TAIL

2947 RIGHTWARDS ARROW THROUGH X2948 SMALL CIRCLE WITH SUPERIMPOSED LEFT

RIGHT ARROW2949 UPWARDS TWO-HEADED ARROW FROM

SMALL CIRCLE294A LEFT-UP-RIGHT-DOWN HARPOON294B LEFT-DOWN-RIGHT-UP HARPOON294C UP-RIGHT-DOWN-LEFT HARPOON294D UP-LEFT-DOWN-RIGHT HARPOON294E LEFT-UP-RIGHT-UP HARPOON294F UP-RIGHT-DOWN-RIGHT HARPOON2950 LEFT-DOWN-RIGHT-DOWN HARPOON2951 UP-LEFT-DOWN-LEFT HARPOON2952 LEFTWARDS HARPOON-UP TO BAR2953 RIGHTWARDS HARPOON-UP TO BAR2954 UPWARDS HARPOON-RIGHT TO BAR2955 DOWNWARDS HARPOON-RIGHT TO BAR2956 LEFTWARDS HARPOON-DOWN TO BAR2957 RIGHTWARDS HARPOON-DOWN TO BAR2958 iexcl UPWARDS HARPOON-LEFT TO BAR2959 cent DOWNWARDS HARPOON-LEFT TO BAR295A pound LEFTWARDS HARPOON-UP FROM BAR295B curren RIGHTWARDS HARPOON-UP FROM BAR295C yen UPWARDS HARPOON-RIGHT FROM BAR295D DOWNWARDS HARPOON-RIGHT FROM BAR295E LEFTWARDS HARPOON-DOWN FROM BAR295F RIGHTWARDS HARPOON-DOWN FROM BAR2960 UPWARDS HARPOON-LEFT FROM BAR2961 DOWNWARDS HARPOON-LEFT FROM BAR2962 LEFTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-DOWN2963 UPWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2964 RIGHTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-DOWN2965 DOWNWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT2966 LEFTWARDS HARPOON-UP ABOVE

RIGHTWARDS HARPOON-UP2967 LEFTWARDS HARPOON-DOWN ABOVE

RIGHTWARDS HARPOON-DOWN2968 RIGHTWARDS HARPOON-UP ABOVE

LEFTWARDS HARPOON-UP2969 RIGHTWARDS HARPOON-DOWN ABOVE

LEFTWARDS HARPOON-DOWN296A LEFTWARDS HARPOON-UP ABOVE LONG

DASH296B LEFTWARDS HARPOON-DOWN BELOW

LONG DASH296C RIGHTWARDS HARPOON-UP ABOVE LONG

DASH296D RIGHTWARDS HARPOON-DOWN BELOW

LONG DASH296E UPWARDS HARPOON-LEFT BESIDE

DOWNWARDS HARPOON-RIGHT296F DOWNWARDS HARPOON-LEFT BESIDE

UPWARDS HARPOON-RIGHT2970 RIGHT DOUBLE ARROW WITH ROUNDED

HEADrarr 2283 superset of

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

(

)

+

-

0

1

2

3

4

5

6

7

8

9

lt

=

gt

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

[

]

^

_

`

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

|

~

2980

2981

2982

2983

2984

2985

2986

2987

2988

2989

298A

298B

298C

298D

298E

298F

2990

2991

2992

2993

2994

2995

2996

2997

2998

2999

299A

299B

299C

299D

299E

299F

29A0

29A1

29A2

29A3

29A4

29A5

29A6

29A7

29A8

29A9

29AA

29AB

29AC

29AD

29AE

29AF

29B0

29B1

29B2

29B3

29B4

29B5

29B6

29B7

29B8

29B9

29BA

29BB

29BC

29BD

29BE

29BF

29C0

29C1

29C2

29C3

29C4

29C5

29C6

29C7

29C8

29C9

29CA

29CB

29CC

29CD

29CE

29CF

29D0

29D1

29D2

29D3

29D4

29D5

29D6

29D7

29D8

29D9

29DA

29DB

29DC

29DD

29DE

29DF

29E0

29E1

29E2

29E3

29E4

29E5

29E6

29E7

29E8

29E9

29EA

29EB

29EC

29ED

29EE

29EF

29F0

29F1

29F2

29F3

29F4

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 34: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 23

29FFMiscellaneous Math Symbols2980

298 299 29A 29B 29C 29D 29E 29F

$

amp

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 25

29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

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ordf

laquo

not

shy

reg

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deg

plusmn

sup2

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acute

micro

para

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cedil

sup1

ordm

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13

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2A00

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2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

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Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

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Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

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Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

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Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

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Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

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Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

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Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

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Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

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Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

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Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 35: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 24

29C7Miscellaneous Math Symbols2980

29A8 $ MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE RIGHT

29A9 MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING UP AND TOTHE LEFT

29AA amp MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE RIGHT

29AB MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING DOWN ANDTO THE LEFT

29AC ( MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDUP

29AD ) MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT AND UP

29AE MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING RIGHT ANDDOWN

29AF + MEASURED ANGLE WITH OPEN ARMENDING IN ARROW POINTING LEFT ANDDOWN

Empty sets29B0 REVERSED EMPTY SET

rarr 2349 apl functional symbol circle backslash29B1 - EMPTY SET OVERBAR29B2 EMPTY SET WITH SMALL CIRCLE ABOVE29B3 EMPTY SET RIGHT ARROW ABOVE29B4 0 EMPTY SET LEFT ARROW ABOVE

Circle symbols29B5 1 CIRCLE WITH HORIZONTAL BAR29B6 2 CIRCLED VERTICAL BAR29B7 3 CIRCLED PARALLEL29B8 4 CIRCLED FALLING DIAGONAL29B9 5 CIRCLED PERPENDICULAR29BA 6 CIRCLE DIVIDED BY HORIZONTAL BAR AND

TOP HALF DIVIDED BY VERTICAL29BB 7 CIRCLE WITH SUPERIMPOSED X29BC 8 CIRCLED ANTICLOCKWISE-ROTATED

DIVISION SIGN29BD 9 UP ARROW THROUGH CIRCLE29BE CIRCLED LARGE CIRCLE

rarr 233E apl functional symbol circle jot29BF CIRCLED FILLED CIRCLE29C0 lt CIRCLED LESS-THAN29C1 = CIRCLED GREATER-THAN29C2 gt CIRCLE WITH SMALL CIRCLE TO THE RIGHT29C3 CIRCLE WITH TWO HORIZONTAL STROKES

TO THE RIGHT

Square symbols29C4 SQUARED RISING DIAGONAL SLASH

rarr 2341 apl functional symbol quad slash29C5 A SQUARED FALLING DIAGONAL SLASH

rarr 2342 apl functional symbol quad backslash29C6 B SQUARED ASTERISK29C7 C SQUARED SMALL CIRCLE

rarr 233B apl functional symbol quad circle

Miscellaneous math symbols2980 D TRIPLE VERTICAL BAR DELIMITER

rarr 2AF4 triple vertical bar with horizontal stroke2981 E Z NOTATION SPOT

bull medium-sized filled circle2982 F Z NOTATION TYPE COLON

Brackets2983 G LEFT WHITE BRACE2984 H RIGHT WHITE BRACE2985 I LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracket2986 J RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracket2987 K Z NOTATION LEFT IMAGE BRACKET2988 L Z NOTATION RIGHT IMAGE BRACKET2989 M Z NOTATION LEFT BINDING BRACKET298A N Z NOTATION RIGHT BINDING BRACKET298B O LEFT BRACKET UNDERBAR298C P RIGHT BRACKET UNDERBAR298D Q LEFT BRACKET WITH REVERSE SOLIDUS

TOP CORNER298E R RIGHT BRACKET WITH REVERSE SOLIDUS

BOTTOM CORNER298F S LEFT BRACKET WITH SOLIDUS BOTTOM

CORNER2990 T RIGHT BRACKET WITH SOLIDUS TOP

CORNER2991 U LEFT ANGLE BRACKET WITH DOT2992 V RIGHT ANGLE BRACKET WITH DOT2993 W LEFT ARC LESS-THAN BRACKET2994 X RIGHT ARC GREATER-THAN BRACKET2995 Y DOUBLE LEFT ARC GREATER-THAN

BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET2997 [ RIGHT MOUSTACHE2998 LEFT MOUSTACHE

Fence2999 ] DOTTED FENCE

bull four close dots vertical

Miscellaneous math symbol299A ^ VERTICAL ZIGZAG LINE

Angles299B _ MEASURED ANGLE OPENING LEFT299C ` RIGHT ANGLE VARIANT WITH SQUARE299D a MEASURED RIGHT ANGLE WITH DOT299E b ANGLE WITH S INSIDE299F c ACUTE ANGLE29A0 d SPHERICAL ANGLE OPENING LEFT29A1 e SPHERICAL ANGLE OPENING UP29A2 f TURNED ANGLE29A3 g REVERSED ANGLE29A4 h ANGLE WITH UNDERBAR29A5 i REVERSED ANGLE WITH UNDERBAR29A6 j LARGE DOWNWARDS POINTING ANGLE29A7 k LARGE UPWARDS POINTING ANGLE

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29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 36: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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29F4Miscellaneous Math Symbols29C8

Error bar symbols29EE l ERROR-BARRED WHITE SQUARE29EF m ERROR-BARRED FILLED SQUARE29F0 n ERROR-BARRED WHITE DIAMOND29F1 o ERROR-BARRED FILLED DIAMOND29F2 p ERROR-BARRED WHITE CIRCLE29F3 q ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol29F4 r RULE-DELAYED

= colon right arrow

29C8 s SQUARED SQUARE29C9 t TWO JOINED SQUARES

Triangle symbols29CA u TRIANGLE WITH DOT OVER29CB v TRIANGLE WITH UNDERBAR29CC w S IN TRIANGLE29CD x TRIANGLE WITH SERIFS AT BOTTOM29CE y RIGHT TRIANGLE ABOVE LEFT TRIANGLE29CF z LEFT TRIANGLE BESIDE VERTICAL BAR29D0 VERTICAL BAR BESIDE RIGHT TRIANGLE

Bowtie symbols29D1 | LEFT FILLED BOWTIE29D2 RIGHT FILLED BOWTIE29D3 ~ FILLED BOWTIE29D4 LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect product29D5 RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect product29D6 WHITE HOURGLASS

= vertical bowtie29D7 FILLED HOURGLASS

Miscellaneous math symbols29D8 MOST POSITIVE29D9 CONGRUENCE SIGN WITH LAZY S29DA REVERSED MOST POSITIVE WITH LINE

BELOW29DB MOST POSITIVE WITH TWO LINES BELOW29DC INFINITY SIGN WITH TOP RIGHT QUADRANT

OMITTED29DD TIE OVER INFINITY29DE INFINITY NEGATED WITH VERTICAL BAR29DF DOUBLE-ENDED MULTIMAP29E0 SQUARE WITH CONTOURED OUTLINE

= DAlembertian29E1 INCREASES AS29E2 SHUFFLE PRODUCT29E3 SLANTED PARALLEL SUPERIMPOSED ON

EQUAL= homethetically congruent to

29E4 TILDE ABOVE SLANTED PARALLELSUPERIMPOSED ON EQUAL

29E5 SLANTED PARALLEL SUPERIMPOSED ONTHREE-LINE EQUAL= congruent and parallel

29E6 TOP ARC ABOVE BOTTOM ARC29E7 THERMODYNAMIC

bull vertical bar crossed by two horizontals29E8 DOWN-POINTING TRIANGLE WITH LEFT

HALF BLACK29E9 DOWN-POINTING TRIANGLE WITH RIGHT

HALF BLACK29EA FILLED DIAMOND WITH DOWN ARROW29EB FILLED LOZENGE29EC CIRCLE WITH DOWN ARROW29ED FILLED CIRCLE WITH DOWN ARROW

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

2A0D

2A0E

2A0F

2A10

2A11

2A12

2A13

2A14

2A15

2A16

2A17

2A18

2A19

2A1A

2A1B

2A1C

2A1D

2A1E

2A1F

2A20

2A21

2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

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2

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5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 37: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 26

2A7FSupplemental Math Operators2A00

2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7

iexcl

cent

pound

curren

yen

brvbar

sect

uml

copy

ordf

laquo

not

shy

reg

macr

deg

plusmn

sup2

sup3

acute

micro

para

middot

cedil

sup1

ordm

13

13

$

amp

(

)

2A00

2A01

2A02

2A03

2A04

2A05

2A06

2A07

2A08

2A09

2A0A

2A0B

2A0C

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2A10

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2A1A

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2A20

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2A22

2A23

2A24

2A25

2A26

2A27

2A28

2A29

2A2A

2A2B

2A2C

2A2D

2A2E

2A2F

2A30

2A31

2A32

2A33

2A34

2A35

2A36

2A37

2A38

2A39

2A3A

2A3B

2A3C

2A3D

2A3E

2A3F

2A40

2A41

2A42

2A43

2A44

2A45

2A46

2A47

2A48

2A49

2A4A

2A4B

2A4C

2A4D

2A4E

2A4F

2A50

2A51

2A52

2A53

2A54

2A55

2A56

2A57

2A58

2A59

2A5A

2A5B

2A5C

2A5D

2A5E

2A5F

2A60

2A61

2A62

2A63

2A64

2A65

2A66

2A67

2A68

2A69

2A6A

2A6B

2A6C

2A6D

2A6E

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 27

2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

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PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 38: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

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2AFFSupplemental Math Operators2A80

2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

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2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

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2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

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2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

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Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

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Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

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Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

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Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

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Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

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Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

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Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

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Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

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Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 39: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 28

2A47Supplemental Math Operators2A00

2A21 Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with bar rightwards

Plus and minus sign operators2A22 PLUS SIGN WITH SMALL CIRCLE ABOVE2A23 PLUS SIGN WITH CIRCUMFLEX ACCENT

ABOVE2A24 PLUS SIGN WITH TILDE ABOVE2A25 PLUS SIGN WITH DOT BELOW2A26 PLUS SIGN WITH TILDE BELOW2A27 PLUS SIGN WITH SUBSCRIPT TWO

= nim-addition2A28 FILLED TRIANGLE WITH PLUS2A29 MINUS SIGN WITH COMMA ABOVE2A2A MINUS SIGN WITH DOT BELOW2A2B FALLING DOTS MINUS2A2C RISING DOTS MINUS2A2D PLUS SIGN IN LEFT HALF CIRCLE2A2E PLUS SIGN IN RIGHT HALF CIRCLE

Multiplication and division sign operators2A2F VECTOR OR CROSS PRODUCT

rarr 00D7 times multiplication sign2A30 MULTIPLICATION SIGN WITH DOT ABOVE2A31 MULTIPLICATION SIGN WITH UNDERBAR2A32 SEMIDIRECT PRODUCT MULTIPLICATION

SIGN WITH BOTTOM CLOSED2A33 SMASH PRODUCT2A34 MULTIPLICATION SIGN IN LEFT HALF

CIRCLE2A35 MULTIPLICATION SIGN IN RIGHT HALF

CIRCLE2A36 CIRCLED MULTIPLICATION SIGN WITH

CIRCUMFLEX ACCENT2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE2A38 CIRCLED DIVISION SIGN

Miscellaneous math operators2A39 PLUS IN TRIANGLE2A3A MINUS IN TRIANGLE2A3B MULTIPLICATION SIGN IN TRIANGLE2A3C INTERIOR PRODUCT2A3D RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not sign2A3E Z NOTATION RELATIONAL COMPOSITION

rarr 2A1F z notation schema composition2A3F AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproduct

Intersections and unions2A40 INTERSECTION WITH DOT2A41 UNION WITH MINUS

= z notation bag subtraction2A42 UNION WITH OVERBAR2A43 13 INTERSECTION WITH OVERBAR2A44 INTERSECTION WITH LOGICAL AND2A45 UNION WITH LOGICAL OR2A46 UNION ABOVE INTERSECTION2A47 INTERSECTION ABOVE UNION

N-ary operators2A00 N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operator2A01 N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plus2A02 N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled times2A03 N-ARY UNION OPERATOR WITH DOT2A04 N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset union2A05 iexcl N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square cap2A06 cent N-ARY SQUARE UNION OPERATOR

rarr 2294 square cup2A07 pound TWO LOGICAL AND OPERATOR

= merge

rarr 2A55 two intersecting logical and

2A08 curren TWO LOGICAL OR OPERATOR

rarr 2A56 two intersecting logical or

2A09 yen N-ARY TIMES OPERATOR

Summations and integrals2A0A brvbar MODULO TWO SUM2A0B sect SUMMATION WITH INTEGRAL2A0C QUADRUPLE INTEGRAL OPERATOR

asymp 222B int 222B int 222B int 222B int2A0D copy FINITE PART INTEGRAL2A0E ordf INTEGRAL WITH DOUBLE STROKE2A0F laquo INTEGRAL AVERAGE WITH SLASH2A10 not CIRCULATION FUNCTION2A11 shy ANTICLOCKWISE INTEGRATION2A12 reg LINE INTEGRATION WITH RECTANGULAR

PATH AROUND POLE2A13 macr LINE INTEGRATION WITH SEMICIRCULAR

PATH AROUND POLE2A14 deg LINE INTEGRATION NOT INCLUDING THE

POLE2A15 plusmn INTEGRAL AROUND A POINT OPERATOR2A16 sup2 QUATERNION INTEGRAL OPERATOR2A17 sup3 INTEGRAL OPERPRINTED WITH LEFTWARDS

ARROW WITH HOOK2A18 acute INTEGRAL OVERPRINTED WITH TIMES SIGN2A19 micro INTEGRAL OVERPRINTED WITH CAP2A1A para INTEGRAL OVERPRINTED WITH CUP2A1B middot UPPER INTEGRAL WITH OVERBAR2A1C cedil LOWER INTEGRAL WITH UNDERBAR

Miscellaneous operators2A1D sup1 JOIN

= large bowtiebull relational database theory

2A1E ordm LARGE LEFT TRIANGLE OPERATORbull relational database theory

2A1F Z NOTATION SCHEMA COMPOSITIONrarr 2A3E z notation relational composition

2A20 raquo Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

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2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 40: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 29

2A97Supplemental Math Operators2A48

2A71 EQUAL ABOVE PLUS2A72 PLUS ABOVE EQUAL2A73 EQUAL ABOVE TILDE OPERATOR2A74 DOUBLE COLON EQUAL2A75 TWO CONSECUTIVE EQUAL SIGNS2A76 THREE CONSECUTIVE EQUAL SIGNS2A77 EQUAL SIGN WITH TWO DOTS ABOVE AND

TWO DOTS BELOW2A78 EQUIVALENT WITH FOUR DOTS ABOVE2A79 LESS-THAN WITH CIRCLE INSIDE2A7A GREATER-THAN WITH CIRCLE INSIDE2A7B LESS-THAN WITH QUESTION MARK ABOVE2A7C GREATER-THAN WITH QUESTION MARK

ABOVE2A7D LESS-THAN OR SLANTED EQUAL TO2A7E GREATER-THAN OR SLANTED EQUAL TO2A7F LESS-THAN OR SLANTED EQUAL TO WITH

DOT INSIDE2A80 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT INSIDE2A81 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE2A82 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE2A83 LESS-THAN OR SLANTED EQUAL TO WITH

DOT ABOVE RIGHT2A84 GREATER-THAN OR SLANTED EQUAL TO

WITH DOT ABOVE LEFT2A85 LESS-THAN OR APPROXIMATE2A86 GREATER-THAN OR APPROXIMATE2A87 LESS-THAN AND NOT ONE-LINE EQUAL TO2A88 GREATER-THAN AND NOT ONE-LINE EQUAL

TO2A89 LESS-THAN AND NOT APPROXIMATE2A8A GREATER-THAN AND NOT APPROXIMATE2A8B LESS-THAN ABOVE TWO-LINE EQUAL

ABOVE GREATER-THAN2A8C GREATER-THAN ABOVE TWO-LINE EQUAL

ABOVE LESS-THAN2A8D LESS-THAN ABOVE SIMILAR OR EQUAL2A8E GREATER-THAN ABOVE SIMILAR OR EQUAL2A8F LESS-THAN ABOVE SIMILAR ABOVE

GREATER-THAN2A90 GREATER-THAN ABOVE SIMILAR ABOVE

LESS-THAN2A91 LESS-THAN ABOVE GREATER-THAN ABOVE

TWO-LINE EQUAL2A92 GREATER-THAN ABOVE LESS-THAN ABOVE

TWO-LINE EQUAL2A93 LESS-THAN ABOVE SLANTED EQUAL

ABOVE GREATER-THAN ABOVE SLANTEDEQUAL

2A94 GREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUAL

2A95 SLANTED EQUAL TO OR LESS-THAN2A96 SLANTED EQUAL TO OR GREATER-THAN2A97 SLANTED EQUAL TO OR LESS-THAN WITH

DOT INSIDE

2A48 UNION ABOVE BAR ABOVE INTERSECTION2A49 INTERSECTION ABOVE BAR ABOVE UNION2A4A UNION BESIDE AND JOINED WITH UNION2A4B INTERSECTION BESIDE AND JOINED WITH

INTERSECTION2A4C CLOSED UNION WITH SERIFS2A4D CLOSED INTERSECTION WITH SERIFS2A4E DOUBLE SQUARE INTERSECTION2A4F DOUBLE SQUARE UNION2A50 13 CLOSED UNION WITH SERIFS AND SMASH

PRODUCT

Logical ands and ors2A51 LOGICAL AND WITH DOT ABOVE2A52 LOGICAL OR WITH DOT ABOVE2A53 DOUBLE LOGICAL AND2A54 DOUBLE LOGICAL OR2A55 TWO INTERSECTING LOGICAL AND

rarr 2A07 pound two logical and operator2A56 TWO INTERSECTING LOGICAL OR

rarr 2A08 curren two logical or operator2A57 SLOPING LARGE OR2A58 SLOPING LARGE AND2A59 LOGICAL OR OVERLAPPING LOGICAL AND2A5A LOGICAL AND WITH MIDDLE STEM2A5B LOGICAL OR WITH MIDDLE STEM2A5C LOGICAL AND WITH HORIZONTAL DASH2A5D LOGICAL OR WITH HORIZONTAL DASH2A5E LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspective2A5F LOGICAL AND WITH UNDERBAR2A60 LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimates2A61 SMALL VEE WITH UNDERBAR2A62 LOGICAL OR WITH DOUBLE OVERBAR2A63 LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular to

Miscellaneous math operators2A64 Z NOTATION DOMAIN ANTIRESTRICTION2A65 Z NOTATION RANGE ANTIRESTRICTION

Relational operators2A66 EQUAL SIGN WITH DOT BELOW2A67 IDENTICAL WITH DOT ABOVE2A68 TRIPLE HORIZONTAL BAR WITH DOUBLE

VERTICAL STROKE= identical and parallel to

2A69$ TRIPLE HORIZONTAL BAR WITH TRIPLEVERTICAL STROKE

2A6A TILDE OPERATOR WITH DOT2A6Bamp TILDE OPERATOR WITH RISING DOTS

rarr 223B homothetic2A6C SIMILAR MINUS SIMILAR2A6D ( CONGRUENT WITH OVERDOT2A6E ) REVERSED CONGRUENT2A6F DOUBLE TILDE OPERATOR WITH

CIRCUMFLEX ACCENT2A70 APPROXIMATELY EQUAL OR EQUAL TO

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 41: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

PFS amstt fonts Version 1fixed Printed 17-Mar-2000 30

2AEASupplemental Math Operators2A98

2AC4 SUPERSET OF OR EQUAL TO WITH DOTABOVE

2AC5 SUBSET OF OR TWO-LINE EQUAL2AC6 SUPERSET OF OR TWO-LINE EQUAL2AC7 SUBSET OF ABOVE TILDE OPERATOR2AC8 SUPERSET OF ABOVE TILDE OPERATOR2AC9 SUBSET OF ABOVE DOUBLE TILDE

OPERATOR2ACA SUPERSET OF ABOVE DOUBLE TILDE

OPERATOR2ACB SUBSET OF OR NOT TWO-LINE EQUAL2ACC SUPERSET OF OR NOT TWO-LINE EQUAL2ACD SQUARE LEFT OPEN BOX OPERATOR2ACE SQUARE RIGHT OPEN BOX OPERATOR2ACF CLOSED SUBSET2AD0 CLOSED SUPERSET2AD1 CLOSED SUBSET OR EQUAL2AD2 CLOSED SUPERSET OR EQUAL2AD3 SUBSET ABOVE SUPERSET2AD4 SUPERSET ABOVE SUBSET2AD5 SUBSET ABOVE SUBSET2AD6 SUPERSET ABOVE SUPERSET2AD7 SUPERSET BESIDE SUBSET2AD8 SUPERSET BESIDE AND JOINED BY DASH

WITH SUBSET

Forks2AD9 ELEMENT OF OPENING DOWNWARDS2ADA PITCHFORK WITH TEE TOP2ADB TRANSVERSAL INTERSECTION

rarr 22D4 pitchfork2ADC FORKING

bull symbol is slashed although positive2ADD NONFORKING

bull negative symbol with no slash

Tacks2ADE SHORT LEFT TACK2ADF SHORT DOWN TACK2AE0 SHORT UP TACK2AE1 PERPENDICULAR WITH S2AE2 VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfies2AE3 DOUBLE VERTICAL BAR LEFT TURNSTILE2AE4 VERTICAL BAR DOUBLE LEFT TURNSTILE2AE5 DOUBLE VERTICAL BAR DOUBLE LEFT

TURNSTILE2AE6 LONG DASH FROM LEFT MEMBER OF

DOUBLE VERTICALrarr 22A9 forces

2AE7 SHORT DOWN TACK WITH OVERBARrarr 22A4 down tack

2AE8 SHORT UP TACK WITH UNDERBARrarr 22A5 up tack

2AE9 SHORT UP TACK ABOVE SHORT DOWNTACK

2AEA DOUBLE DOWN TACK

2A98 SLANTED EQUAL TO OR GREATER-THANWITH DOT INSIDE

2A99 TWO-LINE EQUAL TO OR LESS-THAN2A9A TWO-LINE EQUAL TO OR GREATER-THAN2A9B TWO-LINE SLANTED EQUAL TO OR LESS-

THAN2A9C TWO-LINE SLANTED EQUAL TO OR

GREATER-THAN2A9D SIMILAR OR LESS-THAN2A9E SIMILAR OR GREATER-THAN2A9F SIMILAR ABOVE LESS-THAN ABOVE EQUAL2AA0 SIMILAR ABOVE GREATER-THAN ABOVE

EQUAL2AA1 DOUBLE NESTED LESS-THAN SIGN

= absolute continuity2AA2 DOUBLE NESTED GREATER-THAN SIGN2AA3 DOUBLE LESS-THAN WITH UNDERBAR2AA4 GREATER-THAN OVERLAPPING LESS-THAN2AA5 GREATER-THAN BESIDE LESS-THAN2AA6 LESS-THAN CLOSED BY CURVE2AA7 GREATER-THAN CLOSED BY CURVE2AA8 LESS-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AA9 GREATER-THAN CLOSED BY CURVE ABOVE

SLANTED EQUAL2AAA SMALLER THAN2AAB LARGER THAN2AAC SMALLER THAN OR EQUAL2AAD LARGER THAN OR EQUAL2AAE BUMPY ABOVE TWO-LINE EQUAL2AAF PRECEDES ABOVE ONE-LINE EQUAL2AB0 SUCCEEDS ABOVE ONE-LINE EQUAL2AB1 PRECEDES ABOVE NOT ONE-LINE EQUAL2AB2 SUCCEEDS ABOVE NOT ONE-LINE EQUAL2AB3 PRECEDES ABOVE TWO-LINE EQUAL2AB4 SUCCEEDS ABOVE TWO-LINE EQUAL2AB5 PRECEDES ABOVE NOT TWO-LINE EQUAL2AB6 SUCCEEDS ABOVE NOT TWO-LINE EQUAL2AB7 PRECEDES ABOVE DOUBLE TILDE

OPERATOR2AB8 SUCCEEDS ABOVE DOUBLE TILDE

OPERATOR2AB9 PRECEDES ABOVE NOT DOUBLE TILDE

OPERATOR2ABA SUCCEEDS ABOVE NOT DOUBLE TILDE

OPERATOR2ABB DOUBLE PRECEDES2ABC DOUBLE SUCCEEDS

Subset and superset relations2ABD SUBSET WITH DOT2ABE SUPERSET WITH DOT2ABF SUBSET WITH PLUS BELOW2AC0 SUPERSET WITH PLUS BELOW2AC1 SUBSET WITH MULTIPLICATION SIGN

BELOW2AC2 SUPERSET WITH MULTIPLICATION SIGN

BELOW2AC3 SUBSET OF OR EQUAL TO WITH DOT ABOVE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

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BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 42: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

Annex 3

Excerpts from L200-02

AX0 AX1 AX2

0

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6

7

8

9

A

B

C

D

E

F

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8

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F

Letter-like symbols combining diacritics punctuation

AX00 N GREEK THETA SYMBOL WITH STRAIGHT BARrarr 0472 cyrillic capital letter fitararr 04E8 cyrillic capital letter barred o

AX01 [removed 03D2]AX02 N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

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2

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5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 43: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

AX03 N GREEK SYMBOL REVERSED STRAIGHT EPSILONAX04 N GREEK LETTER Q-KOPPAAX05 N GREEK SMALL LETTER Q-KOPPAAX06 N TURNED SANS SERIF CAPITAL G

= gameAX07 N TURNED SANS SERIF CAPITAL LAX08 N REVERSED SANS SERIF CAPITAL LAX09 N INVERTED SANS SERIF CAPITAL YAX0A N OPEN-FACE GREEK SMALL LETTER GAMMAAX0B N OPEN-FACE GREEK CAPITAL GAMMAAX0C N OPEN-FACE GREEK CAPITAL PIAX0D L OPEN-FACE SUMAX0E D COMBINING REVERSE SOLIDUS OVERLAYAX0F D COMBINING DOUBLE VERTICAL STROKE OVERLAY

= Z NOTATION FINITE FUNCTIONAX10 D ANNUITY SYMBOL

= actuarial bendAX11 N CAPITAL DIFFERENTIAL DAX12 N DIFFERENTIAL DAX13 N EXPONENTIAL EAX14 N IMAGINARY IAX15 N IMAGINARY JAX16 D TRIPLE UNDERDOTAX17 [removed]

AX1A [removed]AX1B LOW ASTERISKAX1C N QUADRUPLE PRIME

[composed U+2032 + U+2032 + U+2032 + U+2032]AX1D [removed]AX1E REVERSED SEMI-COLONAX1F P EM LEADERAX20 N TWO ASTERISKS ALIGNED VERTICALLYAX21 SOLIDUS OVERBARAX22 REVERSE SOLIDUS WITH HORIZONTAL STROKEAX23 B BIG SOLIDUSAX24 B BIG REVERSE SOLIDUS

= Z NOTATION SCHEMA HIDING visually distinguishably bigger than set minus

AX25 TOP SQUARE BRACKETAX26 BOTTOM SQUARE BRACKETAX27 BOTTOM ABOVE TOP SQUARE BRACKETAX28 N TURNED AMPERSANDAX29 [removed]AX2A [removed]AX2B N MEDIUM MATH SPACE

four-eighteenths of an emAX2C [removed 2423]AXD FUNCTION APPLICATIONAXE INVISIBLE TIMESAXF VARIATION SELECTOR

2

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 44: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

Arrows and harpoons combinations fishtails

BX00 R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWBX01 R THREE RIGHTWARDS ARROWSBX02 R LEFTWARDS ARROW WITH VERTICAL STROKEBX03 R RIGHTWARDS ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL FUNCTIONBX04 R LEFT RIGHT ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL RELATIONBX05 R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKEBX06 R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE FUNCTIONBX07 R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE RELATIONBX08 RULE-DELAYED

= colon right arrowBX09 R LEFTWARDS OPEN-HEADED ARROWBX0A R RIGHTWARDS OPEN-HEADED ARROWBX0B R LEFT RIGHT OPEN-HEADED ARROWBX0C R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE

= Z NOTATION PARTIAL SURJECTIONBX0D R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE SURJECTIONBX0E R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX0F R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKEBX10 R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKEBX11 R RIGHTWARDS TWO-HEADED ARROW FROM BAR

= maps toBX12 R LEFTWARDS DOUBLE ARROW FROM BAR

= maps fromBX13 R RIGHTWARDS DOUBLE ARROW FROM BAR

= maps toBX14 R DOWNWARDS ARROW WITH HORIZONTAL STROKEBX15 R UPWARDS ARROW WITH HORIZONTAL STROKEBX16 R UPWARDS TRIPLE ARROWBX17 R DOWNWARDS TRIPLE ARROWBX18 R LEFTWARDS BROKEN ARROWBX19 R RIGHTWARDS BROKEN ARROWBX1A R LEFTWARDS DOUBLY BROKEN ARROWBX1B R RIGHTWARDS DOUBLY BROKEN ARROWBX1C R RIGHTWARDS TWO-HEADED BROKEN ARROWBX1D R RIGHTWARDS ARROW WITH DOTTED STEMBX1E R UPWARDS ARROW TO BARBX1F R DOWNWARDS ARROW TO BARBX20 R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE

= Z NOTATION PARTIAL INJECTIONBX21 R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE

= Z NOTATION FINITE INJECTIONBX22 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL

= bijective mapping= Z NOTATION BIJECTION

BX23 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 45: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

BX24 R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE= Z NOTATION FINITE SURJECTIVE INJECTION

BX25 R LEFTWARDS ARROW-TAILBX26 R RIGHTWARDS ARROW-TAILBX27 R LEFTWARDS DOUBLE ARROW-TAILBX28 R RIGHTWARDS DOUBLE ARROW-TAILBX29 R LEFTWARDS ARROW TO FILLED DIAMONDBX2A R RIGHTWARDS ARROW TO FILLED DIAMONDBX2B R LEFTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2C R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMONDBX2D R NORTH WEST-SOUTH EAST ARROWBX2E R NORTH EAST-SOUTH WEST ARROWBX2F R NORTH WEST ARROW WITH HOOKBX30 R NORTH EAST ARROW WITH HOOKBX31 R SOUTH EAST ARROW WITH HOOKBX32 R SOUTH WEST ARROW WITH HOOKBX33 R NORTH WEST AND NORTH EAST ARROWSBX34 R NORTH EAST AND SOUTH EAST ARROWSBX35 R SOUTH EAST AND SOUTH WEST ARROWSBX36 R SOUTH WEST AND NORTH WEST ARROWSBX37 N RISING DIAGONAL CROSSING FALLING DIAGONALBX38 N FALLING DIAGONAL CROSSING RISING DIAGONALBX39 N SOUTH EAST ARROW CROSSING NORTH EAST ARROWBX3A N NORTH EAST ARROW CROSSING SOUTH EAST ARROWBX3B N FALLING DIAGONAL CROSSING NORTH EAST ARROWBX3C N RISING DIAGONAL CROSSING SOUTH EAST ARROWBX3D N NORTH EAST ARROW CROSSING NORTH WEST ARROWBX3E N NORTH WEST ARROW CROSSING NORTH EAST ARROWBX3F R WAVE ARROW POINTING DIRECTLY TO THE RIGHT

rarr 219D rightwards wave arrowBX40 RIGHTWARDS ARROW CURVING UP

Japanese requestBX41 RIGHTWARDS ARROW CURVING DOWN

Japanese requestBX42 R DOWNWARDS ARROW CURVING LEFTWARDSBX43 R DOWNWARDS ARROW CURVING RIGHTWARDSBX44 R RIGHT-SIDE ARC CLOCKWISE ARROWBX45 R LEFT-SIDE ARC ANTICLOCKWISE ARROWBX46 R TOP ARC ANTICLOCKWISE ARROWBX47 R BOTTOM ARC ANTICLOCKWISE ARROWBX48 R TOP ARC CLOCKWISE ARROW WITH MINUSBX49 R TOP ARC ANTICLOCKWISE ARROW WITH PLUSBX4A R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWBX4B R LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWBX4C R ANTICLOCKWISE CLOSED CIRCLE ARROW

rarr 20DA combining anticlockwise ring overlayBX4D R CLOCKWISE CLOSED CIRCLE ARROW

rarr 20D9 combining clockwise ring overlayBX4E R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWBX4F R LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWBX50 R SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWBX51 R RIGHTWARDS ARROW WITH PLUS BELOWBX52 R LEFTWARDS ARROW WITH PLUS BELOWBX53 R RIGHTWARDS ARROW THROUGH X

4

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 46: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

BX54 R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWBX55 R UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLEBX56 RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWBX57 R LEFT-UP-RIGHT-DOWN HARPOONBX58 R LEFT-DOWN-RIGHT-UP HARPOONBX59 R UP-RIGHT-DOWN-LEFT HARPOONBX5A R UP-LEFT-DOWN-RIGHT HARPOONBX5B R LEFT-UP-RIGHT-UP HARPOONBX5C R UP-RIGHT-DOWN-RIGHT HARPOONBX5D R LEFT-DOWN-RIGHT-DOWN HARPOONBX5E R UP-LEFT-DOWN-LEFT HARPOONBX5F R LEFTWARDS HARPOON-UP TO BARBX60 R RIGHTWARDS HARPOON-UP TO BARBX61 R UPWARDS HARPOON-RIGHT TO BARBX62 R DOWNWARDS HARPOON-RIGHT TO BARBX63 R LEFTWARDS HARPOON-DOWN TO BARBX64 R RIGHTWARDS HARPOON-DOWN TO BARBX65 R UPWARDS HARPOON-LEFT TO BARBX66 R DOWNWARDS HARPOON-LEFT TO BARBX67 R LEFTWARDS HARPOON-UP FROM BARBX68 R RIGHTWARDS HARPOON-UP FROM BARBX69 R UPWARDS HARPOON-RIGHT FROM BARBX6A R DOWNWARDS HARPOON-RIGHT FROM BARBX6B R LEFTWARDS HARPOON-DOWN FROM BARBX6C R RIGHTWARDS HARPOON-DOWN FROM BARBX6D R UPWARDS HARPOON-LEFT FROM BARBX6E R DOWNWARDS HARPOON-LEFT FROM BARBX6F R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWNBX70 R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX71 R RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWNBX72 R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX73 R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UPBX74 R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWNBX75 R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UPBX76 R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWNBX77 R LEFTWARDS HARPOON-UP ABOVE LONG DASHBX78 R LEFTWARDS HARPOON-DOWN BELOW LONG DASHBX79 R RIGHTWARDS HARPOON-UP ABOVE LONG DASHBX7A R RIGHTWARDS HARPOON-DOWN BELOW LONG DASHBX7B R UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTBX7C R DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTBX7D R RIGHT DOUBLE ARROW WITH ROUNDED HEAD

looks like thin supersetBX7E R EQUAL ABOVE RIGHTWARDS ARROWBX7F R TILDE OPERATOR ABOVE RIGHTWARDS ARROWBX80 R LEFTWARDS ARROW ABOVE TILDE OPERATORBX81 R RIGHTWARDS ARROW ABOVE TILDE OPERATORBX82 R RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORBX83 R LESS THAN ABOVE LEFTWARDS ARROWBX84 R LEFTWARDS ARROW THROUGH LESS-THANBX85 R GREATER-THAN ABOVE RIGHTWARDS ARROWBX86 R SUBSET ABOVE RIGHTWARDS ARROWBX87 R LEFTWARDS ARROW THROUGH SUBSETBX88 R SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

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9

A

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The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 47: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

BX89 R LEFT FISH TAILBX8A R RIGHT FISH TAILBX8B R UP FISH TAILBX8C R DOWN FISH TAIL

CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF

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Large operators binary operators relational operators

CX00 R ELEMENT OF WITH LONG HORIZONTAL STROKECX01 R ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX02 R SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX03 R ELEMENT OF WITH DOT ABOVE

6

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 48: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

CX04 R ELEMENT OF WITH OVERBARCX05 R SMALL ELEMENT OF WITH OVERBARCX06 R ELEMENT OF WITH UNDERBARCX0C R ELEMENT OF WITH TWO HORIZONTAL STROKESCX0E R CONTAINS WITH LONG HORIZONTAL STROKECX0F R CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX10 R SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKECX11 R CONTAINS WITH OVERBARCX12 R SMALL CONTAINS WITH OVERBARCX17 R Z NOTATION BAG MEMBERSHIPCX18 L N-ARY CIRCLED DOT OPERATOR

rarr 2299 circled dot operatorCX19 L N-ARY CIRCLED PLUS OPERATOR

rarr 2295 circled plusCX1A L N-ARY CIRCLED TIMES OPERATOR

rarr 2297 circled timesCX1B L N-ARY UNION OPERATOR WITH DOTCX1C L N-ARY UNION OPERATOR WITH PLUS

rarr 228E multiset unionCX1D L N-ARY SQUARE INTERSECTION OPERATOR

rarr 2293 square capCX1E L N-ARY SQUARE UNION OPERATOR

rarr 2294 square cupCX1F L TWO LOGICAL AND OPERATOR

= mergerarr CX76 two intersecting logical and

CX20 L TWO LOGICAL OR OPERATORrarr CX77 two intersecting logical or

CX21 L N-ARY TIMES OPERATORCX22 L MODULO TWO SUMCX23 L SUMMATION WITH INTEGRALCX24 L QUADRUPLE INTEGRAL OPERATOR

[composed U+222B + U+222B + U+222B + U+222B]CX25 L FINITE PART INTEGRALCX26 L INTEGRAL WITH DOUBLE STROKECX27 L INTEGRAL AVERAGE WITH SLASHCX28 L CIRCULATION FUNCTIONCX29 L ANTICLOCKWISE INTEGRATIONCX2A L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLECX2B L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLECX2C L LINE INTEGRATION NOT INCLUDING THE POLECX2D L INTEGRAL AROUND A POINT OPERATORCX2E L QUATERNION INTEGRAL OPERATORCX2F L INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOKCX30 L INTEGRAL OVERPRINTED WITH TIMES SIGNCX31 L INTEGRAL OVERPRINTED WITH CAPCX32 L INTEGRAL OVERPRINTED WITH CUPCX33 L UPPER INTEGRAL WITH OVERBARCX34 L LOWER INTEGRAL WITH UNDERBARCX35 L JOIN

= large bowtie (relational database theory)rarr 22C8 BOWTIE

CX36 L LARGE LEFT TRIANGLE OPERATOR relational database theory

7

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 49: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

CX37 L Z NOTATION SCHEMA COMPOSITIONrarr CX5A Z notation relational composition

CX38 L Z NOTATION SCHEMA PIPINGrarr 226B much greater-than

CX39 L Z NOTATION SCHEMA PROJECTIONrarr 21BE upwards harpoon with barb rightwards

CX3A B PLUS SIGN WITH SMALL CIRCLE ABOVECX3B B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVECX3C B PLUS SIGN WITH TILDE ABOVECX3D B PLUS SIGN WITH DOT BELOWCX3E B PLUS SIGN WITH TILDE BELOWCX3F B PLUS SIGN WITH SUBSCRIPT TWO

= nim-additionCX40 B FILLED TRIANGLE WITH PLUSCX41 B MINUS SIGN WITH COMMA ABOVECX42 B MINUS SIGN WITH DOT BELOWCX43 B FALLING DOTS MINUSCX44 B RISING DOTS MINUSCX47 B PLUS SIGN IN LEFT HALF CIRCLECX48 B PLUS SIGN IN RIGHT HALF CIRCLECX49 B VECTOR OR CROSS PRODUCT

rarr 00D7 multiplication signCX4A B MULTIPLICATION SIGN WITH DOT ABOVECX4B B MULTIPLICATION SIGN WITH UNDERBARCX4C B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDCX4D B SMASH PRODUCTCX4E B MULTIPLICATION SIGN IN LEFT HALF CIRCLECX4F B MULTIPLICATION SIGN IN RIGHT HALF CIRCLECX50 B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTCX51 B MULTIPLICATION SIGN IN DOUBLE CIRCLECX52 B CIRCLED DIVISION SIGNCX53 B PLUS IN TRIANGLECX54 B MINUS IN TRIANGLECX55 B MULTIPLICATION SIGN IN TRIANGLECX56 B INTERIOR PRODUCTCX57 B RIGHTHAND INTERIOR PRODUCT

rarr 2319 turned not signCX5A B Z NOTATION RELATIONAL COMPOSITION

rarr CX37 Z notation schema compositionCX5B [removed 2040]CX5C B AMALGAMATION OR COPRODUCT

rarr 2210 n-ary coproductCX5D B INTERSECTION WITH DOTCX5E B UNION WITH MINUS

= Z NOTATION BAG SUBTRACTIONCX5F B UNION WITH OVERBARCX60 B INTERSECTION WITH OVERBARCX61 B INTERSECTION WITH LOGICAL ANDCX62 B UNION WITH LOGICAL ORCX63 B UNION ABOVE INTERSECTIONCX64 B INTERSECTION ABOVE UNIONCX65 B UNION ABOVE BAR ABOVE INTERSECTIONCX66 B INTERSECTION ABOVE BAR ABOVE UNIONCX67 B UNION BESIDE AND JOINED WITH UNION

8

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 50: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

CX68 B INTERSECTION BESIDE AND JOINED WITH INTERSECTIONCX6B B CLOSED UNION WITH SERIFSCX6C B CLOSED INTERSECTION WITH SERIFSCX6D B DOUBLE SQUARE INTERSECTIONCX6E B DOUBLE SQUARE UNIONCX71 B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72 B LOGICAL AND WITH DOT ABOVECX73 B LOGICAL OR WITH DOT ABOVECX74 B DOUBLE LOGICAL ANDCX75 B DOUBLE LOGICAL ORCX76 B TWO INTERSECTING LOGICAL AND

rarr CX1F two logical and operatorCX77 B TWO INTERSECTING LOGICAL OR

rarr CX20 two logical or operatorCX78 B SLOPING LARGE ORCX79 B SLOPING LARGE ANDCX7A R LOGICAL OR OVERLAPPING LOGICAL ANDCX7B B LOGICAL AND WITH MIDDLE STEMCX7C B LOGICAL OR WITH MIDDLE STEMCX7D B LOGICAL AND WITH HORIZONTAL DASHCX7E B LOGICAL OR WITH HORIZONTAL DASHCX7F B LOGICAL AND WITH DOUBLE OVERBAR

rarr 2306 perspectiveCX80 B LOGICAL AND WITH UNDERBARCX81 B LOGICAL AND WITH DOUBLE UNDERBAR

rarr 2259 estimatesCX82 B SMALL VEE WITH UNDERBARCX83 B LOGICAL OR WITH DOUBLE OVERBARCX84 B LOGICAL OR WITH DOUBLE UNDERBAR

rarr 225A equiangular toCX85 B Z NOTATION DOMAIN ANTIRESTRICTIONCX86 B Z NOTATION RANGE ANTIRESTRICTIONCX87 R EQUAL SIGN WITH DOT BELOWCX8B R IDENTICAL WITH DOT ABOVECX8D R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE

= identical and parallel toCX8E R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92 R TILDE OPERATOR WITH DOTCX94 R TILDE OPERATOR WITH RISING DOTS

rarr 223B homotheticCX97 R SIMILAR MINUS SIMILARCX9E R CONGRUENT WITH OVERDOTCXA0 R REVERSED CONGRUENTCXA1 R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2 R APPROXIMATELY EQUAL OR EQUAL TOCXA6 B EQUAL ABOVE PLUSCXA7 B PLUS ABOVE EQUALCXA8 R EQUAL ABOVE TILDE OPERATORCXA9 R DOUBLE COLON EQUALCXAA R TWO CONSECUTIVE EQUAL SIGNSCXAB R THREE CONSECUTIVE EQUAL SIGNSCXAC R EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXAD R EQUIVALENT WITH FOUR DOTS ABOVECXAE R LESS-THAN WITH CIRCLE INSIDE

9

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 51: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

CXAF R GREATER-THAN WITH CIRCLE INSIDECXB0 R LESS-THAN WITH QUESTION MARK ABOVECXB1 R GREATER-THAN WITH QUESTION MARK ABOVECXB2 R LESS-THAN OR SLANTED EQUAL TOCXB3 R GREATER-THAN OR SLANTED EQUAL TOCXB4 R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB5 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDECXB6 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB7 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVECXB8 R LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTCXB9 R GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTCXBC R LESS-THAN OR APPROXIMATECXBD R GREATER-THAN OR APPROXIMATECXBE R LESS-THAN AND NOT ONE-LINE EQUAL TOCXBF R GREATER-THAN AND NOT ONE-LINE EQUAL TOCXC2 R LESS-THAN AND NOT APPROXIMATECXC3 R GREATER-THAN AND NOT APPROXIMATECXD2 R LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THANCXD3 R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THANCXD4 R LESS-THAN ABOVE SIMILAR OR EQUALCXD5 R GREATER-THAN ABOVE SIMILAR OR EQUALCXD6 R LESS-THAN ABOVE SIMILAR ABOVE GREATER-THANCXD7 R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THANCXD8 R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALCXD9 R GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALCXDA R LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALCXDB R GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALCXDE R SLANTED EQUAL TO OR LESS-THANCXDF R SLANTED EQUAL TO OR GREATER-THANCXE4 R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDECXE5 R SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDECXE6 R TWO-LINE EQUAL TO OR LESS-THANCXE7 R TWO-LINE EQUAL TO OR GREATER-THANCXE8 R TWO-LINE SLANTED EQUAL TO OR LESS-THANCXE9 R TWO-LINE SLANTED EQUAL TO OR GREATER-THANCXEE R SIMILAR OR LESS-THANCXEF R SIMILAR OR GREATER-THANCXF2 R SIMILAR ABOVE LESS-THAN ABOVE EQUALCXF3 R SIMILAR ABOVE GREATER-THAN ABOVE EQUALCXF4 R DOUBLE NESTED LESS-THAN SIGN

= absolute continuityCXF5 R DOUBLE NESTED GREATER-THAN SIGNCXF6 R DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 52: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

The two white and two black squares shown as DXEC DXED DXF0 and DXF1 are meant to form asize-graded sequence with the present Unicode squares 25A0 25A1 25AA and 25AB Ideally thelargest should be just a bit larger than 25A0 (but not as large as 2588) and the smallest justa bit smaller than 25AA (but not quite as small as the dot operator 22C5) These are used adhoc to define various operations with different sizes often indicating the degree of conformity to aparticular notion (Several different geometric shapes are used in this manner the most commonbeing squares and circles)

11

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 53: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

More relations

DX00 R GREATER-THAN OVERLAPPING LESS-THANDX01 R GREATER-THAN BESIDE LESS-THANDX02 R LESS-THAN CLOSED BY CURVEDX03 R GREATER-THAN CLOSED BY CURVEDX04 R LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX05 R GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALDX06 R SMALLER THANDX07 R LARGER THANDX08 R SMALLER THAN OR EQUALDX09 R LARGER THAN OR EQUALDX0E R BUMPY ABOVE TWO-LINE EQUALDX0F R PRECEDES ABOVE ONE-LINE EQUALDX10 R SUCCEEDS ABOVE ONE-LINE EQUALDX11 R PRECEDES ABOVE NOT ONE-LINE EQUALDX12 R SUCCEEDS ABOVE NOT ONE-LINE EQUALDX13 R PRECEDES ABOVE TWO-LINE EQUALDX14 R SUCCEEDS ABOVE TWO-LINE EQUALDX15 R PRECEDES ABOVE NOT TWO-LINE EQUALDX16 R SUCCEEDS ABOVE NOT TWO-LINE EQUALDX17 R PRECEDES ABOVE DOUBLE TILDE OPERATORDX18 R SUCCEEDS ABOVE DOUBLE TILDE OPERATORDX19 R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORDX1A R SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATORDX25 R DOUBLE PRECEDESDX26 R DOUBLE SUCCEEDSDX29 R SUBSET WITH DOTDX2A R SUPERSET WITH DOTDX2B R SUBSET WITH PLUS BELOWDX2C R SUPERSET WITH PLUS BELOWDX2D R SUBSET WITH MULTIPLICATION SIGN BELOWDX2E R SUPERSET WITH MULTIPLICATION SIGN BELOWDX31 R SUBSET OF OR EQUAL TO WITH DOT ABOVEDX32 R SUPERSET OF OR EQUAL TO WITH DOT ABOVEDX33 R SUBSET OF OR TWO-LINE EQUALDX34 R SUPERSET OF OR TWO-LINE EQUALDX35 R SUBSET OF ABOVE TILDE OPERATORDX36 R SUPERSET OF ABOVE TILDE OPERATORDX37 R SUBSET OF ABOVE DOUBLE TILDE OPERATORDX38 R SUPERSET OF ABOVE DOUBLE TILDE OPERATORDX3B R SUBSET OF OR NOT TWO-LINE EQUALDX3C R SUPERSET OF OR NOT TWO-LINE EQUALDX45 R SQUARE LEFT OPEN BOX OPERATORDX46 R SQUARE RIGHT OPEN BOX OPERATORDX47 R CLOSED SUBSETDX48 R CLOSED SUPERSETDX49 R CLOSED SUBSET OR EQUALDX4A R CLOSED SUPERSET OR EQUALDX4B R SUBSET ABOVE SUPERSETDX4C R SUPERSET ABOVE SUBSETDX4D R SUBSET ABOVE SUBSETDX4E R SUPERSET ABOVE SUPERSETDX4F R SUPERSET BESIDE SUBSET

12

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 54: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

DX50 R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETDX51 R ELEMENT OF OPENING DOWNWARDSDX52 R PITCHFORK WITH TEE TOPDX53 R TRANSVERSAL INTERSECTION

rarr 22D4 proper intersectionDX54 R FORKING

symbol is slashed although positiveDX55 R NONFORKING

negative symbol - has no slashDX56 R SHORT LEFT TACKDX57 R SHORT DOWN TACKDX58 R SHORT UP TACKDX59 R PERPENDICULAR WITH SDX5A R VERTICAL BAR TRIPLE RIGHT TURNSTILE

= ordinarily satisfiesDX5B R DOUBLE VERTICAL BAR LEFT TURNSTILEDX5C R VERTICAL BAR DOUBLE LEFT TURNSTILEDX5D R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILEDX5E R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL

rarr 22A9 forcesDX61 R SHORT DOWN TACK WITH OVERBAR

rarr 22A4 down tackrarr 2351 apl functional symbol up tack overbar

DX62 R SHORT UP TACK WITH UNDERBARrarr 22A5 up tackrarr 234A apl functional symbol down tack underbar

DX63 R SHORT UP TACK ABOVE SHORT DOWN TACKDX64 R DOUBLE DOWN TACKDX65 R DOUBLE UP TACK

= independence (probability theory)DX66 R NOT WITH TWO HORIZONTAL STROKESDX67 R REVERSED NOT WITH TWO HORIZONTAL STROKESDX68 F TRIPLE VERTICAL BAR DELIMITER

rarr DX8B triple vertical bar binary relationDX69 F Z NOTATION SPOT

medium-sized filled circleDX6A F Z NOTATION TYPE COLONDX6B O LEFT WHITE BRACEDX6C C RIGHT WHITE BRACEDX6D O LEFT WHITE ANGULAR BRACKET

rarr 3108 left white tortoise shell bracketDX6E C RIGHT WHITE ANGULAR BRACKET

rarr 3109 right white tortoise shell bracketDX6F O Z NOTATION LEFT IMAGE BRACKETDX70 C Z NOTATION RIGHT IMAGE BRACKETDX71 O Z NOTATION LEFT BINDING BRACKETDX72 C Z NOTATION RIGHT BINDING BRACKETDX73 O LEFT BRACKET UNDERBARDX74 C RIGHT BRACKET UNDERBARDX75 O LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERDX76 C RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERDX77 O LEFT BRACKET WITH SOLIDUS BOTTOM CORNERDX78 C RIGHT BRACKET WITH SOLIDUS TOP CORNERDX79 O LEFT ANGLE BRACKET WITH DOT

13

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 55: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

DX7A C RIGHT ANGLE BRACKET WITH DOTDX7B O LEFT ARC LESS-THAN BRACKETDX7C C RIGHT ARC GREATER-THAN BRACKETDX7D DOUBLE LEFT ARC GREATER-THAN BRACKETDX7E DOUBLE RIGHT ARC LESS-THAN BRACKETDX7F RIGHT MOUSTACHEDX80 LEFT MOUSTACHEDX81 [removed AX25]DX82 [removed AX26]DX83 R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHDX84 R CIRCLE WITH VERTICAL LINE BELOWDX85 R VERTICAL LINE WITH CIRCLE BELOWDX86 N TOP WITH CIRCLE BELOWDX87 B PARALLEL WITH HORIZONTAL STROKEDX88 R PARALLEL WITH OVERPRINTED TILDE OPERATORDX89 [removed]DX8A [removed]DX8B B TRIPLE VERTICAL BAR BINARY RELATION

= interleaverarr DX68 triple vertical bar delimiter

DX8C [removed]DX8D B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKEDX8E [removed 2506]DX8F B TRIPLE COLON

logicDX90 F DOTTED FENCE

four close dots verticalDX91 VERTICAL ZIG-ZAG LINEDX92 MEASURED ANGLE OPENING LEFTDX93 RIGHT ANGLE VARIANT WITH SQUAREDX94 MEASURED RIGHT ANGLE WITH DOTDX95 ANGLE WITH S INSIDEDX96 ACUTE ANGLEDX97 SPHERICAL ANGLE OPENING LEFTDX98 SPHERICAL ANGLE OPENING UPDX99 TURNED ANGLEDX9A REVERSED ANGLEDX9B ANGLE WITH UNDERBARDX9C REVERSED ANGLE WITH UNDERBARDX9D [removed]DX9E LARGE DOWNWARDS POINTING ANGLEDX9F LARGE UPWARDS POINTING ANGLEDXA0 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTDXA1 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFTDXA2 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTDXA3 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFTDXA4 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UPDXA5 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UPDXA6 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNDXA7 MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWNDXA8 [removed 2205]DXA9 N REVERSED EMPTY SET

rarr 2349 APL functional symbol circle backslashDXAA N EMPTY SET OVERBAR

14

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 56: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

DXAB N EMPTY SET WITH SMALL CIRCLE ABOVEDXAC N EMPTY SET RIGHT ARROW ABOVEDXAD N EMPTY SET LEFT ARROW ABOVEDXAE CIRCLE WITH HORIZONTAL BARDXB0 B CIRCLED VERTICAL BARDXB1 B CIRCLED PARALLELDXB2 B CIRCLED FALLING DIAGONALDXB3 B CIRCLED PERPENDICULARDXB4 CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICALDXB5 CIRCLE WITH SUPERIMPOSED XDXB6 CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNDXB7 UP ARROW THROUGH CIRCLEDXB8 CIRCLED LARGE CIRCLE

rarr 233E APL functional symbol circle jotDXB9 CIRCLED FILLED CIRCLEDXBA CIRCLED LESS-THANDXBB CIRCLED GREATER-THANDXBC CIRCLE WITH SMALL CIRCLE TO THE RIGHTDXBD CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTDXBE SQUARED RISING DIAGONAL SLASH

rarr 2341 APL functional symbol quad slashDXBF SQUARED FALLING DIAGONAL SLASH

rarr 2342 APL functional symbol quad backslashDXC0 SQUARED ASTERISKDXC1 SQUARED SMALL CIRCLE

rarr 233B APL functional symbol quad circleDXC2 B SQUARED SQUAREDXC3 TWO JOINED SQUARESDXC4 TRIANGLE WITH DOT OVERDXC5 TRIANGLE WITH UNDERBARDXC6 S IN TRIANGLEDXC7 B TRIANGLE WITH SERIFS AT BOTTOMDXCA R RIGHT TRIANGLE ABOVE LEFT TRIANGLEDXCB R LEFT TRIANGLE BESIDE VERTICAL BARDXCC R VERTICAL BAR BESIDE RIGHT TRIANGLEDXCF R LEFT FILLED BOWTIEDXD0 R RIGHT FILLED BOWTIEDXD1 R FILLED BOWTIEDXD2 R LEFT FILLED TIMES

rarr 22C9 left normal factor semidirect productDXD3 R RIGHT FILLED TIMES

rarr 22CA right normal factor semidirect productDXD4 WHITE HOURGLASS

vertical bowtieDXD5 FILLED HOURGLASSDXD6 MOST POSITIVEDXD7 CONGRUENCE SIGN WITH LAZY SDXD8 REVERSED MOST POSITIVE WITH LINE BELOWDXD9 MOST POSITIVE WITH TWO LINES BELOWDXDA [removed 221D]DXDB N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTEDDXDC N TIE OVER INFINITYDXDD N INFINITY NEGATED WITH VERTICAL BARDXDE R DOUBLE-ENDED MULTIMAP

15

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 57: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Math Symbols 2000-03-14

DXDF N SQUARE WITH CONTOURED OUTLINE= DrsquoAlembertian

DXE0 R INCREASES ASDXE1 SHUFFLE PRODUCTDXE2 R SLANTED PARALLEL SUPERIMPOSED ON EQUAL

= homothetically congruent toDXE3 R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALDXE4 R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL

= congruent and parallelDXE5 R TOP ARC ABOVE BOTTOM ARCDXE6 N THERMODYNAMIC

vertical bar crossed by two horizontalsDXE7 N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKDXE8 N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKDXE9 UPPER LEFT TRIANGLEDXEA UPPER RIGHT TRIANGLEDXEB LOWER LEFT TRIANGLEDXEC N WHITE MEDIUM SQUAREDXED N BLACK MEDIUM SQUAREDXEE [removed]DXEF [removed]DXF0 N WHITE VERY SMALL SQUAREDXF1 N BLACK VERY SMALL SQUAREDXF2 N WHITE DIAMOND WITH CENTERED DOTDXF3 N FILLED DIAMOND WITH DOWN ARROWDXF4 FILLED LOZENGEDXF5 [removed]DXF6 [removed 2736]DXF7 N CIRCLE WITH DOWN ARROWDXF8 N FILLED CIRCLE WITH DOWN ARROWDXF9 N ERROR-BARRED WHITE SQUAREDXFA N ERROR-BARRED FILLED SQUAREDXFB N ERROR-BARRED WHITE DIAMONDDXFC N ERROR-BARRED FILLED DIAMONDDXFD N ERROR-BARRED WHITE CIRCLEDXFE N ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 58: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

Symbol variants defined using a Variation Selector (VS)

bull 2268 + VS rarr less-than and not double equal - with vertical strokebull 2269 + VS rarr greater-than and not double equal - with vertical stroke

bull 22DA Q + VS rarr _ less-than above slanted equal above greater-thanbull 22DB R + VS rarr ` greater-than above slanted equal above less-thanbull 2272 + VS rarr ( less-than or similar - following the slant of the lower legbull 2273 amp + VS rarr ) greater-than or similar - following the slant of the lower legbull 2A9D u + VS rarr o similar - following the slant of the upper leg - or less-thanbull 2A9E i + VS rarr p similar - following the slant of the upper leg - or greater-thanbull 2AAC o + VS rarr q smaller than or slanted equalbull 2AAD p + VS rarr r larger than or slanted equal

bull 228A ( + VS rarr subset not equals - variant with stroke through bottom membersbull 228B ) + VS rarr superset not equals - variant with stroke through bottom membersbull 2ACB $ + VS rarr amp subset not two-line equals - variant with stroke through bottom

membersbull 2ACC + VS rarr superset not two-line equals - variant with stroke through bottom

members

bull 2A3B acute + VS rarr sup2 interior product - tall variant with narrow footbull 2A3C micro + VS rarr sup3 righthand interior product - tall variant with narrow foot

bull 2295oplus

+ VS rarr circled plus with white rimbull 2297

otimes+ VS rarr circled times with white rim

bull 229C $ + VS rarr copy equal sign inside and touching a circle

bull 2225 + VS rarr slanted parallelbull + VS + 20E5 rarr slanted parallel with reverse slash

bull 222A cup + VS rarr cup union with serifs bull 2229 cap + VS rarr cap intersection with serifs bull 2293 u + VS rarr u square intersection with serifs bull 2294 t + VS rarr t square union with serifs

Notes

The shape is incorrect owing to unavailability of a suitable font the correct shape will beprovided as soon as possible The associated text correctly describes the desired shape

1

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References
Page 59: ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION … · 2000-03-19 · Math Symbols 2000-03-14 1 ISO INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE

March 15 2000

Mr Mike Ksar1501 Page Mill RoadMS 5ULPalo Alto CA 94304

Dear Mr Ksar

The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions variables operations and other mathematical objects that comprisethe language of mathematics This presents an especially subtle problem because two differentstyles of the same letter or symbol can have completely different meanings Thus it is veryimportant to the community that there is a universally accepted standard encoding for the variousstyles of letters and symbols it uses in its publications If multiple versions of these were beingused in the literature rather than a universally accepted version it would significantly complicatethe communication between researchers especially in the Web environment

It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alphanumeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance Now that this has been accomplished we hopevery much that they will be accepted by WG2

Sincerely yours

John Ewing

PO Box 6248 Providence RI 02940-6248 USA

201 Charles Street Providence RI 02904-2294

Phone 401-455-4000 Fax 401-331-3842

wwwamsorg

John Ewing Executive Director

Phone 401-455-4100 Email jheamsorg

  • Introduction
  • Background
  • Rationale
  • Variants
  • Letter-like Symbols
  • Brace Parts
  • Explanation of Conventions in the Annexes
  • References

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