of 13
8/9/2019 history of zero.docx
1/13
0 (number)
0(zero; BrE: /z r/ or AmE: /ziro/) is both a number [1]and the numerical digit
used to reresent that number in numerals! "t #ul$lls a central role in mathematics
as the additi%e identit&o# the integers' real numbers' and man& other algebraic
structures! As a digit' is used as a laceholder in lace %alue s&stems! ames #orthe number in Englishinclude zero' noughtor (*+) naught(/nt/)' nil' or , in
conte-ts .here at least one adacent digit distinguishes it #rom the letter 00 , oh
or o(/o/)! "n#ormal or slang terms #or zero include zilchand zip![2]Oughtor aught
(/t/) has also been used historicall&![3]
Contents
1 Et&molog&
2 4istor&
o 2!1 Eg&t
o 2!2 5esootamia
o 2!3 "ndia
o 2!6 7ambodia
o 2!8 7hina
o 2!9 "slamic .orld
o 2! ree 5edie%al Euroe
o 2!? Americas
3 5athematics
o 3!1 Elementar& algebra
o 3!2 ther branches o# mathematics
o 3!3 =elated mathematical terms
6 @h&sics
8 7hemistr&
9 7omuter science
ther $elds
http://en.wikipedia.org/wiki/British_Englishhttp://en.wikipedia.org/wiki/American_Englishhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/0_(number)#cite_note-1http://en.wikipedia.org/wiki/Numerical_digithttp://en.wikipedia.org/wiki/Numeral_systemhttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Additive_identityhttp://en.wikipedia.org/wiki/Integerhttp://en.wikipedia.org/wiki/Real_numberhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Positional_notationhttp://en.wikipedia.org/wiki/Names_for_the_number_0_in_Englishhttp://en.wikipedia.org/wiki/Names_for_the_number_0_in_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/0_(number)#cite_note-2http://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/0_(number)#cite_note-3http://en.wikipedia.org/wiki/0_(number)#Etymologyhttp://en.wikipedia.org/wiki/0_(number)#Historyhttp://en.wikipedia.org/wiki/0_(number)#Egypthttp://en.wikipedia.org/wiki/0_(number)#Mesopotamiahttp://en.wikipedia.org/wiki/0_(number)#Indiahttp://en.wikipedia.org/wiki/0_(number)#Cambodiahttp://en.wikipedia.org/wiki/0_(number)#Chinahttp://en.wikipedia.org/wiki/0_(number)#Islamic_worldhttp://en.wikipedia.org/wiki/0_(number)#Greeks_and_Romanshttp://en.wikipedia.org/wiki/0_(number)#Medieval_Europehttp://en.wikipedia.org/wiki/0_(number)#Americashttp://en.wikipedia.org/wiki/0_(number)#Mathematicshttp://en.wikipedia.org/wiki/0_(number)#Elementary_algebrahttp://en.wikipedia.org/wiki/0_(number)#Other_branches_of_mathematicshttp://en.wikipedia.org/wiki/0_(number)#Related_mathematical_termshttp://en.wikipedia.org/wiki/0_(number)#Physicshttp://en.wikipedia.org/wiki/0_(number)#Chemistryhttp://en.wikipedia.org/wiki/0_(number)#Computer_sciencehttp://en.wikipedia.org/wiki/0_(number)#Other_fieldshttp://en.wikipedia.org/wiki/American_Englishhttp://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/0_(number)#cite_note-1http://en.wikipedia.org/wiki/Numerical_digithttp://en.wikipedia.org/wiki/Numeral_systemhttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Additive_identityhttp://en.wikipedia.org/wiki/Integerhttp://en.wikipedia.org/wiki/Real_numberhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Positional_notationhttp://en.wikipedia.org/wiki/Names_for_the_number_0_in_Englishhttp://en.wikipedia.org/wiki/Names_for_the_number_0_in_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/0_(number)#cite_note-2http://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/0_(number)#cite_note-3http://en.wikipedia.org/wiki/0_(number)#Etymologyhttp://en.wikipedia.org/wiki/0_(number)#Historyhttp://en.wikipedia.org/wiki/0_(number)#Egypthttp://en.wikipedia.org/wiki/0_(number)#Mesopotamiahttp://en.wikipedia.org/wiki/0_(number)#Indiahttp://en.wikipedia.org/wiki/0_(number)#Cambodiahttp://en.wikipedia.org/wiki/0_(number)#Chinahttp://en.wikipedia.org/wiki/0_(number)#Islamic_worldhttp://en.wikipedia.org/wiki/0_(number)#Greeks_and_Romanshttp://en.wikipedia.org/wiki/0_(number)#Medieval_Europehttp://en.wikipedia.org/wiki/0_(number)#Americashttp://en.wikipedia.org/wiki/0_(number)#Mathematicshttp://en.wikipedia.org/wiki/0_(number)#Elementary_algebrahttp://en.wikipedia.org/wiki/0_(number)#Other_branches_of_mathematicshttp://en.wikipedia.org/wiki/0_(number)#Related_mathematical_termshttp://en.wikipedia.org/wiki/0_(number)#Physicshttp://en.wikipedia.org/wiki/0_(number)#Chemistryhttp://en.wikipedia.org/wiki/0_(number)#Computer_sciencehttp://en.wikipedia.org/wiki/0_(number)#Other_fieldshttp://en.wikipedia.org/wiki/British_English8/9/2019 history of zero.docx
2/13
> +&mbols and reresentations
? ear label
1 +ee also
11 otes
12 =e#erences
13 E-ternal lin]are used! +e%eral sorts
ha%e seci$c .ords #or zero' such as nilin #ootball' lovein tennisand a duckin
cric
8/9/2019 history of zero.docx
3/13
History
Egypt
Ancient Eg&tian numerals.ere base 1! he& used hierogl&hs#or the digits and
.ere not ositional! B& 16 B7E' the Eg&tians had a s&mbol #or zero in accounting
te-ts! he s&mbol n#r' meaning beauti#ul' .as also used to indicate the base le%el in
dra.ings o# tombs and &ramids and distances .ere measured relati%e to the base
line as being abo%e or belo. this line![1]
Mesopotamia
B& the middle o# the 2nd millennium B7' the Bab&lonian mathematicshad asohisticated se-agesimalositional numeral s&stem! he lac< o# a ositional %alue
(or zero) .as indicated b& a spacebet.een se-agesimal numerals! B& 3 B7' a
unctuation s&mbol (t.o slanted .edges) .as cooted as a laceholderin the
same Bab&lonian s&stem! "n a tablet unearthed at Lish(dating #rom about B7)'
the scribe BMlbNnalu .rote his zeros .ith three hoo
(3O9)' 6 and 26 (6O9)' loo
8/9/2019 history of zero.docx
4/13
he concet o# zero as a number and not merel& a s&mbol or an emt& sace #or
searation is attributed to "ndia' .here' b& the ?th centur& AP' ractical calculations
.ere carried out using zero' .hich .as treated li AP' "ndian mathematician and astronomer Ar&abhatastated that 0sthVnVt
sthVnaW daRaguXaW s&Vt;0[1?]i!e!' 0#rom lace to lace each is ten times the
receding'0[1?][2].hich is the origin o# the modern decimalbased lace %alue
notation![21][22]
=ules o# Brahmaguta
he rules go%erning the use o# zero aeared #or the $rst time in BrahmagutaFs
boo< $rahmasputha Siddhanta%&he Opening o the 'niverse('[23].ritten in 92> AP!
4ere Brahmaguta considers not onl& zero' but negati%e numbers' and the
algebraic rules #or the elementar& oerations o# arithmetic .ith such numbers! "n
some instances' his rules diKer #rom the modern standard! 4ere are the rules o#
Brahmaguta:[23]
he sum o# zero and a negati%e number is negati%e!
he sum o# zero and a ositi%e number is ositi%e!
he sum o# zero and zero is zero!
he sum o# a ositi%e and a negati%e is their diKerence; or' i# their absolute
%alues are eQual' zero!
A ositi%e or negati%e number .hen di%ided b& zerois a #raction .ith the zero
as denominator!
http://en.wikipedia.org/wiki/0_(number)#cite_note-bourbaki46-12http://en.wikipedia.org/wiki/0_(number)#cite_note-ebcal-13http://en.wikipedia.org/wiki/Pingalahttp://en.wikipedia.org/wiki/Binary_numeral_systemhttp://en.wikipedia.org/wiki/Morse_codehttp://en.wikipedia.org/wiki/0_(number)#cite_note-14http://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81http://en.wikipedia.org/wiki/0_(number)#cite_note-kim-15http://en.wikipedia.org/wiki/Sutrahttp://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/0_(number)#cite_note-kim-15http://en.wikipedia.org/wiki/Positional_notationhttp://en.wikipedia.org/wiki/Lokavibhagahttp://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81http://en.wikipedia.org/wiki/0_(number)#cite_note-16http://en.wikipedia.org/wiki/Glyphhttp://en.wikipedia.org/wiki/Chaturbhuj_Temple_(Orchha)http://en.wikipedia.org/wiki/Gwaliorhttp://en.wikipedia.org/wiki/0_(number)#cite_note-17http://en.wikipedia.org/wiki/0_(number)#cite_note-18http://en.wikipedia.org/wiki/0_(number)#cite_note-multiref1-11http://en.wikipedia.org/wiki/Aryabhatahttp://en.wikipedia.org/wiki/0_(number)#cite_note-Aryab-19http://en.wikipedia.org/wiki/0_(number)#cite_note-Aryab-19http://en.wikipedia.org/wiki/0_(number)#cite_note-20http://en.wikipedia.org/wiki/0_(number)#cite_note-21http://en.wikipedia.org/wiki/0_(number)#cite_note-22http://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Brahmasphutasiddhantahttp://en.wikipedia.org/wiki/0_(number)#cite_note-brahmagupta-23http://en.wikipedia.org/wiki/0_(number)#cite_note-brahmagupta-23http://en.wikipedia.org/wiki/Division_by_zerohttp://en.wikipedia.org/wiki/0_(number)#cite_note-bourbaki46-12http://en.wikipedia.org/wiki/0_(number)#cite_note-ebcal-13http://en.wikipedia.org/wiki/Pingalahttp://en.wikipedia.org/wiki/Binary_numeral_systemhttp://en.wikipedia.org/wiki/Morse_codehttp://en.wikipedia.org/wiki/0_(number)#cite_note-14http://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81http://en.wikipedia.org/wiki/0_(number)#cite_note-kim-15http://en.wikipedia.org/wiki/Sutrahttp://en.wikipedia.org/wiki/Exponentiationhttp://en.wikipedia.org/wiki/0_(number)#cite_note-kim-15http://en.wikipedia.org/wiki/Positional_notationhttp://en.wikipedia.org/wiki/Lokavibhagahttp://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81http://en.wikipedia.org/wiki/0_(number)#cite_note-16http://en.wikipedia.org/wiki/Glyphhttp://en.wikipedia.org/wiki/Chaturbhuj_Temple_(Orchha)http://en.wikipedia.org/wiki/Gwaliorhttp://en.wikipedia.org/wiki/0_(number)#cite_note-17http://en.wikipedia.org/wiki/0_(number)#cite_note-18http://en.wikipedia.org/wiki/0_(number)#cite_note-multiref1-11http://en.wikipedia.org/wiki/Aryabhatahttp://en.wikipedia.org/wiki/0_(number)#cite_note-Aryab-19http://en.wikipedia.org/wiki/0_(number)#cite_note-Aryab-19http://en.wikipedia.org/wiki/0_(number)#cite_note-20http://en.wikipedia.org/wiki/0_(number)#cite_note-21http://en.wikipedia.org/wiki/0_(number)#cite_note-22http://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Brahmasphutasiddhantahttp://en.wikipedia.org/wiki/0_(number)#cite_note-brahmagupta-23http://en.wikipedia.org/wiki/0_(number)#cite_note-brahmagupta-23http://en.wikipedia.org/wiki/Division_by_zero8/9/2019 history of zero.docx
5/13
Yero di%ided b& a negati%e or ositi%e number is either zero or is e-ressed
as a #raction .ith zero as numerator and the $nite Quantit& as denominator!
Yero di%ided b& zero is zero!
"n sa&ing zero di%ided b& zero is zero' Brahmaguta diKers #rom the modern
osition! 5athematicians normall& do not assign a %alue to this' .hereas comuters
and calculators sometimes assign a' .hich means 0not a number!0 5oreo%er'
nonzero ositi%e or negati%e numbers .hen di%ided b& zero are either assigned no
%alue' or a %alue o# unsigned in$nit&' ositi%e in$nit&' or negati%e in$nit&!
Cambodia
he number 98 in Lhmer numerals' #rom the +ambor inscritions in 9>3 AP! he
earliest
8/9/2019 history of zero.docx
6/13
te-t using a round s&mbol #or zero! [2>]7hinese authors had been #amiliar .ith the
idea o# negati%e numbers b& the 4an P&nast&(2nd centur& 7E)' as seen in the &he
-ine hapters on the +athematical )rt'[2?]much earlier than the $#teenth centur&
.hen the& became .ell established in Euroe![2>]
Islamic world
he Arabiclanguage inheritance o# science .as largel& ree
8/9/2019 history of zero.docx
7/13
s&stem other.ise using alhabetic ree< numerals! Because it .as used alone' not
ust as a laceholder' this 4ellenistic zero.as erhas the $rst documented use o#
a num"erzero in the ld orld! 4o.e%er' the ositions .ere usuall& limited to the
#ractional art o# a number (called minutes' seconds' thirds' #ourths' etc!),the&
.ere not used #or the integral art o# a number! "n later B&zantinemanuscrits o#
@tolem&Fs Synta0is +athematica(also
8/9/2019 history of zero.docx
8/13
adding certain things #rom m& o.n understanding and inserting also certain things
#rom the niceties o# EuclidFs geometric art! " ha%e stri%en to comose this boo< in its
entiret& as understandabl& as " could' di%iding it into $#teen chaters! Almost
e%er&thing .hich " ha%e introduced " ha%e disla&ed .ith e-act roo#' in order that
those #urther see 9 8 6 3 2 1!
ith these nine $gures' and .ith the sign !!! an& number ma& be .ritten! [36][38]
4ere Heonardo o# @isa uses the hrase 0sign 0' indicating it is li
8/9/2019 history of zero.docx
9/13
he 5esoamerican Hong 7ount calendarde%eloed in southcentral 5e-ico and
7entral America reQuired the use o# zero as a laceholder .ithin its %igesimal
(base2) ositional numeral s&stem! 5an& diKerent gl&hs' including this artial
Quatre#oil, ,.ere used as a zero s&mbol #or these Hong 7ount dates' the
earliest o# .hich (on +tela 2 at 7hiaa de 7orzo' 7hiaas) has a date o# 39 B7!
[39]
+ince the eight earliest Hong 7ount dates aear outside the 5a&a homeland' [3]it is
assumed that the use o# zero in the Americas redated the 5a&a and .as ossibl&
the in%ention o# the lmecs! 5an& o# the earliest Hong 7ount dates .ere #ound
.ithin the lmec heartland' although the lmec ci%ilization ended b& the 6th
centur& B7' se%eral centuries be#ore the earliest
8/9/2019 history of zero.docx
10/13
he number is neither ositi%e nor negati%e and aears in the middle o# a
number line! "t is neither a rime numbernor a comosite number! "t cannot be
rime because it has an in$nitenumber o# #actorsand cannot be comosite
because it cannot be e-ressed b& multil&ing rime numbers ( must al.a&s be
one o# the #actors)![6]Yero is' ho.e%er' e%en!
he #ollo.ing are some basic (elementar&) rules #or dealing .ith the number !
hese rules al& #or an& real or comle- number0' unless other.ise stated!
Addition:0` J `0J0! hat is' is an identit& element(or neutral
element) .ith resect to addition!
+ubtraction:0 J0and 0J 0!
5ultilication:0 J 0J !
Pi%ision: 0J ' #or nonzero0! But 0is unde$ned' because has no
multilicati%e in%erse(no real number multilied b& roduces 1)' aconseQuence o# the re%ious rule!
E-onentiation:0J 0/0J 1' e-cet that the case0J ma& be le#t unde$ned
in some conte-ts! Cor all ositi%e real0' 0J !
he e-ression ' .hich ma& be obtained in an attemt to determine the limit o# an
e-ression o# the #orm (0)g(0)as a result o# al&ing the limoerator indeendentl&
to both oerands o# the #raction' is a socalled 0indeterminate #orm0! hat does not
siml& mean that the limit sought is necessaril& unde$ned; rather' it means that the
limit o# (0)g(0)' i# it e-ists' must be #ound b& another method' such as lF4italFs rule!
he sum o# numbersis ' and the roduct o# numbersis 1! he #actorial
e%aluates to 1!
$ther branches of mathematics
"n set theor&' is the cardinalit&o# the emt& set: i# one does not ha%e an&
ales' then one has ales! "n #act' in certain a-iomatic de%eloments o#
mathematics #rom set theor&' is defnedto be the emt& set! hen this is
done' the emt& set is the Don eumann cardinal assignment#or a set .ith
no elements' .hich is the emt& set! he cardinalit& #unction' alied to the
emt& set' returns the emt& set as a %alue' thereb& assigning it elements!
Also in set theor&' is the lo.est ordinal number' corresonding to the emt&
set %ie.ed as a .ellordered set!
"n roositional logic' ma& be used to denote the truth %alue#alse!
http://en.wikipedia.org/wiki/Number_linehttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Composite_numberhttp://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Divisorhttp://en.wikipedia.org/wiki/0_(number)#cite_note-40http://en.wikipedia.org/wiki/Parity_(mathematics)http://en.wikipedia.org/wiki/Identity_elementhttp://en.wikipedia.org/wiki/Defined_and_undefinedhttp://en.wikipedia.org/wiki/Multiplicative_inversehttp://en.wikipedia.org/wiki/0_to_the_power_of_0http://en.wikipedia.org/wiki/Limit_of_a_functionhttp://en.wikipedia.org/wiki/Indeterminate_formhttp://en.wikipedia.org/wiki/L'H%C3%B4pital's_rulehttp://en.wikipedia.org/wiki/Empty_sumhttp://en.wikipedia.org/wiki/Empty_producthttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Von_Neumann_cardinal_assignmenthttp://en.wikipedia.org/wiki/Ordinal_numberhttp://en.wikipedia.org/wiki/Well-orderhttp://en.wikipedia.org/wiki/Propositional_calculushttp://en.wikipedia.org/wiki/Truth_valuehttp://en.wikipedia.org/wiki/Number_linehttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Composite_numberhttp://en.wikipedia.org/wiki/Infinityhttp://en.wikipedia.org/wiki/Divisorhttp://en.wikipedia.org/wiki/0_(number)#cite_note-40http://en.wikipedia.org/wiki/Parity_(mathematics)http://en.wikipedia.org/wiki/Identity_elementhttp://en.wikipedia.org/wiki/Defined_and_undefinedhttp://en.wikipedia.org/wiki/Multiplicative_inversehttp://en.wikipedia.org/wiki/0_to_the_power_of_0http://en.wikipedia.org/wiki/Limit_of_a_functionhttp://en.wikipedia.org/wiki/Indeterminate_formhttp://en.wikipedia.org/wiki/L'H%C3%B4pital's_rulehttp://en.wikipedia.org/wiki/Empty_sumhttp://en.wikipedia.org/wiki/Empty_producthttp://en.wikipedia.org/wiki/Factorialhttp://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Cardinalityhttp://en.wikipedia.org/wiki/Definitionhttp://en.wikipedia.org/wiki/Von_Neumann_cardinal_assignmenthttp://en.wikipedia.org/wiki/Ordinal_numberhttp://en.wikipedia.org/wiki/Well-orderhttp://en.wikipedia.org/wiki/Propositional_calculushttp://en.wikipedia.org/wiki/Truth_value8/9/2019 history of zero.docx
11/13
"n abstract algebra' is commonl& used to denote a zero element' .hich is a
neutral element#or addition (i# de$ned on the structure under consideration)
and an absorbing element#or multilication (i# de$ned)!
"n lattice theor&' ma& denote the bottom elemento# a bounded lattice!
"n categor& theor&' is sometimes used to denote an initial obecto# a
categor&!
"n recursion theor&' can be used to denote theuring degreeo# the artial
comutable #unctions!
!elated mathematical terms
A zero o# a #unctionis a oint0in the domain o# the #unction such that (0)
J ! hen there are $nitel& man& zeros these are called the roots o# the
#unction! his is related to zeroso# a holomorhic #unction!
he zero #unction (or zero ma) on a domain is the constant #unction.ith
as its onl& ossible outut %alue' i!e!' the #unction de$ned b& (0) J #or all
0in ! A articular zero #unction is a zero morhismin categor& theor&; e!g!'
a zero ma is the identit& in the additi%e grou o# #unctions! he determinant
on nonin%ertible sQuare matricesis a zero ma!
+e%eral branches o# mathematics ha%e zero elements' .hich generalise
either the roert& `0J0' or the roert& O0J ' or both!
%hysics
he %alue zero la&s a secial role #or man& h&sical Quantities! Cor some
Quantities' the zero le%el is naturall& distinguished #rom all other le%els' .hereas #or
others it is more or less arbitraril& chosen! Cor e-amle' #or an absolute temerature
(as measured in Lel%in) zerois the lo.est ossible %alue (negati%e temeraturesare
de$ned but negati%e temerature s&stems are not actuall& colder)! his is in
contrast to #or e-amle temeratures on the 7elsius scale' .here zero is arbitraril&
de$ned to be at the #reezing ointo# .ater! 5easuring sound intensit& in decibelsor
hons' the zero le%el is arbitraril& set at a re#erence %alue,#or e-amle' at a %alue
#or the threshold o# hearing! "n h&sics' the zerooint energ&is the lo.est ossible
energ& that a Quantum mechanicalh&sical s&stemma& ossess and is the energ&
o# the ground stateo# the s&stem!
Chemistry
Yero has been roosed as the atomic numbero# the theoretical element
tetraneutron! "t has been sho.n that a cluster o# #our neutronsma& be stable
enough to be considered an atomin its o.n right! his .ould create an element
.ith no rotonsand no charge on its nucleus!
http://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Zero_element_(disambiguation)http://en.wikipedia.org/wiki/Identity_elementhttp://en.wikipedia.org/wiki/Absorbing_elementhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Greatest_elementhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Category_theoryhttp://en.wikipedia.org/wiki/Initial_and_terminal_objectshttp://en.wikipedia.org/wiki/Category_(mathematics)http://en.wikipedia.org/wiki/Recursion_theoryhttp://en.wikipedia.org/wiki/Turing_degreehttp://en.wikipedia.org/wiki/Computable_functionhttp://en.wikipedia.org/wiki/Computable_functionhttp://en.wikipedia.org/wiki/Root_of_a_functionhttp://en.wikipedia.org/wiki/Zero_(complex_analysis)http://en.wikipedia.org/wiki/Holomorphic_functionhttp://en.wikipedia.org/wiki/Constant_functionhttp://en.wikipedia.org/wiki/Zero_morphismhttp://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Zero_element_(disambiguation)http://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Absolute_zerohttp://en.wikipedia.org/wiki/Negative_temperaturehttp://en.wikipedia.org/wiki/Melting_pointhttp://en.wikipedia.org/wiki/Decibelhttp://en.wikipedia.org/wiki/Phonhttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Zero-point_energyhttp://en.wikipedia.org/wiki/Quantum_mechanicshttp://en.wikipedia.org/wiki/Physical_systemhttp://en.wikipedia.org/wiki/Stationary_statehttp://en.wikipedia.org/wiki/Atomic_numberhttp://en.wikipedia.org/wiki/Tetraneutronhttp://en.wikipedia.org/wiki/Neutronhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Chemical_elementhttp://en.wikipedia.org/wiki/Protonhttp://en.wikipedia.org/wiki/Atomic_nucleushttp://en.wikipedia.org/wiki/Abstract_algebrahttp://en.wikipedia.org/wiki/Zero_element_(disambiguation)http://en.wikipedia.org/wiki/Identity_elementhttp://en.wikipedia.org/wiki/Absorbing_elementhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Greatest_elementhttp://en.wikipedia.org/wiki/Lattice_(order)http://en.wikipedia.org/wiki/Category_theoryhttp://en.wikipedia.org/wiki/Initial_and_terminal_objectshttp://en.wikipedia.org/wiki/Category_(mathematics)http://en.wikipedia.org/wiki/Recursion_theoryhttp://en.wikipedia.org/wiki/Turing_degreehttp://en.wikipedia.org/wiki/Computable_functionhttp://en.wikipedia.org/wiki/Computable_functionhttp://en.wikipedia.org/wiki/Root_of_a_functionhttp://en.wikipedia.org/wiki/Zero_(complex_analysis)http://en.wikipedia.org/wiki/Holomorphic_functionhttp://en.wikipedia.org/wiki/Constant_functionhttp://en.wikipedia.org/wiki/Zero_morphismhttp://en.wikipedia.org/wiki/Determinanthttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Zero_element_(disambiguation)http://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Absolute_zerohttp://en.wikipedia.org/wiki/Negative_temperaturehttp://en.wikipedia.org/wiki/Melting_pointhttp://en.wikipedia.org/wiki/Decibelhttp://en.wikipedia.org/wiki/Phonhttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Zero-point_energyhttp://en.wikipedia.org/wiki/Quantum_mechanicshttp://en.wikipedia.org/wiki/Physical_systemhttp://en.wikipedia.org/wiki/Stationary_statehttp://en.wikipedia.org/wiki/Atomic_numberhttp://en.wikipedia.org/wiki/Tetraneutronhttp://en.wikipedia.org/wiki/Neutronhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Chemical_elementhttp://en.wikipedia.org/wiki/Protonhttp://en.wikipedia.org/wiki/Atomic_nucleus8/9/2019 history of zero.docx
12/13
As earl& as 1?29' @ro#essor Andreas %on AntrooK coined the term neutronium#or a
conectured #orm o# mattermade u o# neutrons .ith no rotons' .hich he laced
as the chemical element o# atomic number zero at the head o# his ne. %ersion o#
the eriodic table! "t .as subseQuentl& laced as a noble gas in the middle o#
se%eral siral reresentations o# the eriodic s&stem #or classi#&ing the chemical
elements!
Computer science
he most common ractice throughout human histor& has been to start counting at
one' and this is the ractice in earl& classic comuter sciencerogramming
languages such as Cortranand 7BH! 4o.e%er' in the late 1?8s H"+@introduced
zerobased numbering#or arra&s .hile Algol 8>introduced comletel& Ie-ible
basing #or arra& subscrits (allo.ing an& ositi%e' negati%e' or zero integer as base
#or arra& subscrits)' and most subseQuent rogramming languages adoted one or
other o# these ositions! Cor e-amle' the elements o# an arra&are numbered
starting #rom in 7' so that #or an arra& o# nitems the seQuence o# arra& indicesruns #rom to n1! his ermits an arra& elementFs location to be calculated b&
adding the inde- directl& to address o# the arra&' .hereas 1 based languages
recalculate the arra&Fs base address to be the osition one element be#ore the
$rst!
here can be con#usion bet.een and 1 based inde-ing' #or e-amle Ua%aFsUPB7
inde-es arameters #rom 1 althoughUa%aitsel# uses based inde-ing!
"n databases' it is ossible #or a $eld not to ha%e a %alue! "t is then said to ha%e a
null %alue! Cor numeric $elds it is not the %alue zero! Cor te-t $elds this is not blan
