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SETS OF NUMBERSUNIONS, INTERSECTIONS, AND VENN DIAGRAMS
Section 10.2 & 18.2
Symbols and Sets of Numbers
Identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
Find the intersection of two sets.Find the union of two sets.
Intersection and Union of Sets
Set A collection of elements separated by commas and
enclosed in {braces}. {2, 4, 6, 8}
The empty set is the set containing no elements. Represented by the symbol Ø
Natural Numbers
The natural numbers make up the set of all counting numbers.
Which of the following are natural numbers?a. -7b. 0c. 28d. 6.2e. ¾
1,2,3,4,5,...,infinity
braces indicate set etc.
Whole Numbers
The whole numbers make up the set of natural numbers, plus zero.
Which of the following are whole numbers?a. 13b. 0c. -3d. 2/3 e. 6,127
0,1,2,3,4,5,...,
Integers
The integers are made up of the whole numbers and the negatives of all the natural numbers.
Which of the following are integers?a. 5.2b. 5c. -2d. 2/5e. 0
,..., 3, 2, 1,0,1,2,3,...,
Rational Numbers
The rational numbers make up the set of all numbers that can be written as a fraction of integers. In decimal form, rational numbers either terminate or repeat.
Which of the following are rational numbers?a. 2/7b. -12c. 0/5d. .137e. -.64
Fractions Containing Zero
0/number = 0 Try in Calculator
number/0 = undefined Try in Calculator
Irrational Numbers
The irrational numbers are all numbers that cannot be written as a fraction of integers. In decimal form, irrational numbers never terminate or repeat.
Which of the following are irrational numbers?a. .272727…b. 6.01364…c. .378d. √2e. π
Intersection and Union of Sets
Venn Diagram A diagram used to depict collections of sets and
represent their relationships.
Intersection and Union of Sets
Intersection of Two Sets The set containing
only the elements that appear in both sets. Represented by the
symbol .
Union of Two Sets The set containing all
the elements found in either set. Represented by the
symbol .
A B A B
Finding the Intersection of Two Sets
Find
Find
,
If is an odd number greater than 0 and less than 10
and 1,2,3,4
A x x
B
A B
A B
1,3
1,2,3,4,5,7,9
1
3
5
7
94
2
1,3,5,7,9Set-builder Notation
Symbols and Sets of Numbers
Hierarchy of Numbers Natural (Counting)
1, 2, 3, 4, … Whole
0, 1, 2, 3, 4, … Integers
…-3, -2, -1, 0, 1, 2, 3, … Rational Numbers
Any number that can be expressed as a fraction
3, ½, 6.333 Irrational Numbers
Numbers that cannot be expressed as fractions
π, √5 Real Numbers
The set of all rational and all irrational numbers.
mutually exclusive