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