1. Sets of Numbers Unions, Intersections, and Venn Diagrams

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.

3. Intersection and Union of Sets
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

4. Natural Numbers
The natural numbers make up the set of all counting numbers.
Which of the following are natural numbers? -7 28
6.2
infinity
braces indicate set
etc.

5. Whole Numbers
The whole numbers make up the set of natural numbers, plus zero.
Which of the following are whole numbers? 13 -3
2/3
6,127

6. Integers
The integers are made up of the whole numbers and the negatives of all the natural numbers.
Which of the following are integers?
5.2 5 -2
2/5

7. 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?
2/7
-12
0/5
.137
-.64

8. Fractions Containing Zero
0/number = 0
Try in Calculator
number/0 = undefined
Try in Calculator

9. 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? … …
.378 √2 π

10. Intersection and Union of Sets
Venn Diagram
A diagram used to depict collections of sets and represent their relationships. A B

11. 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

12. Finding the Intersection of Two Sets
Set-builder Notation
Find A B 4 5 1 9 3 2 7

13. 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