1. Algebra 1
Section 1.1

2. Definitions Set: a collection of objects
Element or Member: each object in a set
Empty or Null Set: a set with no elements

3. Symbols
Empty set: { } or Ø
Element: 
Not an element: 

4. Definitions
Union of sets: the set of elements that appear in any of the sets
Symbol: 

5. Definitions
Intersection of sets: the set of elements common to all of the sets
Symbol: 

6. Venn Diagram
Represents sets in picture form

7. Venn Diagram
C = {1, 2, 3, 4, 5, 6}
D = {2, 4, 6, 8, 10}

8. Venn Diagram
C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10} C D 1 8 2 3 4 10 5 6

9. Venn Diagram
C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10} C D
C  D 1 8 2 3 4 10 5 6

10. Venn Diagram
C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10} C D
C  D 1 8 2 3 4 10 5 6

11. Definitions
One set is a subset of another set if every element of the first is contained in the second
Symbol: 
A  B: “A is a subset of B” B A

12. Example 2 a. {5, 6}  C b. C  D  C c. Ø  C d. C  C e. 6  D
f. C  D  D
True
False

13. Number Sets Natural Numbers N = {1, 2, 3,...} Whole Numbers

14. Definitions Finite set: the number of elements is a whole number
Infinite set: a set that is not finite

15. Number Sets Natural Numbers N = {1, 2, 3,...} Whole Numbers
Integers
Z = {...-3, -2, -1, 0, 1, 2, 3,...}

16. Number Sets
N  W
N  W  Z

17. Number Sets
Rational numbers are numbers that can be written as a ratio of two integers when the denominator is not equal to zero
Q = a  Z, b  Z, and b  0 a b

18. Number Sets
The set of Irrational numbers, Q (“Q prime”), consists of numbers that cannot be expressed as a ratio of integers

19. Example 3
a. 5
b. 9
c. 6 d
Rational
Irrational

20. Example 3  4 e.
f. 0.16 g
Irrational
Rational

21. Number Sets
The set of Real numbers, R, is the union of the sets of rational (Q) and irrational (Q) numbers
This course deals only with the real number system
N  W  Z  Q

22. Homework:
pp. 5-6