1. Set – collection of objects

2. Element or member – object in a set

3. A = {3, 6, 12, 24}
6 A
8 A

4. Finite set – has a whole number amount of elements

5. Infinite set – cannot count the elements

6. B = {2, 4, 6, 8, …}

7. Empty set – contains no elements
or { } ∅
but NOT { } ∅

8. Disjoint sets – have no members in common

9. C D 6 13 12 5

10. Subset – All members of this set also belong to another set.

11. A C 6 3
C A U 12 24

12. ∅
every set U
A A U

13. Union – set formed by combining two sets

14. D E 6 1 24 3 8 5 10
D U E = {1, 2, 3, 4, 5, 6, 8, 10}

15. Intersection – set of elements which belong to two sets
“∩”

16. D E 6 1 24 3 8 5 10
D ∩ E = {2, 4}

17. 15 15
Real numbers R
5 9 –
5 9 – Q Z
– 41
– 41 W √5 √5
Irrationals N
.72
.72
√16
√16 π π

18. Commutative
a + b = b + a
ab = ba

19. Associative
(a + b) + c = a + (b + c)
(ab)c = a(bc)

20. Identity
a + 0 = a
a • 1 = a

21. Zero
a • 0 = 0

22. Inverse
a + (–a) = –a + a = 0

23. Inverse Property of Multiplication
For any number a ≠ 0, a ( ) = ( a ) = 1.
1 a

24. Reciprocal
Two nonzero numbers are reciprocals, or multiplicative inverses, of one another if their product is one.

25. Inverse Property of Addition and Zero Property of Multiplication
Example 2
Name the property illustrated by the following.
15.3(8 – 8) = 0
Inverse Property of Addition and Zero Property of Multiplication

26. Associative Property of Multiplication
Example 2
Name the property illustrated by the following.
1 2
1 3
2 5
1 2
1 3
2 5 – – – x – =
Associative Property of Multiplication

27. Inverse Property of Addition
Example 2
Name the property illustrated by the following. –
√17
√17
= 0
Inverse Property of Addition

28. Inverse Property of Multiplication
Example 2
Name the property illustrated by the following. 27 72
= 1
Inverse Property of Multiplication

29. Exercise
Can you always find a rational number between any two given rational numbers? How many rational numbers are there?