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Set – collection of objects
Element or member – object
in a set
A = {3, 6, 12, 24}
6
A
8
A
Finite set – has a whole
number amount of
elements
Infinite set – cannot count
the elements
B = {2, 4, 6, 8, …}
Empty set – contains no
elements
∅ or { }
but NOT { ∅ }
Disjoint sets – have no
members in common
C
6
D
13
12
5
Subset – All members of
this set also belong to
another set.
A
C
12
24
C
U
3
6
A
U
∅
every set
U
A
A
Union – set formed by
combining two sets
“U”
D
1
3
5
2
4
E
6
8
10
D U E = {1, 2, 3, 4, 5, 6, 8, 10}
Intersection – set of
elements which belong to
two sets
“∩”
D
1
3
5
2
4
E
6
8
10
D ∩ E = {2, 4}
.72
0
√16
π
Real numbers R
Q
Z
W
N
Irrationals
15
–5
9
– 41
√5
Commutative
a+b=b+a
ab = ba
Associative
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Identity
a+0=a
a•1=a
Zero
a•0=0
Inverse
a + (–a) = –a + a = 0
Inverse Property of
Multiplication
For any number a ≠ 0,
1
1
a ( ) = ( a ) = 1.
a
a
Reciprocal
Two nonzero numbers are
reciprocals, or multiplicative
inverses, of one another if
their product is one.
Example 2
Name the property illustrated
by the following.
15.3(8 – 8) = 0
Inverse Property of Addition
and Zero Property of
Multiplication
Example 2
Name the property illustrated
by the following.
1
1
2
–
–
2 3
5
1
1
= –2x 3
2
–
5
Associative Property of
Multiplication
Example 2
Name the property illustrated
by the following.
– √17 + √17 = 0
Inverse Property of Addition
Example 2
Name the property illustrated
by the following.
2
7
7
=
1
2
Inverse Property of
Multiplication
Exercise
Can you always find a
rational number between any
two given rational numbers?
How many rational numbers
are there?