The Complex Number System
THREE TYPES OF SETS
1) finite – a set whose elements can be counted.
Example: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} or { x: x  10 and x  N }
2) infinite – a set whose elements cannot be counted.
Example: The Set of Natural Numbers or {1, 2, 3, 4, …}
3) Null (empty) – a set without any members.
 or { } represents the empty or null set, never {}
SUBSETS



Every set except  has at least 2 subsets – itself and .
The null set, , has only one subset – itself.
The null set, , is a subset of every set.
A set with one element has two subsets.
A = {5}
subsets: {5} and 
A set with two elements has four subsets.
B = {1, 2}
subsets: {1}, {2}, {1, 2} and 
A set with three elements had eight subsets. C = {a, b, c} subsets: {a}, {b}, {c}, {a, b}, {a, c}, {b, c},
{a, b, c}and 
A set with n elements has 2n elements.
Set

A
B
C
# of Elements
0
1
2
3
# of Subsets
20 = 1
21 = 2
22 = 4
23 = 8
Remember to use each symbol correctly.
Let Set A = {1, 2, 3, 4, 5}
3 is an element of Set A:
3A
3  A is not a correct statement.
3 is a subset of Set A:
{3}  A
{3}  A is not a correct statement.