# 1. Definitions

`// Set A contains elements 1,2 and 3A = {1,2,3}// 2 is an element of A2∈A// 4 is not an element of A4∉A`

# 2. Number Sets

`Naturals    N = {1,2,3,4,...}Integers    Z = {...,-2,-1,0,1,2,...}Rationals   Q = Ratio of 2 integers. example: 1/2Irrationals Q′= Can't be represented as ratios of integersReal        R = Q and Q′Imaginary   I = Everything not in the reals. Ex: (√x = -1)Complex     C = Reals and imaginaries`

# 3. Set Equality

The order and repetition of elements does not matter

`A = {1,2,3}B = {2,3,2,2,3,1,2,3,2,1,1,2,3,2,2,3,1,1,3,2,1}A = B`

# 4. Set Builder Notation

`A = {1,2,3,4,5,6,7,8,9}// B is equal to all elements of A (x∈A), such that (|), // the elements are less than 5 (x<5)B = { x∈A | x<5 }B = {1,2,3,4}`

# 5. Types of Sets

`Universal           U            Empty               {} or ϕFiniteInfiniteSubset`

# 6. Cardinality

The number of distinct elements in a set.

`n(A) or |A|`

# 7. Equivalence

Sets are equivalent when their cardinality is the same. NOT to be mistaken with equality.

`A = {1,2,3,4}B = {5,6,7,8}// A and B are equivalentA~B`

# 8. Subsets

Subsets: ⊆

Proper subsets: ⊂

`A = {1,2,3,4}B = {2,3}// A is a subset of A, but not a PROPER subset of A// ⊆A⊆A// B is a proper subset of AB⊂A`

# 9. Power Sets

A power set P(A) is the set of all of the subsets of A.

`A    = {1,2,3}P(A) = {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}`