# Discrete Math 1: Set Theory

# 1. Definitions

// Set A contains elements 1,2 and 3

A = {1,2,3}// 2 is an element of A

2∈A// 4 is not an element of A

4∉A

# 2. Number Sets

`Naturals N = {1,2,3,4,...}`

Integers Z = {...,-2,-1,0,1,2,...}

Rationals Q = Ratio of 2 integers. example: 1/2

Irrationals Q′= Can't be represented as ratios of integers

Real 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 ϕ

Finite

Infinite

Subset