Discrete Math 1: Set Theory

Cheat Sheet

Photo by Gabby K from Pexels (not actually discrete math)

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

6. Cardinality