Set

Definition

A collection of elements where:

• The elements are distinct (distinguishable)
• The order of elements does not matter

Example

Curly braces denote sets

• $S=\{1,2,3,4\}$ is a set of 4 elements $1,2,3,4$
• $A=\{red,blue,green\}$ is a set of 3 elements
• $B=\{\{1,2\},\{3,4\},\{5,6\}\}$ is a set of 3 elements which are all sets An empty set is denoted as $\varnothing$

Set Operators

$A\cup B$ Intersection $A\cap B$ Union $A\setminus B$ Difference $A△B$ Symmetric Difference $\overline{A}$ $A^{\prime }$ Complement

Elementhood

$x\in A$ x is a element of A

$x\notin A$ x is not in A Not In

Concepts

• Set-Builder Notation
• Closed
• Supremum
• Infimum
• Upper Bound
• Lower Bound
• Max
• Min