130. Sets

A set is a collection of distinct elements

Membership

If is a set and is an element of :

If is a set and is not an element of :

Example

Let be the set of real numbers whose cosine is greater than :

Universal Sets and Complements

: universal set (sample space)

Compliment of a set

Key identities:

: the empty set

Subsets

If set is a subset of the set :

This means:

Union

Membership Rule

Intersection

Membership Rule

130.1. Infinite Collection of Sets

Let

Countable Union

Countable Intersection

Set properties