1. Set Theory

Basic Definitions

A set is a collection of elements.

There are finite sets, infinite sets, {a | a is an English letter}, empty set

Cardinality = number of elements in a set

$S=\{\{\}\}$ $|S|$ = 1

$S=\{\{\},\{\{\},1\}\}$ $|S|=2$

subset relation $\subseteq$

intersect (when in both) $\cap$

union (when in either) $\cup$

complement $\overline{S},S^c$

The empty set counts as an element within another set, increasing its cardinality