Mathematical Notation

Sets

Set: ${ x : P(x) }$

Where $x$ is an element and $P(x)$ is a condition on $x$.

Given That (Rule or Pattern or Condition): "$:$" or "$|$"

Subsets: $\subseteq$

Strict Subset: $\subset$

Element: $\in$

Common Sets

Empty Set: $\emptyset$

Natural Numbers: $\mathbb{N}$

Integers: $\mathbb{Z}$

Rational Numbers: $\mathbb{Q}$

Real Numbers: $\mathbb{R}$

Set Operations

Union: $\cup$

Intersection: $\cap$

Cartesian-Product: $\times$

Set Equality:

General

Such That: "s.t."

There Exists: $\exists$

For All: $\forall$

Logic

Proposition: "p" - A statement that is either True or False

Implies: $\Rightarrow$

If and Only if / Equivalent: $\iff$