Function

$f:A\to B$ A function is a mapping from one set $A$ to another set $B$, such that each element x in the domain of $A$ has exactly one element of the Codomain in set $B$. functions only return one output.

Formal Definition

A Binary Relation, Left Total Relation and Right Unique Relation

Functions With Set Input

• With Set $S$
• Then, $f(S)=\{f(x)|x\in S\}$

Types

• Multi-Variate Function
• Involution
• Bijective
• Surjective
• Injective
• Isomorphic