A function $f$ is a mapping / [[Relation]] between an input [[Set]] ([[Domain]]) to an output [[Set]] ([[Codomain]]). To denote a function that maps the [[Domain]] $X$ to the [[Codomain]] $Y$. $\huge \huge f: X\mapsto Y $ #### Formal A [[Function]] with [[Domain]] $X$ and [[Codomain]] $Y$ is a [[Binary Relation]] $R$ between $X$ and $Y$ that satisfies: - $\forall x\in X$ there exists $\exists y\in Y$ such that $(x, y) \in R$. - If $(x,y)\in R$ and $(x,z)\in R$, then $y=z$.