Function

A mathematical object between two sets.

Formally, a function $f$ with the domain $X$ and codomain $Y$ can be encoded as a 3-tuple $(X,Y,G)$ such that:

• $G\subset X\times Y$
• $\mathrm{\forall }x\in X\mathrm{\exists }y\in Y((x,y)\in G)$
• $\mathrm{\forall }(x,y)\in G\mathrm{\forall }(x,y^{\prime })\in G(y=y^{\prime })$

---