\begin{definition}[Definition:Bijection/Definition 5]
A relation $f \subseteq S \times T$ is a '''bijection''' {{iff}}:
:$(1): \quad$ for each $x \in S$ there exists one and only one $y \in T$ such that $\tuple {x, y} \in f$
:$(2): \quad$ for each $y \in T$ there exists one and only one $x \in S$ such that $\tuple {x, y} \in f$.
\end{definition}