\begin{definition}[Definition:Mapping/Definition 3]
Let $S$ and $T$ be sets.
A '''mapping $f$ from $S$ to $T$''', denoted $f: S \to T$, is a relation $f = \struct {S, T, R}$, where $R \subseteq S \times T$, such that:
:$\forall \tuple {x_1, y_1}, \tuple {x_2, y_2} \in f: y_1 \ne y_2 \implies x_1 \ne x_2$
and
:$\forall x \in S: \exists y \in T: \tuple {x, y} \in f$
\end{definition}