Definition:Mapping/Definition 2

Definition
Let $S$ and $T$ be sets. A mapping $f$ from $S$ to $T$, denoted $f: S \to T$, is a relation $f = \struct {S, T, G}$, where $G \subseteq S \times T$, such that:


 * $\forall x \in S: \forall y_1, y_2 \in T: \tuple {x, y_1} \in G \land \tuple {x, y_2} \in G \implies y_1 = y_2$

and
 * $\forall x \in S: \exists y \in T: \tuple {x, y} \in G$

Also see

 * Equivalence of Definitions of Mapping