Definition:Mapping/Definition 1

Definition
Let $S$ and $T$ be sets. A mapping from $S$ to $T$ is a binary relation on $S \times T$ which associates each element of $S$ with exactly one element of $T$.

Also defined as
Some sources do not place emphasis on the uniqueness of the element of $T$ that is being mapped to.

Also see

 * Equivalence of Definitions of Mapping