Definition:Mapping/Defined

Definition
A mapping $f \subseteq S \times T$ is defined at $x \in S$ :
 * $\exists y \in T: \tuple {x, y} \in f$

If for some $x \in S$, one has:
 * $\forall y \in T: \tuple {x, y} \notin f$

then $f$ is not defined or (undefined) at $x$, and indeed, $f$ is not technically a mapping at all.

Also see

 * Definition:Well-Defined Mapping
 * Definition:Partial Mapping