\begin{definition}[Definition:Mapping/Defined]
A mapping $f \subseteq S \times T$ is '''defined''' at $x \in S$ {{iff}}:
:$\exists y \in T: \tuple {x, y} \in f$
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.
\end{definition}