\begin{definition}[Definition:Image (Set Theory)]
The definition of a relation as a subset of the Cartesian product of two sets gives a "static" sort of feel to the concept.
However, we can also consider a relation as being an operation, where you feed an element $s \in S$ (or a subset $S_1 \subseteq S$) in at one end, and you get a set of elements $T_s \subseteq T$ out of the other.
Thus we arrive at the following definition.
== Relation ==
{{:Definition:Image (Set Theory)/Relation}}
== Mapping ==
{{:Definition:Image (Set Theory)/Mapping}}
\end{definition}