\begin{definition}[Definition:Mapping/Diagrammatic Presentations]
The following diagram illustrates the mapping $f: S \to T$.
:500px
: $\Dom f$ is the domain of $f$.
: $\Cdm f$ is the codomain of $f$.
: $\Img f$ is the image of $f$.
Note that by Image is Subset of Codomain:
:$\Img f \subseteq \Cdm f$
There are no other such constraints upon the domain, image and codomain.
\end{definition}