\begin{definition}[Definition:Inverse Mapping/Also defined as]
Let $S$ and $T$ be sets.
Let $f: S \to T$ be an injection.
Then its '''inverse mapping''' is the mapping $g$ such that:
:its domain $\Dom g$ equals the image $\Img f$ of $f$
:$\forall y \in \Img f: \map f {\map g y} = y$
Thus $f$ is seen to be a surjection by tacit use of Restriction of Mapping to Image is Surjection.
{{ProofWiki}} does not endorse this approach, and considers that its use can cause important insight to be missed.
\end{definition}