\begin{definition}[Definition:One-Sided Inverse]
Let $S, T$ be sets where $S \ne \O$, that is, $S$ is not empty.
A '''one-sided inverse (mapping)''' from $S$ to $T$ is a mapping which is either:
:a '''left inverse mapping'''
or:
:a '''right inverse mapping'''
but (specifically) not both.
\end{definition}