\begin{definition}[Definition:Left Inverse Mapping]
Let $S, T$ be sets where $S \ne \O$, that is, $S$ is not empty.
Let $f: S \to T$ be a mapping.
Let $g: T \to S$ be a mapping such that:
:$g \circ f = I_S$
where:
:$g \circ f$ denotes the composite mapping $f$ followed by $g$;
:$I_S$ is the identity mapping on $S$.
Then $g: T \to S$ is called '''a left inverse (mapping)'''.
\end{definition}