\begin{definition}[Definition:Generated Submonoid/Generator]
Let $\struct {M, \circ}$ be a monoid
Let $S \subseteq M$.
Let $\struct {H, \circ}$ be the '''submonoid of $\struct {M, \circ}$ generated by $S$'''.
Then $S$ is known as a '''generator''' of $\struct {H, \circ}$.
\end{definition}