\begin{definition}[Definition:Finite Semigroup]
A '''finite semigroup''' is a semigroup of finite order.
That is, a semigroup $\struct {S, \circ}$ is a '''finite semigroup''' {{iff}} its underlying set $G$ is finite.
That is, a '''finite semigroup''' is a semigroup with a finite number of elements.
\end{definition}