\begin{definition}[Definition:Infinite Group]
A group which is not finite is an '''infinite group'''.
That is, an '''infinite group''' is a group of infinite order.
That is, a group $\struct {G, \circ}$ is an '''infinite group''' {{iff}} its underlying set $G$ is infinite.
That is, an '''infinite group''' is a group with an infinite number of elements.
\end{definition}