\begin{definition}[Definition:Order of Group Element/Finite/Definition 1]
Let $G$ be a group whose identity is $e_G$.
Let $x \in G$ be an element of $G$.
$x$ '''is of finite order''', or '''has finite order''' {{iff}} there exists $k \in \Z_{> 0}$ such that $x^k = e_G$.
\end{definition}