\begin{definition}[Definition:Fixed Element of Permutation/Set of Fixed Elements]
Let $S$ be a set.
Let $\pi: S \to S$ be a permutation on $S$.
The set of elements of $S$ which are fixed by $\pi$ can be denoted $\Fix \pi$.
Note that:
:$x \notin S \implies x \in \Fix \pi$
\end{definition}