Definition:Fixed Element of Permutation/Set of Fixed Elements

Definition
Let $S$ be a set.

Let $\pi: S \to S$ be a permutation on $S$.

The set of elements fixed by $\pi$ can be denoted $\operatorname{Fix} \left({\pi}\right)$.

Note that:
 * $x \notin S \implies x \in \operatorname{Fix} \left({\pi}\right)$