Definition:Fixed Element of Permutation
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Let $S$ be a set.
Let $\pi: S \to S$ be a permutation on $S$.
Let $x \in S$.
$x$ is fixed by $\pi$ if and only if:
- $\map \pi x = x$
$x$ moved by $\pi$ if and only if:
- $\map \pi x \ne x$
A fixed element of a permutation is a particular instance of a fixed point.