\begin{definition}[Definition:Invariant Subset]
Let $S$ be a set.
Let $T \subseteq S$ be a subset of $S$.
Let $f: S \to S$ be a self-map on $S$.
Then $T$ is '''invariant under''' $f$ {{iff}}:
:$\forall t \in T: \map f t \in T$
\end{definition}