Definition:Invariant Mapping Under Equivalence Relation
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Definition
Let $S$ and $T$ be sets.
Let $\RR$ be an equivalence relation on $S$.
Let $f: S \to T$ be a mapping.
Then $f$ is invariant under $\RR$ if and only if:
- $x \mathrel \RR y \implies \map f x = \map f y$