View source for Canonical projection of an equivalence relation

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==Definition==
Let {{M|X}} be a [[set]] and {{M|\sim\subseteq X\times X}} an [[equivalence relation]] on {{M|X}}. Then the [[map]]:
* {{M|\pi:X\rightarrow X/\sim}} given by {{M|\pi:x\mapsto [x]}} (where {{M|[x]}} denotes the [[equivalence class]] of {{M|x}}) is a [[function]].
We call this map the "''canonical projection of the equivalence relation''", sometimes just the "''canonical map of the equivalence relation''" for short.
==References==
<references/>
{{Definition|Elementary Set Theory|Set Theory|Abstract Algebra}}