Equivalence class
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Definition
Given an Equivalence relation [ilmath]\equiv[/ilmath] the equivalence class of [ilmath]a[/ilmath] is denoted as follows:
[math][a]=\{b|a\equiv b\}[/math]
Equivalence relations partition sets
An equivalence relation is a partition
Equivalence classes are either the same or disjoint
This is the motivation for how cosets partition groups.
TODO: Add proofs and whatnot
