Equivalence class

Definition

Given an Equivalence relation $\sim$ the equivalence class of $a$ is denoted as follows:

$$[a]=\{b|a\sim b\}$$

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.

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TODO: Add proofs and whatnot

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