Equivalence Class

up:: Equivalence Relation

Given an Equivalence Relation $\sim$ over a set $X$, an equivalence class is the set of all points equivalent to each other (under $\sim$). We usually denote all equivalence classes by $[x]$, choosing some $x$ inside it to represent it.

Note that All different equivalence classes are disjoint, since having a single point in common would make them both equivalent.