Equivalence class

Given an equivalence relation $R$ on a set $S$ , the equivalence class of an element $s \in S$ is $\{ t \in S | R(s, t)\}$ .

For example, the relation "equivalence modulo 6" is an equivalence relation on the integers. The equivalence class of 2 under this relation is the set of all those integers which are equivalent to 2, in other words $\{\ldots, -10, -4, 2, 8, 14, \ldots\}$ .

Given an equivalence class $C \subset S$ , an element $c \in C$ is said to be a representative of that equivalence class.

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Equivalence class