What is an equivalence class?

This article is about equivalency in mathematics. For equivalency in music, see equivalence class (music).

Congruence is an example of an equivalence relation. The leftmost two triangles are congruent, while the third and fourth triangles are not congruent to any other triangle shown here. Thus, the first two triangles are in the same equivalence class, while the third and fourth triangles are each in their own equivalence class.

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

                              The information is from https://en.wikipedia.org/wiki/Equivalence_class

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