In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element x in X is the subset of all elements in X which are equivalent to x. Equivalence classes among elements of a structure are often used to produce a smaller structure whose elements are the classes, distilling a relationship every element of the class shares with at least one other element of another class. This is known as modding out by the class. The class may assume the identity of one of the original elements, as when fractions are put in reduced form.
Read more about Equivalence Class: Notation and Formal Definition, Analogy With Division, Examples, Properties, Invariants
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—W. Winwood Reade (1838–1875)