Equivalence class a mathematical concept is a subset of given set induced by an equivalence relation on that given set. (If the given set is empty then the equivalence relation is empty and there are no equivalence classes; otherwise the equivalence relation and its concomitant equivalence classes are all non-empty.) Elements of an equivalence class are said to be equivalent under the equivalence relation to all the other elements of the same equivalence class. For each equivalence relation there is a collection of equivalence classes. Any two different equivalence classes are disjoint and the union over all of the equivalence classes is the given set. Equivalence classes and their corresponding equivalence relation are defined in set theory a vital foundation for mathematics and those fields that use mathematics. More details can be found in a study of equivalence relation.
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