n. a class the elements of which are all those members of the underlying set that are related to one another by an equivalence relation on it. Since each of the equivalence classes is closed under the equivalence relation, and since two elements belong to the same equivalence class if and only if the relation holds between them, the set of all such classes constitutes a partition of the underlying set. For example, each of the n distinct residue classes modulo n is an equivalence class under congruence mod n; the classes of measurable functions that agree almost everywhere are equivalence classes.