Equivalence class

In mathematics, when a set has an equivalence relation defined on its elements, there is a natural grouping of elements that are related to one another, forming what are called equivalence classes. Notationally, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a. It follows from the definition of the equivalence relations that the equivalence classes form a partition of X. The set of equivalence classes is sometimes called the quotient set or the quotient space of X by ~ and is denoted by X / ~.