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 and an equivalence relation on , the equivalence class of an element in is the subset of all elements in which are equivalent to . It follows from the definition of the equivalence relations that the equivalence classes form a . The set of equivalence classes is sometimes called the quotient set or the quotient space of by and is denoted by .