Equivalence Class

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

Famous quotes containing the word class:

    I never feel so conscious of my race as I do when I stand before a class of twenty-five young men and women eager to learn about what it is to be black in America.
    Claire Oberon Garcia, African American college professor. As quoted in the Chronicle of Higher Education, p. B3 (July 27, 1994)