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:
“The prostitute is the scapegoat for everyone’s sins, and few people care whether she is justly treated or not. Good people have spent thousands of pounds in efforts to reform her, poets have written about her, essayists and orators have made her the subject of some of their most striking rhetoric; perhaps no class of people has been so much abused, and alternatively sentimentalized over as prostitutes have been but one thing they have never yet had, and that is simple legal justice.”
—Alison Neilans. “Justice for the Prostitute—Lady Astor’s Bill,” Equal Rights (September 19, 1925)