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:
“What exacerbates the strain in the working class is the absence of money to pay for services they need, economic insecurity, poor daycare, and lack of dignity and boredom in each partner’s job. What exacerbates it in upper-middle class is the instability of paid help and the enormous demands of the career system in which both partners become willing believers. But the tug between traditional and egalitarian models of marriage runs from top to bottom of the class ladder.”
—Arlie Hochschild (20th century)