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 do not deny that there may be other well-founded causes for the hatred which various classes feel toward politicians, but the main one seems to me that politicians are symbols of the fact that every *class* must take every other *class* into account.”

—José Ortega Y Gasset (1883–1955)