View source for Class (set theory)

In [[set theory]] and its applications throughout [[mathematics]], a '''class''' is a collection of [[Set (mathematics)|sets]] (or sometimes other [[Mathematical object|mathematical objects]]) that can be unambiguously defined by a property that all its members share.

== Description ==

The precise definition of "class" depends on foundational context.

In work on [[Zermelo–Fraenkel set theory]], the notion of class is informal, whereas other set theories, such as [[Von Neumann–Bernays–Gödel set theory]], axiomatize the notion of "proper class", e.g., as entities that are not members of another entity.

A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class. For instance, the class of all [[Ordinal number|ordinal numbers]], and the class of all sets, are proper classes in many formal systems.

Outside set theory, the word "class" is sometimes used synonymously with "set". This usage dates from a historical period where classes and sets were not distinguished as they are in modern set-theoretic terminology. Many discussions of "classes" in the 19th century and earlier are really referring to sets, or perhaps to a more ambiguous concept.

== See also ==

* [[Set theory]]

== External links ==

* [https://en.wikipedia.org/wiki/Class_(set_theory) Class (set theory)] @ Wikipedia.org 



[[Category:Mathematics]]
[[Category:Set theory]]