Axiom of regularity
id:
axiom-of-regularity-172-253320
title:
Axiom of regularity
text:
In mathematics, the axiom of regularity is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads:
- ∀ x. The axiom of regularity together with the axiom of pairing implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice, this result can be reversed: if there are no such infin
brand slug:
wiki
category slug:
encyclopedia
description:
Axiom of set theory
original url:
https://en.wikipedia.org/wiki/Axiom_of_regularity
date created:
2001-09-30T12:00:52Z
date modified:
2024-09-01T17:56:43Z
main entity:
{"identifier":"Q470981","url":"https://www.wikidata.org/entity/Q470981"}
image:
fields total:
13
integrity:
15