Axiom of regularity

HomePage | Recent changes | View source | Discuss this page | Page history | Log in |

Printable version | Disclaimers | Privacy policy

In set theory, the axiom of regularity, also known as the axiom of foundation, is that for every set S there is an element a in it which is disjoint from S. Under the axiom of choice, this axiom is equivalent to saying there is no infinite sequence {an} such that ai+1 is a member of ai. Some corollaries are that no set belongs to itself, since otherwise {S} would violate the axiom of regularity.