Encyclopedia > Axiom of Regularity

  Article Content

Axiom of regularity

Redirected from Axiom of Regularity

In set theory, the axiom of regularity, also known as the axiom of foundation, is that for every non-empty 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 for all i. It follows as a corollary that no set belongs to itself: if the set S were a member of itself, then {S} would violate the axiom of regularity.

External link

http://www.trinity.edu/cbrown/topics_in_logic/sets/sets contains an informative description of the axiom of regularity under the section on Zermelo-Fraenkel set theory.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Islip Terrace, New York

... of 485.1/km² (1,260.4/mi²). The racial makeup of the town is 95.82% White, 0.50% African American, 0.04% Native American, 1.49% Asian, 0.00% Pacific Islander, ...

This page was created in 23.2 ms