The Axiom of Regularity is the same as the Axiom of Descent that I mentioned. Perhaps it has become more widely used; when I learned set theory, it was introduced as an additional axiom that need not be included, similar to the Axiom of Choice or Continuum Hypothesis. Franklin T. Adams-Watters -----Original Message----- From: dasimov@earthlink.net Franklin wrote: << The normal axioms of set theory don't require [that a set cannot be a member of itself]. I'm not sure which axioms you're thinking of, but the Axiom of Regularity of Zermelo-Frankel set theory (cf. http://en.wikipedia.org/wiki/Axiom_of_regularity) does indeed imply that no set can be a member of itself. --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ___________________________________________________ Try the New Netscape Mail Today! Virtually Spam-Free | More Storage | Import Your Contact List http://mail.netscape.com