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Nathan
Posts:
188
Registered:
12/13/04


Re: Equality and set theory
Posted:
Sep 18, 2006 3:18 PM


agapito6...@aol.com wrote: > The Axiom of Extensionality defines equality of sets. Is there some > axiom in the theory that also defines equality for individuals?
What are "individuals"? In ZFC everything is a set.
> For example if one wants to prove > {x: ~(x=x)} = 0 > one would need something like > Az z=z. Does this belong in set theory or it must be "imported" from > somewhere?
Extensionality takes care of this just fine. If you have ~(x=x) then x has an element y such that y is not an element of x. So the set of all such x is empty.



