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Topic: Equality and set theory
Replies: 7   Last Post: Sep 19, 2006 10:34 AM

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Posts: 188
Registered: 12/13/04
Re: Equality and set theory
Posted: Sep 18, 2006 3:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply 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.

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