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Axiom Schema of Separation

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Lleu's picture
Joined: Oct 2006
Axiom Schema of Separation

I was studying set theory, and part of it made absolutely no sense to me. It's not exactly AP Calculus related, but I had no idea where else I could find a group of really smart math people.

I understand the Axiom of Abstraction, that for some y, given any x, x is an element of y if and only if phi(x). I see how you get Russel's paradox from that, but then the book I'm using resolves it by saying

For some y, given any x, x is an element of y if and only if x is an element of z and phi(x). Where did the z come from and what is it supposed to be?

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