In naive set theory, Russell's paradox shows that the "set" [itex]S:=\{X:X \in X\}[/itex] satisfies the weird property [itex]S \in S[/itex] and [itex]S\notin S[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

How does the set theory of Zermelo and Fraenkel get rid of this "paradox"? I.e., which axioms or theorem prohibit S above to be a set?

Thank you.

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# How does ZF fixes Russell's paradox?

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