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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How does ZF fixes Russell's paradox?

**Physics Forums | Science Articles, Homework Help, Discussion**