# Russell's paradox in ZF theory : Enderton's Elements of set theory : Ch.2

I am reading chapter 2 of Elements of set theory by Herbert Enderton and I have a confusion.

Can we contruct a set from subset axiom of ZF set theory, such that the set of all sets which does not belongs to itself. I think its true ( $\{ x \mid x \text { does not belongs to itself} \}$ ) and if it can be constructed than such a set should exist as we are constructing the set from subset axiom.

But I have also heard that ZF set theory avoids Russell's paradox through its axioms.

Please explain, where am I going wrong. Thanks. Forgive my latex as I am typing this via phone.