Defeating Russell's paradox I am not very big in mathematics yet(will be hopefully), naive set theory has a problem with Russell's paradox, how do they defeat this sort of problem in mathematics? Is there a greater form of set theory than naive set theory that beats this problem? (Maybe something like superposition if is both or neither)?

Suppose there exists a set $r$ such that, for any object $x$, $x\in r$ if and only if $x\notin x$. This leads to the obvious contradiction that $r\in r$ if and only if $r\notin r$. Therefore, no such set can exist. This is only a problem if, as in naive set theory, such a set must exist simply because you can define it. So, a consistent set theory cannot allow such a set to exist. The widely used Zermelo-Fraenkel axioms of set theory have been particularly successful in this regard. After over a century of intensive scrutiny, no such contradictions have been shown to arise from these axioms.
