The solution to russel's paradox is that sets can not contain themselves. There is a carefully crafted set of rules describing what sorts of sets exist, and it

The solution to russel's paradox is that sets can not contain themselves. There is a carefully crafted set of rules describing what sorts of sets exist, and it is designed to avoid paradoxes such as that one. These rules are the ZFC axioms (https://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html https://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html)