Cantor’s paradox

Cantor's paradox, discovered by Georg Cantor, highlights a contradiction within naive set theory. It arises from the concept of a "set of all sets." If such a set existed, its power set (the set of all its subsets) would, by Cantor's theorem, have a larger cardinality. However, the power set of any set must be a subset of the original set. This leads to a contradiction: the power set is both larger than and a subset of the same set. This paradox, along with Russell's paradox, demonstrated the need for a more rigorous, axiomatic approach to set theory, leading to systems like the Zermelo-Fraenkel axioms.123