Cantor's paradox

Cantor's paradox arises from comparing the size of the set of all possible sets (or the "set of all sets") with the set of all its subsets. According to set theory, the power set (set of all subsets) of any set is always larger than the set itself. However, if one considers the "set of all sets" to contain itself, its power set would be even larger, creating a contradiction—implying the set is both itself and larger than itself simultaneously. This paradox highlights limitations in naive notions of "the set of all sets" and underscores the need for careful axiomatic definitions in set theory.