 Note the similarity between this sequence of equivalences and the corresponding sequences of equivalences derived for Russell’s and Grelling’s paradoxes above. Now consider the special case of Cantor’s theorem where \(S\) is the universal set. Then we can simply choose \(f\) to be the identity function, since \(\wp(U)\) must necessarily be a subset of the universal set \(U\). But then \(C\) becomes the Russell set! Thus Cantor’s paradox is nothing more than a slight variant of Russell’s paradox; the core argument leading to the contradiction is the same in both. 