 Cantor’s theorem just proved shows that for any set \(A\), there is a set \(\wp(A)\) which is larger. Cantor’s paradox arises if we try to apply Cantor’s theorem to the set of all sets (or to the universal set, if we suppose (with common sense) that not all objects are sets). If \(V\) is the universal set, then \(\wp(V)\), the power set of the universal set (the set of all sets) must have larger cardinality than \(V\). But clearly no set can be larger in cardinality than the set which contains everything!