 Cantor’s paradox is based on an application of Cantor’s theorem. Cantor’s theorem states that given any finite or infinite set \(S\), the power set of \(S\) has strictly larger cardinality (greater size) than \(S\). The theorem is proved by a form of diagonalisation, the same idea underlying Richard’s paradox. Cantor’s paradox considers the set of all sets. Let us call this set the universal set and denote it by \(U\). The power set of \(U\) is denoted \(\wp(U)\). Since \(U\) contains all sets it will in particular contain all elements of \(\wp(U)\). Thus \(\wp(U)\) must be a subset of \(U\) and must thus have a cardinality (size) which is less than or equal to the cardinality of \(U\). However, this immediately contradicts Cantor’s theorem. 