 Novel with Cantor was the demonstration (1872) that there are infinite sets of different sizes according to this criterion. Cantor’s paradox, for which an original reference is difficult to find, is an immediate corollary of this result. If \(A\) is a set, define the power set of \(A\) as the set of all subsets of \(A: \wp(A) = \{B \mid \forall x(x \in B \rightarrow x \in A)\}\). Cantor proved that there can be no bijection between \(A\) and \(\wp(A)\) for any set \(A\). Suppose that \(f\) is a bijection from \(A\) to \(\wp(A)\). Define \(C\) as \(\{a \in A \mid a \not\in f(a)\}\). Because \(f\) is a bijection there must be \(c\) such that \(f(c) = C\). Now we notice that \(c \in C \leftrightarrow c \not\in f (c) = C\), which is a contradiction.