  (where \(\Pow(X)\) is the class of subclasses of a class \(X)\) can be surjective; that is, \(F\) cannot be such that every member \(b\) of \(\Pow(X)\) is equal to \(F(a)\) for some element \(a\) of \(X\). This can be phrased “intuitively” as the fact that there are more subsets of \(X\) than elements of \(X\). The proof of this fact is so simple and basic that it is worthwhile giving it here. Consider the following subset of \(X\):