Exercise 5, § 6

If E is an infinite set, the set of all permutations of E is equipotent to $\mathfrak{P}(E)$. (Use Proposition 3 of no. 4 to show that, for each subset A of E whose complement does not consist of a single element, there exists a permutation $f$ of E such that A is the set of elements of E which are invariant under $f$.)