17. Generalize exercise 5 and show that if A is a set of any ‘‘cardinality,’’ the power set of A has greater cardinality; that is to say, its elements cannot be put into one-toone correspondence with the elements of A. (Hint: Assume there is such a correspondence, and define f ðaÞ as the 1 : 1 function that connects A and its power set. In other words, f ðaÞ ¼ Aa, the unique subset of A associated with

a. Consider the set A0 ¼ fa j a B Aag. Then there is an a0 A A so that this collection is produced by f ða0Þ; that is, A0 ¼ Aa0 . Show that a0 A Aa0 i¤ a0 B Aa0 .)