On 04.12.2012 17:37, Shmuel (Seymour J.) Metz wrote: > In<Pine.NEB.firstname.lastname@example.org>, on 12/04/2012 > at 02:01 AM, William Elliot<email@example.com> said: > >> Case |X|< k. Let Y be a set with |Y| = k. >> |Y\X| = k; Y\X and X are disjoint. > > That doesn't work if k is finite. > You are right. But for finite k the situation is trivial.