On 4 Apr., 22:30, Virgil <vir...@ligriv.com> wrote:
> A statement about the members of a set may not be true when referring to > the set itslef. A set of even integers is not itself an even integer.
True. But if all even integers are removed, then nothing remains. Induction is valid for the set of all even integers. Therefore it is possible to remove all of them, if it is pissble to remove 2 and with n also n + 2.
> So an infinite set remains infinite when any one finite subset is > removed from it, but not when EVERY finite subset has been removed from > it as WM's claim implies.
If the set |N is actually infinite, then every finite subset of lines of the set 1 1, 2 1, 2, 3 ... can be removed without changing the infinite union of all finite lines.