On 4/4/2013 3:56 PM, WM wrote: > 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.
Sets are not defined by the acts of language users.