Date: Apr 4, 2013 5:31 PM
Author: fom
Subject: Re: Matheology § 224

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.