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.