Date: Apr 4, 2013 12:13 PM
Author: William Hughes
Subject: Re: Matheology § 224
On Apr 4, 5:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 4 Apr., 16:01, William Hughes <wpihug...@gmail.com> wrote:

>

<snip>

>

> > If you remove "every finite line"

> > your are removing an infinite thing

> > "an infinite collection of finite things"

>

> If an infinite collection of infinite things exists actually, i.e., IF

> it is not only simple nonsense, to talk about an actually infinite set

> of finite numbers, then I can remove this infinite thing because it

> consists of only all finite things for which induction is valid.

Nope. The fact that the collection contains only things for which

induction is valid, does not mean induction is valid for the

collection.

Induction is not valid for the collection, and you cannot

remove it without changing the union.