Date: Apr 4, 2013 2:30 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 4 Apr., 19:45, William Hughes <wpihug...@gmail.com> wrote:

> On Apr 4, 6:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

>

>

>

>

> > On 4 Apr., 18:13, William Hughes <wpihug...@gmail.com> wrote:

>

> > > 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.

>

> > And you believe that, therefore, always elements must exists which in

> > principle are subject to induction but in fact are not subjected to

> > induction?

>

> Nope, just that you can have a collection where everything in the

> collection

> is subject to induction, but where the collection itself is not

> subject to

> induction.

If the collection is something else than all its elements, then you

may be right. Show this "else". In fact, an actually infinite set must

constitute such a thing that cannot be removed when every finite set

of elements is removed.

>

> You can remove any one thing that is in the collection.

Of course. Consider a colllection of three lements. You can remove

three elements.

> You cannot remove the collection.

Piffle. Tell me what natural number has to remain from three and what

has to remain from all. Your pure claim is not convincing. Claims

without proofs carry little weight in mathematics.

Regards, WM