Date: Mar 24, 2013 5:08 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 24 Mrz., 01:41, Virgil <vir...@ligriv.com> wrote:

> In article

> <5c674f26-92a7-44ed-b080-692d23ec3...@g4g2000yqd.googlegroups.com>,

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > Do you think it is not a contradiction, to have the statements:

> > 1) 0.111... has more 1's than any finite sequence of 1's.

> > 2) But if we remove all finite sequences of 1's, then nothing remains.

>

> In proper English (1) should read

> "the infinite sequence represented by 0.111... has more 1's in it

> than in any finite sequence of 1's."

You seem to have difficulties when terminology of proper mathematics

is in question. 0.111... is an infinite sequence that represents a

number - it is not only representing an infinite sequence.

>

> And if WM wishes to prevail, he WM must explain how he intends to remove

> all finite sequences of 1's without removing all 1's in the process.

That is simple: All finite sequences like

0.1

0.11

0.111

...

can be removed from 1/9 without ever removing all. So, if 1/9 has a

decimal representation, something must remain, nat least the

counterfactual belief of matheologians.

>

> The fact is that one cannot remove every set containing a natural from a

> family of sets some of which contain that natural of without removing

> that natural from the union of set of remaining sets.

of without removing? Proper English?

>

I proved that every FISON and all its predecessors can be removed from

the matheological union |N of all FISONs without changing this union.

Everybody with a minimum of mathematical knowledge can do so by

himself or can at least understand my proof.

Regards, WM