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