Date: Feb 19, 2013 5:48 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 19 Feb., 02:36, Virgil <> wrote:
> > In article
> > <>,
> >
> >  WM <> wrote:

> > > On 17 Feb., 22:24, Virgil <> wrote:
> > > > In article
> > > > There is, however, a natural larger than any previously given natural.

> >
> > > Nevertheless it is a natural number and therefore finite.
> >
> > but for every one of them there is  successor which is also one of them.

> This is true for the list
> 1
> 12
> 123
> ...
> as well as for its unchanged diagonal.
> You cannot get a diagonal that is longer than every line of the list.

I can get one that is longer than any line you present for comparison
> >
> >
> > But for lines that are not finite there are no FISs equal to those lines.

> For natural numbers that are not finite your statement may be
> relevant. But we can ignore it, since the premise is false.

Only in WOLKENMUEKENHEIM is any such premise false.

In ZF and most of standard mathematics, there is a set which contains {}
and which for each of its members, m, also contains m union {m}.
> >
> >
> > Does WM claim to know of a natural that does NOT have a successor
> > natural?

> No, that is just my argument. There is no last finite line in the
> list. Therefore the diagonal cannot surpass every line.

In order NOT to surpass every line, at least in the world of TND, where
most of us live, there must be a line that it does not surpass,.
> >
> > Unless WM, or someone else, can name a d_n that d cannot not exceed,

> Irrelevant.

Not in the world of TERTIUM NON DATUR.

In our world of TND either there is a specific d_n that d cannot exceed
or d exceeds every d_n, and there is no third alterntive.

If WM does not choose to live in that world, it is his prerogative, but
he has not the power to force anyone who chooses live there to leave it.

And the vast majority of mathematicians live in the world of TND, and do
not choose to leave it for anyplace as shoddy as WOLKENMUEKENHEIM.