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Topic: Matheology § 246
Replies: 246   Last Post: Apr 26, 2013 2:37 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 246
Posted: Apr 24, 2013 12:40 PM

On 23 Apr., 22:40, Virgil <vir...@ligriv.com> wrote:
> In article
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 23 Apr., 16:35, fom <fomJ...@nyms.net> wrote:
> > > On 4/23/2013 3:59 AM, WM wrote:
>
> > > > 1
> > > > 2, 1
> > > > 3, 2, 1
> > > > ...

>
> > > WM is an unabashed ultrafinitist
>
> > No. There is no largest number.
>
> That's our line!

And there are not aleph_0 natural numbers.
>
> But there are numbers larger than any natural number.
>
> The number of naturals is such a number.

Then this number of numbers must be in all lines without being in one
single line. So it must distributed over at least two lines.

This can be accomplished for |N by two lines like

123 567...
1234 678...

or for (a, b, c) by two or three lines

ab
bc
ac

or by more lines. But we see that at least two elements a, b and two
lines exist, such that there is a line with a and without b and a line
witout a and with b.

> > Every element of the first column is in a line. There is no actually
> > infinite line.

>
> That may be in physics, but does not hold in mathamatics, in which a
> line may be extended beyond every finite point.

In physics we cannot prove anythig like that but just in mathematics
we can prove that it is impossible.

Regards, WM

Date Subject Author
4/12/13 mueckenh@rz.fh-augsburg.de
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4/12/13 JT
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