Date: Dec 5, 2012 1:49 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 170

On 4 Dez., 22:30, Virgil <vir...@ligriv.com> wrote:
> In article
> <0aa8193b-9fae-4fdf-83a8-4bc68e25e...@m13g2000vbd.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 4 Dez., 10:04, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <d9d8e2b0-0bda-4a42-a057-c4caa47c3...@r14g2000vbd.googlegroups.com>,

>
> > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > Matheology 170
>
> > > > The infinite triangle formed by the sequence
>
> > > > 0.1
> > > > 0.11
> > > > 0.111
> > > > ...

>
> > > > has height aleph_0 but width less than aleph_0 (because the limit 1/9,
> > > > the first line with aleph_0 digits, does not belong to the triangle).
> > > > This lack of symmetry is disturbing for a physicist.

>
> > > In order to be a mathematically valid triangle, your figure would have
> > > to have a last line, which means that you must be claiming that there is
> > > a largest natural number corresponding to that last line, which is not
> > > only disturbing to real physicists but also to real mathematicians.

>
> > Your objection is tantamount to requiring: In order be a
> > mathematically valid set, the natural numbers would have to have a
> > last number.

>
> Not at all. Sets have no geometrical constraints, triangles do.
> Most sets are not triangles, including the set you describe above.


This set has, like many mathematical entities, a geometrical and an
alytical property:

0.1
0.11
0.111
...
It is a triangle and it is a sequence too.


> > Like every finite initial segment of naturals has a last number every
> > triangle of the sequences has three limiting lines.

>
> On certainly can think of it as a set or sequence of triangles, but a
> set need to be a triangle


But in case of the set above the terms of the sequence are rational
numbers and the limit 1/9, which is not in the sequence, is a rational
number too. So wie have aleph_0 lines but never aleph_0 digits 1 in
one line.

My construction does nothing else but to cover every 1 in an
alternative way. Nothing more nothing less. My construction shows that
there is never a completed infinity aleph_0, neither in the width nor
in the height.

> WM's sloppy thinking

Sloppy thinking is not to distinguish between actual and potential
infinity like matheologians do here and on many other occasions.

Regards, WM