Date: Dec 4, 2012 4:30 PM
Author: Virgil
Subject: Re: Matheology � 170
In article

<0aa8193b-9fae-4fdf-83a8-4bc68e25e787@m13g2000vbd.googlegroups.com>,

WM <mueckenh@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.

>

> 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 and the limit of a sequence, if it ere ro

exist at all need not be the same thing as the mambers of the sequence

are. For no limit of a strictly increasing sequence of naturals is

natural.

WM's sloppy thinking again has lead him out of mathematics and into

WMytheology.

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