Date: Dec 4, 2012 4:30 PM
Subject: Re: Matheology � 170
WM <firstname.lastname@example.org> 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
WM's sloppy thinking again has lead him out of mathematics and into