```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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