```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 analytical property:0.10.110.111 ...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 triangleBut in case of the set above the terms of the sequence are rationalnumbers and the limit 1/9, which is not in the sequence, is a rationalnumber too. So wie have aleph_0 lines but never aleph_0 digits 1 inone line.My construction does nothing else but to cover every 1 in analternative way. Nothing more nothing less. My construction shows thatthere is never a completed infinity aleph_0, neither in the width norin the height.> WM's sloppy thinkingSloppy thinking is not to distinguish between actual and potentialinfinity like matheologians do here and on many other occasions.Regards, WM
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