```Date: Jan 13, 2013 5:05 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 190

On 13 Jan., 22:59, Virgil <vir...@ligriv.com> wrote:> In article> <fcbf94db-8b22-4a16-b837-ccd23e176...@k6g2000yqf.googlegroups.com>,>>>>>>  WM <mueck...@rz.fh-augsburg.de> wrote:> > On 13 Jan., 00:26, Virgil <vir...@ligriv.com> wrote:> > > In article> > > <4bffb7f3-9bfa-4dae-9108-da5e24389...@f4g2000yqh.googlegroups.com>,>> > >  WM <mueck...@rz.fh-augsburg.de> wrote:> > > > On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote:> > > > > In article> > > > > <c0615860-6190-4c10-9185-78ed2f6a2...@x10g2000yqx.googlegroups.com>,>> > > > >  WM <mueck...@rz.fh-augsburg.de> wrote:> > > > > > Matheology 190>> > > > > > The Binary Tree can be constructed by aleph_0 finite paths.>> > > > > >         0> > > > > >       1, 2> > > > > >   3, 4, 5, 6> > > > > > 7, ...>> > > > > Finite trees can be built having finitely many finite paths.> > > > > A Complete Infinite Binary Tree cannot be built with only finite paths,> > > > > as none of its paths can be finite.>> > > > Then the complete infinite set |N cannot be built with only finite> > > > initial segments {1, 2, 3, ..., n} and not with ony finite numbers 1,> > > > 2, 3, ...? Like Zuhair you are claiming infinite naturals!>> > > A finite initial segment of |N is not a path in the unary tree |N.>> > > And neither |N  as a unary tree nor any Complete Infinite Binary Tree> > > has any finite paths.>> > >    "A Complete Infinite Binary Tree cannot be built with only> > >    finite paths, as none of its paths can be finite.">> > > Means the same as>> > >    "A Complete Infinite Binary Tree cannot be built HAVING only> > >    finite paths, as none of its paths can be finite.">> > > WM has this CRAZY notion that a path in a COMPLETE INFINITE BINARY TREE> > > can refer to certain finite sets of nodes.>> > > And no one is claiming any infinite naturals, only infinitely many> > > finite naturals.>> > So each n belongs to a finite initial segment (1,2,3,...,n).> > Same is valid for the nodes of the Binary Tree: Each node belongs to a> > finite initial segment of a path, the natural numbers (1,2,3,...,n)> > denoting the levels which the nodes belong to.>> Since every binary path has a node at every "level" (distance from the> root), it can only be represented by an infinite set of naturals in this> way.Irrelevant. Every distance is finite. There is no distance that islarger than every finite distance. All finite distances are countable.Note: There is no natural number larger than every natural number. Andthe number of natural numbers is completely irrelevant in thiscontext.Regards, WMRegards, WM
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