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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 3:33 AM
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On 25 Dez., 21:59, Virgil <vir...@ligriv.com> wrote:
> In article
> <76daea40-3902-4687-ae1c-53fe5356b...@b11g2000yqh.googlegroups.com>,
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>
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> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 24 Dez., 20:14, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <d85d67ab-aa37-4091-9474-a089288c3...@x10g2000yqx.googlegroups.com>,
>
> > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > On 23 Dez., 21:20, Zuhair <zaljo...@gmail.com> wrote:
>
> > > > > Also the proof of Cantor is actually about uncountability of paths
> > > > > that are distinguishable on finite basis.
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> > > > That is the point!
>
> > > The Cantor argument only deals with distinguishability on a finite basis
> > > (each individual listed entry differs from the "diagonal" at an
> > > "individual finite position") but shows that it can occur infinitely
> > > often
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> > without leaving the finite domain, i.e., the Binary Tree that contains
> > nothing but all finite paths.
>
> Any such tree is incomplete as a binary tree, as it necessarily contains
> paths of all sorts of different lengths (different numbers of nodes or
> numbers of branches), while in a complete infinite binary tree all paths
> are of exactly the same length.
>
I construct the complete Binary Tree, i.e., all its nodes, by
countably many infinite paths, all of same length. Try to find and
identify by nodes only one further path. Then your claim may be
considered by rational and sober thinkers. Everything else may be
considered by drunk tinkers.
Regards, WM
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