Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 25, 2012 3:59 PM
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In article
<76daea40-3902-4687-ae1c-53fe5356b0a3@b11g2000yqh.googlegroups.com>,
WM <mueckenh@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.
> >
> > > 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
>
> 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.
So that WM is WRONG!
AGAIN!!
AS USUAL!!!
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