```Date: Dec 13, 2012 5:06 PM
Author: Virgil
Subject: Re: On the infinite binary Tree

In article <b7cf8590-2265-4643-8964-5bd97e0bcc39@c14g2000vbd.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 13 Dez., 21:23, Virgil <vir...@ligriv.com> wrote:> > In article> > > > MY Binary Tree contains the paths of real numbers of the unit> > > interval.> >> > Provably not all of them.> > My Binary Tree contains all nodes. {0,1,2,3,4,5,6,7,8,9} contains all decimal digits, but not all strings of them.> We could also use a decimal tree.> That contains all digits at all finite positions. Provably. And it is> constructed by a countable set of decimal paths.Not so!, The set of paths in  decimal tree is no more countable that the set of paths in a binary tree.A set being  countable means, by definition, that one can prove existence of a surjection from N to that set.Whereas for the set of paths of a complete infinite binary, or decimal, tree is provably not surjectible from N, via the Cantor argument.  > >> > > > where is that proof? please show us> >> > > I will it show it to you for all the paths that I used to construct> > > the above tree  and, in addition, for all the paths that you can> > > identify as beeing missing there.> >> > Promises, promises!> > No, I stand by my offer. Tell me which paths you can identify as> missing in the tree that I constructed by countably many infinite> paths. I will show the bijection.Show us your listing and we will show you just as many more that it missed.--
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