```Date: Jan 12, 2013 5:27 PM
Author: Virgil
Subject: Re: Matheology � 191

In article <9bd988c2-6cab-4e48-b272-f20119401e1e@z8g2000yqo.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 12 Jan., 19:34, Zuhair <zaljo...@gmail.com> wrote:> > On Jan 12, 3:26 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> >> >> >> >> > > On 12 Jan., 12:45, Zuhair <zaljo...@gmail.com> wrote:> >> > > > On Jan 12, 11:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > > > Matheology § 191> >> > > > > The complete infinite Binary Tree can be constructed by first> > > > > constructing all aleph_0 finite paths and then appending to each path> > > > > all aleph_0 finiteley definable tails from 000... to 111...> >> > > > No it cannot be constructed in that manner, simply because it would no> > > > longer be a BINARY tree.> >> > > No? What node or path would be there that is not a node or path of the> > > Binary Tree? This is again an assertion of yours that has no> > > justification, like many you have postes most recently, unfortunately.> >> > Notice also that one can have a COUNTABLE tree (i.e. a tree that has> > countably many paths and nodes) that has finite paths> > indistinguishable from the finite paths of the complete binary tree by> > labeling of their nodes.> > I noticed that already some years ago.> >> > Let me show an example at finite level, take the three level binary> > tree:> >> >     0> >    /  \> >   0   1> >  / \   | \> > 0 1  0 1> >> > I can have the following tree:> >> >        0> >  /  /  | \ \  \> > 0 1  0 0 1 1> >        |  |  |  |> >        0 1 0 1> >> > Hope that helps.> > No, you have not understood. By attaching one or more infinite tails> to every finite path the Binary Tree is not changed in any discernible> way. The path have exactly the nodes that belong to the tree. The only> difference is that infinitely many paths cross each node. But even> that is not really a difference, because it was the case in the> original Binary Tree too. Try to find out what the reason is.Every path in a Complete Infinite Binary Tree can be represented as a binary sequence of successive left child versus right child branchings and every such sequence determines a unique path.And Cantor showed that no sequnce of such infinite binary sequences cannot be complete, thus cannot be countable.And no matter how WM squirms, he cannot make it otherwise.--
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