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Topic: On the infinite binary Tree
Replies: 64   Last Post: Dec 17, 2012 11:06 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: On the infinite binary Tree
Posted: Dec 13, 2012 7:50 AM

On 13 Dez., 11:42, Zuhair <zaljo...@gmail.com> wrote:
> On Dec 13, 9:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:> > Ah I see, so you are imposing another condition on the definition of a
> > > path,
>
> > No, that is *the* definition of a path in a Binary Tree.
>
> Actually it is not. There is no need at all to stipulate that a path
> must begin by 0. It is a fixed
> definition.

MY Binary Tree contains the paths of real numbers of the unit
interval. Of course a path starts at the root node, And as you wanted
to contradict MY argument concerning the set of real numbers, other
paths would be completely meaningless. You have made a mistake but
don't want to confess it. That's all.
>
> I already showed you that the number of paths in a second degree
> binary tree (or third degree if you want to adop the empty path) IS
> larger than the total number of nodes. And what I mean by paths those
> that can start with 1 or with 0, but with the condition that it must
> be unidirectional. And showed it clearly and I've illustrated each
> path. You have 9 paths (inclusive of the empty path) and only 7 nodes.

Are you are too dishonest, to confess your error? Or do you really not
understand, that your pieces of paths are irrelevant?

> > No. I proved that the number of infinite paths is countable by
> > constructing all nodes of the Binbary Tree by a countable set of
> > infinite paths.

>
> This only means that you can have a bijective function from a
> countable subset of infinite paths of the binary tree to the set of
> all nodes, which everyone already know that this is possible, because
> we all agree that the total number of nodes of the infinite binary
> tree is countable.

There is a bijective function between N and all finite words.
All distinct paths are defined by finite words.
Infinite words and infinite paths cannot be distinguished as I proved
by this complete infinite Binary Tree:

0
0 1
...

What kind of paths did I use to construct it?

> What would be a proof is if you manage to define an injection from the
> set of ALL infinite paths of the binary tree to the set of all nodes
> of the binary tree.
>
> If you managed to do that, the next question is:
>
>  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.

Regards, WM

Date Subject Author
12/12/12 Zaljohar@gmail.com
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 trj
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Virgil
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/14/12 Zaljohar@gmail.com
12/14/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Tanu R.
12/14/12 Virgil
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/12/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/12/12 george
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 george
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Tanu R.
12/14/12 Virgil
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/15/12 Tanu R.
12/14/12 Charlie-Boo
12/14/12 forbisgaryg@gmail.com
12/15/12 ross.finlayson@gmail.com
12/15/12 forbisgaryg@gmail.com
12/15/12 ross.finlayson@gmail.com
12/16/12 forbisgaryg@gmail.com
12/17/12 ross.finlayson@gmail.com
12/16/12 Ciekaw
12/16/12 Virgil