Date: Dec 13, 2012 7:50 AM Author: mueckenh@rz.fh-augsburg.de Subject: Re: On the infinite binary Tree 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