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Topic: The uncountability infinite binary tree.
Replies: 118   Last Post: Dec 17, 2012 8:49 PM

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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Re: The uncountability infinite binary tree.
Posted: Dec 15, 2012 1:53 PM
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On Dec 15, 9:39 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 15 Dez., 19:28, Zuhair <zaljo...@gmail.com> wrote:
>

> > You are the one who is DREAMING. I told you that neither you nor
> > anybody else can construct the complete infinite binary tree by
> > countably many paths, this is just impossible, this is like saying I
> > can draw the circle that is not a circle.

>
> No. I did it several times. Years ago I did it twice before breakfast
> already. And I will show you that my construction does not leave out
> one single node. But before  i tell you my construction try to find a
> path that I did not use in the countably set of all paths that are
> sufficient,
>
>
>

> > I showed you the impossibility of that and yet you are not
> > understanding what is written.

>
> > Take any complete infinite binary tree then if you say it is countable
>
> The set of paths that I used is countable. And you will see it when I
> tell you what I used. But before I unveil my construction let me know
> whether the constructed Binary Tree is complete in your opinion. Here
> it is:
>
>      0.
>   0   1
> 0 1 0 1
> ...
>
> Every level starts with 0, is alternating between 0 an 1, and has
> twice as many nodes as the level above.
>
> Regards, WM


The complete binary tree that I know is a tree that have its root node
labeled by 0.
and for each node of it there is exactly TWO child nodes each having a
different label from the other. And Every node of it is labeled by
exactly ONE label that is either 0 or 1.
It goes like that

0
/ \
0 1
/ \ / \
0 1 0 1
...........
.
.
.

This tree has ALL possible binary paths as paths of it.

In other words it is COMPLETE.

Zuhair



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12/14/12
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Zaljohar@gmail.com
12/14/12
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m. m. m.
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m. m. m.
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Virgil

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