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

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: The uncountability infinite binary tree.
Posted: Dec 16, 2012 3:43 AM

On 16 Dez., 07:18, Zuhair <zaljo...@gmail.com> wrote:
> On Dec 16, 12:12 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 15 Dez., 21:27, Zuhair <zaljo...@gmail.com> wrote:
>
> > > On Dec 15, 10:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > What do you mean I appended the sequence 000..., Can you explain that
> > > in details. I mean the full detail of how did you construct this tree
> > > by this appending. How do you prove the the resulting constructed tree
> > > is the infinite binary tree. DETAILS please. At least refer me to an
> > > article that has all the details about that alleged construction if
> > > there is any.

>
> > The finite paths are the following:
> > 0.
> > 0.0
> > 0.1
> > 0.00
> > 0.01
> > 0.10
> > 0.11
> > ...

>
> > Each of these paths now is equipped with an infinite tail 000...
>
> > 0.000...
> > 0.0000...
> > 0.1000...
> > 0.00000...
> > 0.01000...
> > 0.10000...
> > 0.11000...
> > ...

>
> > Some paths appear more than once. Some nodes are constructed more than
> > once. But that does not matter. This set of paths is nevertheless
> > countable.
> > And there is no "diagonal" that *at a finite level n* differs from all
> > paths.

>
> Ok but the resulting construction is not the INFINITE binary tree

Liar! The resulting construction is what you accepted as the complete
infinite Binary Tree CIBT. Should I

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.

You said: This tree has ALL possible binary paths as paths of it.
In other words it is COMPLETE.

> For example the path representing the decimal
> expansion of pi is not among the paths of your constructed tree.

First: pi is not a real number of the unit interval
Second: Every finite initial segment of pi - 3 is in the CIBT.

And even pi - 3 is there because I cheated. I did not use the tails
000... but the tails with the bit-string of pi-3.

>Of
> course the tree you've constructed that way is COUNTABLE, I agree, but
> it is not a complete infinite binary tree, it is not even near.

You are dreaming. But let us play again. I construct a CIBT by using
tails that I do not publish. You have to find out what paths are
missing.

> Now
> even if you add any tail of your choice, I mean suppose you have a
> countable set of tails T of your choice, and you append those tails to
> countably many finite stumps of the infinite binary tree, still the
> resulting construction is countable, but it is not the complete
> infinite binary tree, why because simply and I say simply apply the
> method I've showed you in the head post on your so constructed tree
> and you will recover a path of the complete binary tree that is not
> among the paths of your constructed tree. I showed you that, but you
> keep refusing to understand that part.

If you are really unable to recognize it yourself, then listen to
others like George Greene: The CIBT is complete. It is impossible to
find a digit sequence defined by nodes that is not contained in it.

Regards, WM

Date Subject Author
12/14/12 Zaljohar@gmail.com
12/14/12 Virgil
12/15/12 Zaljohar@gmail.com
12/14/12 William Elliot
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Rupert
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 trj
12/15/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Zaljohar@gmail.com
12/15/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/16/12 Zaljohar@gmail.com
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Zaljohar@gmail.com
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Zaljohar@gmail.com
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Virgil
12/16/12 ross.finlayson@gmail.com
12/16/12 Virgil
12/16/12 Zaljohar@gmail.com
12/16/12 Zaljohar@gmail.com
12/16/12 Virgil
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
12/15/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/15/12 Tanu R.
12/15/12 Virgil
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Virgil
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
12/15/12 Virgil
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Virgil
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
12/15/12 Virgil
12/15/12 Rupert
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 netzweltler
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/15/12 Tanu R.
12/15/12 Zaljohar@gmail.com
12/15/12 Virgil
12/15/12 Tanu R.
12/15/12 namducnguyen
12/15/12 Tanu R.
12/15/12 namducnguyen
12/15/12 Tanu R.
12/16/12 Rupert
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/16/12 ross.finlayson@gmail.com
12/16/12 Rupert
12/16/12 ross.finlayson@gmail.com
12/16/12 Rupert
12/16/12 ross.finlayson@gmail.com
12/16/12 Rupert
12/16/12 ross.finlayson@gmail.com
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 fom
12/17/12 Virgil
12/17/12 Virgil
12/16/12 Virgil
12/16/12 Virgil
12/16/12 m. m. m.
12/16/12 Virgil
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Roland Franzius
12/17/12 Virgil
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
12/17/12 fom
12/16/12 Virgil
12/16/12 m. m. m.
12/16/12 Virgil
12/16/12 m. m. m.
12/16/12 Virgil
12/16/12 ross.finlayson@gmail.com
12/16/12 trj
12/16/12 Zaljohar@gmail.com
12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Virgil
12/16/12 Virgil
12/15/12 Virgil
12/15/12 Tanu R.
12/15/12 Virgil
12/15/12 Virgil
12/15/12 Virgil