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

 Messages: [ Previous | Next ]
 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: The uncountability infinite binary tree.
Posted: Dec 16, 2012 4:37 AM

On Dec 16, 11:43 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> 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

The CIBT (complete infinite binary tree) is defined in the following
manner:

CIBT is a Tree
The root node of CIBT is labeled 0
Each node of CIBT has two child nodes each having a different label
from the other
Any node of ClBT receives only ONE label that is either 0 or 1.

The ClBT is COMPLETE, in the sense that all possible binary paths
belong to it. I already said that.

But YOUR construction which is done by appending infinite paths to
countably many finite stumps of the of the ClBT is NOT the CIBT
itself, it is another tree, at best it is a proper substree of the
CIBT, actually it can even be not a subtree of CIBT, however I'll take
that the appending process is respective of the binary structure of
CIBT, so this constructed tree of yours would be as I said just a
PROPER subtree of the CIBT. And the countability of your constructed
tree is not important since it is not the CIBT itself. It is very easy
to show a missing path from your constructed tree that of course
belongs to the CIBT. As I said again and again just apply the diagonal
argument on your so constructed tree and you'll see the missing path.

Can you tell me what is your proof that the tree you've constructed by
the appending process is the CIBT??? try to prove it, and you will see
that you cannot.

All you have done up till now is to provide a blind assertion that the
tree constructed by the appending process is the CIBT itself? I didn't
see any proof of that, you didn't present any? so if you have a proof
of that then show it, so that one can see if it is valid or not?

YOU (and anyone who agree to your claims) is the one who must supply a
proof that the tree constructed by the appending process is the
complete infinite binary tree itself. But do you have such a proof? I
simply think you CANNOT have any. But lets see if you have.

Again, supply the proof that your constructed tree is the CIBT?

Zuhair

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