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

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: The uncountability infinite binary tree.
Posted: Dec 15, 2012 4:12 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

Regards, WM



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12/14/12
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Zaljohar@gmail.com
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12/15/12
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Virgil
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Tanu R.
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12/16/12
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Virgil
12/17/12
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