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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 3:49 PM

On 16 Dez., 21:34, Rupert <rupertmccal...@yahoo.com> wrote:

>
> It is mathematics. Mathematics includes discourse about uncountable
> sets.

But it does not include discourse using uncountably many characters,
because for that sake infinite strings of bits would be required. By
finite strings of bits only countably many characters could be used.
And if we restrict our conversation to those usable characters and
omit the others, then we discuss in a countable language.

> The fact that it would not be possible for a human to use such a
> language is irrelevant

It would not only be impossible for a human but impossible per se,
because there might be sentences that do never end.

Mathematics may contain many foolish ideas, They can be discussed. But
the language applied to discuss them must be free of foolish items and
must be usable by humans and other intellects. That's the way
mathematics works: It is mainly a discussion with others or with
oneself. Every item (including uncountable sets and inaccessible
cardinals) must have finite definitions. Therefore there is no
uncountable alphabet and there are not uncountably many languages.

And all mathematics that has been done by Cantor can be discussed in
any natural (i.e. countable) language. Further Cantor's diagonal
argument works solely with digits (i.e., nodes). A proof that nobody
can distinguish more than countable many paths in the Binary Tree is a

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
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12/16/12 Zaljohar@gmail.com
12/16/12 Virgil
12/17/12 mueckenh@rz.fh-augsburg.de
12/17/12 Virgil
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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
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12/17/12 Virgil
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12/16/12 Rupert
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12/16/12 Rupert
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12/16/12 Rupert
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12/16/12 Rupert
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12/16/12 Rupert
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12/16/12 mueckenh@rz.fh-augsburg.de
12/16/12 Rupert
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12/16/12 Rupert
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12/16/12 Rupert
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12/17/12 mueckenh@rz.fh-augsburg.de
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12/16/12 Rupert
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12/16/12 Rupert
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12/15/12 Virgil
12/15/12 Tanu R.
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12/15/12 Virgil
12/15/12 Virgil