Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Rupert

Posts: 3,806
Registered: 12/6/04
Re: The uncountability infinite binary tree.
Posted: Dec 16, 2012 4:43 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Dec 16, 10:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 16 Dez., 22:01, Rupert <rupertmccal...@yahoo.com> wrote:
>

> > > 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
> > > contradiction of uncountability.

>
> > It's not.
>
> Why then should we be able to distinguish the diagonal from the
> entries of the list?


Suppose that you list all the real numbers that are definable in some
countable language. You must then be working in some metalanguage in
which you can talk about the countable language. The anti-diagonal
number can be defined in this metalanguage.

> Why then do we need the diagonal argument at all?

It is necessary to show that the real numbers are uncountable.

> If we are ready to believe that there are undefinable and
> undistinguishable reals, we need no diagonal argument. We could simply
> believe.


No, the question of whether the real numbers are countable or
uncountable is something which requires a proof one way or the other.
Cantor had to think hard about this question before he got the answer.

> Cantor would be very sad seing that his famous proof is
> completely superfluous.
>


It's not.

> Regards, WM



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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.