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Topic: UNCOUNTABILITY
Replies: 59   Last Post: Dec 24, 2012 2:06 PM

 Messages: [ Previous | Next ]
 William Hughes Posts: 2,330 Registered: 12/7/10
Re: UNCOUNTABILITY
Posted: Dec 22, 2012 4:06 PM

On Dec 22, 8:55 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 22 Dez., 00:34, William Hughes <wpihug...@gmail.com> wrote:
>

> > > Yes it is definable. It has been defined. Nevertheless it does not
> > > exist, because the sets do not exist.

>
> > It is definable which means that WM can use it to prove that the
> > bijection exists, but it does not exist.

>
> The bijection of all finite words with all natural numbers has been
> defined in binary:

However, the bijection you need is all definitons with a subset
of the natural numbers. And there is no way to define this subset.
If you put restrictions on the 0/1 sequences you allow to exist you
put restrictions on the subsets you allow to exist. Note, that
subcountable
does not mean countable.

>
> 0
> 1
> 00
> 01
> 10
> 11
> 000
> and so on.
>
> From this definition the natural number belonging to any desired
> finite word can be obtained. It can easily be translated into any
> other language. Or do you need some help?
>
> Nevertheless there is no set of all natural numbers and no set of all
> infinite words.
>
> It is the same with pi. The (potentially) infinite string of digits of
> pi can be defined. In fact there are (potentially) infinitely many
> definitions. Nevertheless there is no actually infinite string
> expressing pi.
>
> Yes, I know that is not easy to understand. That's why so many
> mathematicians have gone astray.
>
> Regards, WM

Date Subject Author
12/19/12 george
12/20/12 Zaljohar@gmail.com
12/20/12 Barb Knox
12/20/12 ross.finlayson@gmail.com
12/20/12 Zaljohar@gmail.com
12/20/12 ross.finlayson@gmail.com
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/20/12 Graham Cooper
12/20/12 mueckenh@rz.fh-augsburg.de
12/20/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 William Hughes
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/22/12 William Hughes
12/22/12 Graham Cooper
12/23/12 Virgil
12/23/12 William Hughes
12/24/12 Graham Cooper
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 William Hughes
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 Virgil
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/21/12 Virgil
12/20/12 Virgil
12/20/12 Graham Cooper
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 Graham Cooper
12/21/12 Graham Cooper