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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: UNCOUNTABILITY
Posted: Dec 22, 2012 4:57 PM

In article
WM <mueckenh@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:
>
> 0
> 1
> 00
> 01
> 10
> 11
> 000
> and so on.

While I can see some binaries, I do not see any words being paired off
with them. Thus WM's claim fails.
>
> 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?

What is the natural number of the word "help"?
>
> Nevertheless there is no set of all natural numbers and no set of all
> infinite words.

In standard mathematics, like in ZFC, for example, there is a set of all
natural numbers, or at least a set having all the properrties one wants
or needs for a set of natural numbers.
>
> 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.

On the other hand, the ratio of the circumference of a circle to its
diameter is perfectly well defined.
>
> Yes, I know that is not easy to understand.

WM certainly illustrates his own difficulty in understanding quite
clearly!
--

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