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Topic: Matheology � 258
Replies: 104   Last Post: May 5, 2013 2:26 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 258
Posted: May 4, 2013 6:05 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 4 Mai, 20:31, Dan <dan.ms.ch...@gmail.com> wrote:
>
>

> > For the record , language is man-made . Mathematics is not .Its
> > universality is proof enough.

>
> Mathematics is, in large parts, discourse between mathematicians. That
> requires a language that can be spoken and understood, i.e., a finite
> language.

A considerable portion of the mathematics being created at any time is
only in "discourse" between the creator and him-or-her-self.

Once the mathematics has been created, only then need it be
communicated, so only then is any such discourse required.
> >
> > >Either you have digits 1 at finite positions only. Then your number is
> > >in the list

If one has a digit at every finite position, then one has infinitely may
digits, one in each of those infinitely many finite positions.
At least everywhere outside Wolkenmuekenheim.

>
> The list contains, by definition and by sober thinking, all digits
> that have natural indices.

But not all of them in any one line.
And that is the line that is missing in your list.

>
> > Now , since 0.11111.....  is on our list , the question is:
> > At what index n is  0.11111.....  on our list?

>
> It is not in our list

It may not be on your list, but it is on everyone else's completed list
as the union of all prior lines.

> Therefore there are no actually infinite sequences at all - and there
> is no Cantor-list, other than finitely defined lists.

WM may be able to bar common sense and the obvious from
Wolkenmuekenheim, but elsewhere he cannot.

****** ON COUNTABILITY ******

Countability and listability are equivalent notions, at least outside of
Wolkenmuekenheim:

Any set, S, is defined to be COUNTABLE if and only if
there is a surjective mapping from |N onto S.

And S is othewise said to be UNCOUNTABLE.

So set S being countable is equivalent to saying that the members of S
are listable in natural number order with no members of S being left
out.

NOTE:members of S may appear in such a listing more than once, as long
as each of them appears at least once, withut destroying countability.

So that unless WM can provide such a listing of the reals, in which each
real can be proven to appear at least once, he is NOT justified in
claiming that the set of reals is known to be countable.

And Cantor has provided two entirely different proofs that no such
complete listings of the set of reals are possible.

Neither of which WM, nor anyone else, has yet disproved.

Ergo, |R is uncountable.
--

Date Subject Author
4/29/13 Virgil
4/29/13 mueckenh@rz.fh-augsburg.de
4/29/13 Virgil
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 JT
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Ed Prochak
5/2/13 Virgil
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 dan.ms.chaos@gmail.com
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Virgil
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 Virgil
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 ross.finlayson@gmail.com
5/5/13 LudovicoVan
5/5/13 fom
5/5/13 ross.finlayson@gmail.com
5/5/13 ross.finlayson@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 dan.ms.chaos@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 fom
5/4/13 Virgil
5/4/13 ross.finlayson@gmail.com
5/4/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/4/13 trj
5/4/13 Virgil
5/3/13 Virgil
5/3/13 Virgil
5/3/13 fom
5/3/13 dan.ms.chaos@gmail.com
5/3/13 fom
5/3/13 gus gassmann
5/3/13 Virgil
5/2/13 Virgil
5/1/13 Virgil
5/1/13 JT
5/1/13 Virgil
5/1/13 JT
5/1/13 Bergholt Stuttley Johnson
5/1/13 rt servo
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
4/30/13 Virgil
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
4/29/13 ross.finlayson@gmail.com
4/29/13 Virgil