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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 258
Posted: May 1, 2013 7:52 AM

On 1 Mai, 13:15, Dan <dan.ms.ch...@gmail.com> wrote:
> On May 1, 1:01 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 1 Mai, 11:36, Dan <dan.ms.ch...@gmail.com> wrote:
>
> > >http://webdocs.cs.ualberta.ca/~contest/ACPC2007/contest/problems/e.html
> > > This is a way to enumerate all rational numbers between 0 and 1 .
> > > What's wrong with it?

>
> > Wrong is the assumption that *all* rational numbers can be enumerated.
> > *Every* rational can be enumerated. But for *every* rational number we
> > have: There are infinitely many not enumerated numbers remaining.
> > Briefly:

>
> > forall n : the quantification "forall n" is wrong.
>
> > Regards, WM
>
> forall n , exists n + 1 .

for every n exists n + 1.

all n, according to a calculation by Cantor, have the sum aleph_0.
>
> Babies get poked in needles. The needle *is wrong* .
> You're going to to have to be a lot more specific than '"forall n" is
> wrong' .

If "for all" shall have a meaning, than it must be able to prove that
all are there. That's impossible without knowing the last - at least
in a serious science.
>
> If the natural numbers can be enumerated , then the rational numbers
> can be enumerated .

This statement is true, but the premise is wrong.

> Do you think the natural numbers *can be enumerated*?

"The" natural numbers can be enumerated, but there are never all
natural numbers, because this would imply to check that all is
correctly applied - at least in a serious science.

The problem is this: Zermelo wrote the axiom of infinity. For every a
there is {a}. This together with the axiom of empty set axiomatizes
induction. But it does not support the completely mislead
interpretation of "there exist" with respect to a completed infinite
set of all elements. Look also here:
http://www.hs-augsburg.de/~mueckenh/KB/Open%20Letter.pdf

Regards, WM

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
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4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
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5/1/13 Virgil
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