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Topic: Matheology � 233
Replies: 37   Last Post: May 12, 2014 10:24 AM

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mueckenh@rz.fh-augsburg.de

Posts: 15,737
Registered: 1/29/05
Re: Matheology § 233
Posted: Apr 1, 2013 5:04 PM
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On 1 Apr., 22:44, Virgil <vir...@ligriv.com> wrote:

> > You do not believe that a sequence or list of all rational numbers can
> > be constructed?

>
> One can "enumerate" the  set of all rationals by formula, as has been
> quite often done, but not by physically listing all of them.


A formula giving every entry is enough.
>
> Note that one cannot ennumerate by listing even sufficiently large
> finite sets, so being listable other than by formula is not a  relevant
> criterion.


Constructing a list by a formula is enough to prove what I said.
That physical listing is impossible is well known.

Can you prove that for every FIS of d there are infinitely many
rationals in the list having the same FIS? This holds up to every line
number n - and there are no further lines.

Regards, WM



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