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

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Posts: 18,076
Registered: 1/29/05
Re: Matheology § 233
Posted: Apr 2, 2013 4:17 PM
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On 2 Apr., 02:01, Virgil <> wrote:
> In article
> <>,
>  WM <> wrote:

> > On 1 Apr., 22:44, Virgil <> 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.
> And enough to disprove what WM has said as well.

Then try it.
What did I say?
This: After every line n of the list of all rational numbers there are
infinitely many rational numbers that up to digit n are identical with
the anti-diagonal up to digit n.

This holds for the digits up to every finite n. And more digits cannot
be expected to exist in any decimal representation of a number.

Regards, WM

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