Re: [FWP] japhy had a silly idea...

[Piers Cawley <pdcawley@iterative-software.com> (by way ofowner-fwp@technofile.org)]

>From fwp-l Mon May 28 17:36:27 2001

"Abigail" <abigail@foad.org> writes:

> On Tue, May 29, 2001 at 11:41:56AM +1200, Jasvir Nagra wrote:
> > Ronald J Kimball <rjk@linguist.thayer.dartmouth.edu> writes:
> >
> > > On Tue, May 29, 2001 at 12:51:26AM +0200, Marc Lehmann wrote:
> > > > On Mon, May 28, 2001 at 10:57:17PM +0200, Abigail <abigail@foad.org>
>wrote:
> > > > > can match infinite strings as well. And since there is an obvious,
> > > > > 1-to-1 mapping between the set of reals between 0 and 1 and the set
>of
> > > > > strings (including the infinite length strings) consisting of
>digits onl
>                                --------
>                                   ^
>                                  /|\
> > > >                             |
> > > > actually, there isn't on obv|ous mapping (which is the problem with
>this
> > > > argument). the set of all st|ings is countable, the set of reals
>isn't.
> > > > there are a lot of examples |ut there that prove that the integers are
> > > > uncountable by extnding them|with zeroes, for example.
> > > >                             |
> > >                               |
> > > I don't follow you.  Integers |re obviously countable:
> > >                               |
> > > 0, 1, -1, 2, -2, 3, -3, 4, -4,|...
> > >                               |
> > > You say that the set of all st|ings is countable....  Then, as Abigail
> > > said, the set of reals between|0 and 1 must be countable, because each
>real
> > > can be represented as a string| specifically a string of digits.
> >                                 |
> > Not quite.  The set of all reals|can't be represented as *finite*
>                                   |                         ------
>                                   |                           |
>                                   +---------------------------+
> > strings.  In particular, fr'instance, you can't represent pi as a
> > string of digits.
>
>
> Please prove this claim.

You know, I'm pretty certain that the set of all strings is
uncountable, by Cantor's Diagonalization.

-- 
Piers Cawley
www.iterative-software.com

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