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

[Jasvir Nagra <jas@cs.auckland.ac.nz>]

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 infite length strings) consisting of digits only,
> > 
> > actually, there isn't on obvious mapping (which is the problem with this
> > argument). the set of all strings is countable, the set of reals isn't.
> > there are a lot of examples out there that prove that the integers are
> > uncountable by extnding them with zeroes, for example.
> > 
> 
> I don't follow you.  Integers are obviously countable:
> 
> 0, 1, -1, 2, -2, 3, -3, 4, -4, ...
> 
> You say that the set of all strings 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.

Jas

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