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