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

[Ronald J Kimball <rjk@linguist.thayer.dartmouth.edu>]

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.

Ronald

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