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

[Neil Kandalgaonkar <neilk@ActiveState.com>]

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.

huh? The set of all strings must include the set of all the 
string representations of all the reals between zero and one. 

So if reals are uncountable, so are the strings, unless I've really
missed something.


> there are a lot of examples out there that prove that the integers are
> uncountable by extnding them with zeroes, for example.

the set of integers can be trivially mapped to the set of integers * 10.

I think you may be using a definition of "countable" that's different
from the standard one.

Try this:
http://forum.swarthmore.edu/dr.math/problems/merrill11.12.97.html

-- 
Neil Kandalgaonkar, Web Application Developer, ActiveState 
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