On Sat, Oct 08, 2005 at 12:26:45PM -0400, Hal Ruhl wrote: > > For each natural number n there should be countably infinite [is, is > not] pairs of descriptions of lengths [n, countably infinite]. There > are countably infinite n's. There are also countably infinite [is, > is not] pairs of descriptions of lengths [countably infinite, > countably infinite]. >

I don't think this is right, but I could be grasping the wrong end of the stick. I think of your definition division as the division of an infinite length symbol string into a finite head, and a countably infinite long tail. If true, then there are A^n heads of length n, and c (=A^\aleph_0) tails. Therefore, there are c pairs of descriptions. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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