At 07:48 PM 10/8/2005, you wrote:
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
If true, then there are A^n heads of length n, and
c (=A^\aleph_0) tails.
Therefore, there are c pairs of descriptions.
Ok, if you mean that there are c pairs of descriptions in which one
of the pairs is of length n etc. etc. I find this [I think] even
more satisfying than my above. However, I see the basic result as
being the same i.e. the number of descriptions of any particular type
is always c so there is no preponderance of any type of description.