Hi Russell:

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
tail.

Ok

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.

Yours

Hal Ruhl

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