Re: A question re measure

From: Hal Ruhl <HalRuhl.domain.name.hidden>
Date: Sat, 08 Oct 2005 22:34:47 -0400

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
Received on Sat Oct 08 2005 - 22:36:50 PDT