On Wed, Oct 05, 2005 at 10:45:28AM -0400, Hal Ruhl wrote: > I am not a mathematician and so ask the following: > > In my model the ensemble of descriptions [kernels in my All] gets > populated by divisions of my list of fragments of descriptions into > two sub lists via the process of definition. > > The list is assumed to be countably infinite. > > The cardinality of the resulting descriptions is c [a power set of a > countably infinite set] > > Small descriptions describe simple worlds and large ones describe > complex worlds. > > To me there should be far more highly asymmetric sized divisions > [finite vs countably infinite] of the list than symmetric or nearly > symmetric [countably infinite vs countably infinite] ones. > > However, for each small [finite] description there is a large > [countably infinite] description. > > The result seems to be that there are more large descriptions than small > ones. > > If the above is correct then mathematically what are the measures of > the two types of descriptions? > > Hal Ruhl > > >
A measure is a function m(x) on your set obeying additivity:
m(\empty)=0
m(A u B) = m(A) + m(B) - m(A^B)
where u and ^ are the usual union and intersection operations. The
range of m(x) is also often taken to be a positive real number.
Does this answer your question? Measure is generally speaking
unrelated to cardinality, which is what you're referring to with
finite, countable and uncountable sets.
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
----------------------------------------------------------------------------
pgpJg5TPHgKkc.pgp
Description: PGP signature
