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(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.

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