Re: Orlow cardinality question

*** T. Winter said:
> In article <d8uvn4$ih1$1@xxxxxxxxxxxx> stephen@xxxxxxxxxx writes:
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> ...
> > >> How do you, TO, define "number of elements" of a set?
> > >> It is not that we do not understand in general, it is that we do not
> > >> know what your understanding about that phrase is.
> >
> > > How about the integral of the density over the domain? Does that satisfy
> > > your need for mathematical definition?
> >
> > Not even close. Consider the set of regular languages over the alphabet
> > {a,b}.
> > What is the "integral of the density over the domain" of this set?
>
> Much simpler. What is the "integral of the density over the domain" for
> the even numbers in the integers? The density is approximately 2 everywhere,
> the domain is the naturals, what is the integral?
>
The density is 1/2. The integral over that range is N/2. If the density
changes, rather than being constant, then we can still often get some non-zero
value here relative to N, by taking an integral sum over that range. This is
really just another way of using the inverse of the mapping function.
--
Smiles,

Tony
.