Re: Orlow cardinality question

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?
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