Re: Orlow cardinality question

In article <MPG.1d20c5f5a5694629989e47@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> *** 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.

Don't step in the oongah!
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