Re: Orlow cardinality question

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> Virgil said:
>> In article <MPG.1d1b9b0c5dea7d6c989e09@xxxxxxxxxxxxxxxxxxxxxxxxx>,
>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>>
>>
>> > > Who says that number of elements is the one universal measure of
>> > > sets? That is something you just made up. You have to define
>> > > "number of elements" before the question even makes sense.
>>
>> > Which term do you not understand, "number" or "element"?
>>
>> 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?

> There are several ways to state this, but
> "number of elements" is the most basic, and the way we intuitively think about
> sets. A set is a number of elements, members, units, or whatever.

I do not see how "number of elements" is in general related to
"integral of the density over the domain". When I think
of sets, I do not think of integrals or density.

Stephen
.