Re: Orlow cardinality question

In article <MPG.1d20ca46741558a1989e4a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <MPG.1d1ccb0af4b7d541989e1b@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > 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?
> >
> > No. There is no guarantee that any such "integral" exists. there is
> > certainly no real valued function representing density at each real
> > number of any interval.
> >
> Your declarations do not make it so.

It is the obligation of one who declare that something exists to prove
it does exist rather than the duty of someone who doubts it to prove his
doubts.

Prove that your alleged density function exists and that the alleged
integral of that function exists.
.

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