Re: Relative Cardinality



Virgil wrote:

>
> Still false for B = set of irrationals and A = set of rationals.

Obviously Card(Q) >= Card (X).
> >
> > > Apart from that, cardinality of a set is a property of the number of
> > > elements, and not of their values. So orderedness is not fundamental
> > > to cardinality.

Of course, you are right. But order can help to count the elements. Do
you know that Cantor's alephs (which I do not get by my method, perhaps
you intermingled these notions with cardinality) can only be definied
for well-ordered sets? Although cardinality has nothing to do with
order? Do you know that one even introduced the axiom of choice in
order to be sure that any consistent set can be well-ordered? In order
to get its aleph?
> >
> > Of course order is not fundamental, but if an order can be established,
> > then my definition is a sharp criterion to determine whether other
> > criteria are meaningful.
>
> Except that it is a false criterion.

It is a very fine criterion! Would Kronecker already have seen it,
nobody knew set theory today.

> WM's criterion is
> leading to false results and, therefore, it is worhtless.

It is an excellent criterion! And I can warmly recommend it to everyone
who wants to see instead to believe. Or do you too believe in "glowing
is better than knowing"?

If not, then try to find out why it leads to false results (not "that"
it does so; I know you do firmly believe that the results are wrong;
but what do you think: why is it so misleading?).

Regards, WM

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