Re: Relative Cardinality

*** T. Winter wrote:
> If you can order the elements of P(N) (and I think this requires
> quite a bit more) you can show that WMCard(N) <= WMCard(P(N)), but
> not the reverse. Because the reverse would mean that there is a
> bijection between the two.

If there is a bijection between two sets, then their WMCards are
"equal". However, equal WMCards does not mean that a bijection
exists.

It isn't too hard to find an ordering of P(N) \/ N such that there is
an element of N between any two elements of P(N).


Hey, I'll join in the ordering fun too! Suppose that A and B are
disjoint and we can find a total ordering on A \/ B such that for all
x0 in B, there exists y in A with x0 < y and there does not exist x1
in B such that x0 < x1 < y. Then we say that TLCard(B) <= TLCard(A).

I think this type of cardinality should be used universally in
mathematics.


- Tim
.

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