Re: Infinities

Hal Finney (
Sat, 8 Nov 1997 22:41:35 -0800

This is getting a little bit long, so I will just make one point.
The URL I posted yesterday should shed more light.

John K Clark, <>, writes:
> Not so, there is a set called the Power Set Of Omega (Pw) that has been
> proven to contain aleph-one members.

No, Pw has been proven to have larger cardinality than aleph null, and
it has been proven to have the same cardinality as the real numbers.
But it is not known whether it is equal to aleph one. As I posted the
other day, some people have suggested that it might be aleph two.

Think about this, too. How could Pw be shown to be equal to aleph one?
You'd have to prove that there is NO transfinite cardinal between aleph
null and Pw, that the very next cardinal after aleph null was Pw. Nothing
in between. Show me such a proof! You would revolutionize mathematics
if you could.