Isn't that the "Continuum Hypothesis", which has been proven
unprovable either way? So it's an arbitrary choice of axiom.
Kennita asks
: By this do you mean that there are B integers and 2^B points on a line,
: and we don't know if there's anything in between?
Yes, if B = aleph-null. Think of the set of real numbers (points
on a line) as expressed in binary: B bits running to the left, B bits
running to the right, thus the members of the set are 2^B. Cantor
used a charming trick to show that this set is non-countable, i.e.
cannot be mapped one-to-one with the set of integers.
Anton Sherwood *\\* +1 415 267 0685 *\\* DASher@netcom.com