From: John K Clark (johnkc@well.com)
Date: Wed Nov 05 1997 - 22:58:11 MST
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On Tue, 04 Nov 1997 Kennita Watson <kwatson@netcom.com> Wrote:
>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?
No. B is alpha -null (the number of integers) and C is the number of points
on a line, Cantor proved that C > B and C + B = C and C * B =C and
C * C = C and B^B = C and even that C^B =C but was never able to prove
that 2^B = C. Even today the "Continuum Hypothesis" which states that C is
equal to alpha-one (2^B) has never been proven and remains of the great
mysteries of mathematics.
Cantor also showed that C^C = F > C where F is the number of all one valued
functions, there are more curves in the plane than there are points.
It's known that F is one of the alpha numbers (alpha -two?) but it's not
known which one.
John K Clark johnkc@well.com
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