10/14/02
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Continuum Hypothesis
Many consider set theory as the most complex and the
most beautiful creation of
mathematical logic. But there are insurmountable
problems when it deals with infinite sets. One of them is the Continuum
Hypothesis.
A possible solution: Take aleph_1 as the set of all
subsets of aleph_0 of cardinality
aleph_0.
A plausible argument: The
set of subsets of aleph_0 of cardinality
aleph_0 is the largest set of subsets possible
within aleph_0. Hence,
aleph_1 = 2^aleph_0.