In <firstname.lastname@example.org>, on 02/26/2013 at 12:51 AM, Don Kuenz <email@example.com> said:
>Answering my own question, Cantor's conjectures concern set theory >and only tangentially touch on the infinities of complex variables. >Using beginner's language, Cantor uses two sets to define two levels >of infinity. One set, Aleph-0, holds countable infinity. The other >set, Aleph-1, holds continuum infinity, which includes Aleph-0, along >with every possible arrangement of Aleph-0.
No; Cantor's work on cardinality has nothing to do with Complex Analysis, And Aleph-1 is not the cardinality unless you assume the Continuum Hypothesis. Aleph-1 is simply the next cardinal after Aleph-0. Without the Continuum Hypothesis, the power set of a countable set might have cardinality greater than Aleph-1.
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