Date: Feb 26, 2013 2:39 PM
Author: Shmuel (Seymour J.) Metz
Subject: Re: Problems with Infinity?

In <20130225b@crcomp.net>, on 02/26/2013
at 12:51 AM, Don Kuenz <garbage@crcomp.net> 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.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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