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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