Date: Feb 26, 2013 6:57 AM
Author: Frederick Williams
Subject: Re: Problems with Infinity?

Don Kuenz wrote:

>
> 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,


That the cardinality of the continuum (c = 2^{aleph_0}) is equal to
aleph_1 is Cantor's continuum hypothesis which modern set theory settles
neither one way nor the other.

> which includes Aleph-0, along with
> every possible arrangement of Aleph-0. The infinities of complex
> variables belong to both sets, as does every other common infinity
> found in mathematical literature.


Surely not.

> That's the sole connection between
> Cantor's continuum hypothesis and complex variables.


--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting