Date: Feb 25, 2013 6:03 PM
Author: Frederick Williams
Subject: Re: Problems with Infinity?
Don Kuenz wrote:
> Shmuel (Seymour J.) Metz <email@example.com> wrote:
> > In <firstname.lastname@example.org>, on 02/24/2013
> > at 01:00 AM, Don Kuenz <email@example.com> said:
> >>A question for the group, if you please.
> > It's not a question, since it is full of meaningless terms.
> I'm a beginner, but a quick learner. Allow me to re-phrase my question.
> How are infinity, a Moebius transformation, the Riemann Sphere, and the
> Cantorian idea of different-size infinities related? Please explain
> using simple language that a beginner can understand.
I can relate the first and fourth, and the second and third.
Two uses of the word infinity occur in Cantor's theories of infinity:
there are infinite ordinals and infinite cardinals.
"Every Möbius transformation is a bijective conformal map of the Riemann
sphere to itself. Indeed, every such map is by necessity a Möbius
transformation." so says
http://en.wikipedia.org/wiki/Moebius_transformation (wherein you may
find links to articles on the various technical terms.)
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