Don Kuenz wrote: > > Shmuel (Seymour J.) Metz <firstname.lastname@example.org> wrote: > > In <email@example.com>, on 02/24/2013 > > at 01:00 AM, Don Kuenz <firstname.lastname@example.org> 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