Date: Feb 28, 2013 1:23 AM
Author: Shmuel (Seymour J.) Metz
Subject: Re: Problems with Infinity?

In <20130227b@crcomp.net>, on 02/27/2013   at 11:20 PM, Don Kuenz <garbage@crcomp.net> said:>Let S(z) be a Moebius transformation. My old textbook suggests>choosing S(oo) so that S(z) has a limit at oo. That's about the >only role for infinity in a Moebius transformation.Well, oo has the same role as any other point on the Riemann Sphere<http://en.wikipedia.org/wiki/Riemann_sphere> C+; in a Moebustransformation<http://en.wikipedia.org/wiki/M%C3%B6bius_transformation>     f(z) = \frac{a z + b}{c z + d} f(-d/c) = ooIMHO the easiest way to visualize it is to consider the Riemann Sphereas a complex manifold with two coördinate neighborhoods: C and C+\{0}.From this perspective there's nothing special about either 0 or oo.-- Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>Unsolicited bulk E-mail subject to legal action.  I reserve theright to publicly post or ridicule any abusive E-mail.  Reply todomain Patriot dot net user shmuel+news to contact me.  Do notreply to spamtrap@library.lspace.org