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 Moebus
transformation
<http://en.wikipedia.org/wiki/M%C3%B6bius_transformation>

f(z) = \frac{a z + b}{c z + d}

f(-d/c) = oo

IMHO the easiest way to visualize it is to consider the Riemann Sphere
as a complex manifold with two co├Ârdinate 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>

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