Fredrik Johansson wrote: > On 6/24/09, Luke <hazelnu...@gmail.com> wrote: > >> Here is the link to the Wolfram Documentation for ComplexInfinity: >> http://reference.wolfram.com/mathematica/ref/ComplexInfinity.html >> >> Their one line documentation is: >> represents a quantity with infinite magnitude, but undetermined >> complex phase. >> >> Everything I've tried in Wolfram returns ComplexInfinity, but I'm >> still not understanding why this behavior is more desirable than >> regular infinity. I'm fine with implementing it this way, but it >> would be nice to understand why this way is more correct or general, >> if indeed it is. >> > > ComplexInfinity is just unsigned infinity. In a purely real context, > this means an infinity that could be positive or negative, and in the > complex context it could have any complex direction. > UndirectedInfinity or UnsignedInfinity would be an equally appropriate > name. > > For example, complex infinity is a correct value for 1/sin(x) at x = 0 > because the limit could be -infinity or +infinity depending on the > direction of the limit along the real line, or it could be an infinity > with any complex phase when approached through the complex plane. > > On the other hand log(0) = -infinity because log(x) tends to -infinity > no matter the direction of approach. > > Fredrik > > > > > Is complex infinity just the north pole of the Riemann sphere.
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