Date: Mar 8, 2013 5:30 AM
Subject: Re: Elementary complex analysis
William Hughes wrote:
>> Then R approaches to 0 at infinity, hence since g also
>> approaches 0 at infinity, so does g - R.
>(I have to start getting more sleep)
No, you correctly identified a flaw.
The work-around was not to choose any old rational function
R with the same principal parts as g, but to choose R as the
sun of the principal parts of g.
Even after showing g = R, a little more argument was needed
to show that 1/R is actually a polynomial, not just a rational