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lark
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Complex analysis has a lot of nice theorems that real analysis doesn't have: if you can take the complex derivative once, you can take it [tex]\infty[/tex] many times. Maximum modulus theorem; inside the radius of convergence the Taylor series of a function converges to the function.
So what I wonder is, is the elegance of complex analysis related to the fact that the complex #'s are algebraically complete?
Complex analysis can be used to show that the complex #'s are algebraically complete. So one could ask if that same proof works over other fields that are both metrically complete and algebraically complete. To try and get a handle on the question.
Laura
So what I wonder is, is the elegance of complex analysis related to the fact that the complex #'s are algebraically complete?
Complex analysis can be used to show that the complex #'s are algebraically complete. So one could ask if that same proof works over other fields that are both metrically complete and algebraically complete. To try and get a handle on the question.
Laura
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