- #1

lark

- 163

- 0

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

Last edited: