Best Theorems!

ITT best theorems you know so far

Picard's Theorem is pretty nifty.

Any entire complex function that omits two values in a constant.

>>22
Uh what? The definition of an analytic function on an open subset D of the reals is precisely that it can be expressed as a power series on D. The "definition" you're probably thinking of is that Analytic on D <=> C1 on D, which in actuality is just a consequence of the real definition of analytic in the complex plane.

>>21
>>20
I think >>19 and >>9 mean a sequence of _consecutive_ integers, as otherwise the problem is trivial.