Hope someone could give me some help with a couple of problems. First: Proof of - A function f:G -->Complex Plane is continuous on G iff for every sequence C(going from 1 to infinity) of complex numbers in G that has a limit in G we have limit as n --> infinity f(C) = f(limit as n --> infinity C) Should I use the definition of the complex limit? Limit proofs always scare me. Next I need to provide a proof of "Every Cauchy sequence in the complex plane is convergent" I'm a little shaky on the definition of a Cauchy sequence if someone could provide one in more layman's terms that would be greatly appreciated. And lastly, were asked to "show that every Cauchy sequence of integers has a limit in the set of integers (Z) Again I feel with a better understanding of the definition of a Cauchy sequence I would have a shot at getting it.