# Riemann Sphere Complex Analysis

I've been posed with the task of explaining, if $\{x_n\}$ is a sequence of points on the Riemann Sphere which converges to $(0,0,1)$ why does the corresponding sequence $\{z_n\}$ in the complex plane go to inf? Also, why is the converse true as well?

I understand the problem abstractly as to why this is, but am having trouble articulating this into a proof form.

• I guess you need to know the correspondence between the two spaces. Then elementary calculus. – GEdgar Oct 4 '15 at 22:39
• Consider a small disk around (0,0,1). What does that map to in the complex plane? – John Douma Oct 4 '15 at 22:42