analytic functions and poles I have the following theorem on my notes of a course on complex analysis I'm taking:
If f(z) is not bounded in a neighborhood of its isolated singular point z0, then z0 is a pole.
I think this cannot be right, for example sin(1/z) at z0=0 is not bounded, but has an essential singularity, not a pole. Just need some confirmation. Thanks.

Yes you are right. Great Picard's theorem states that if $w$ is an essential singularity of the analytic function $f$, then in any open set containing $w$, $f$ takes all possible values (with at most one exception), infinitely often.
