1. The problem statement, all variables and given/known data i'm using Fisher's Complex Variables for my complex analysis class and there is a proof for Liouville's theorem. It says "Set g(z)=(F(z) - F(0)) / z; Then g is an entire function" 2. Relevant equations N/A 3. The attempt at a solution I am confused by that statement. Doesn't g have a singularity at z=0? How can it be analytic over the entire complex plane? Thank you and sorry if it seems like a very stupid question.