It says to write f(z) as g(z)/[(z-zo)^n] and then write g(z) as a0 + a1(z-z0) .... etc. and that we can deduce that the Laurent series for f(z) begins with (z-z0)^(-n) unless a0 = 0 i.e g(z0) = 0. Therefore the order of the pole is n. However, how can we be sure that g(z) does not contain terms of the form (z-z0)^(-n) ? Is this just by assumption?

thanks for your help.