Given an Annulus with $A(0,r,R)$ show by considering Cauchy's Theorem for primitives that there is no holomorphic function with $f'(z)=1/z$
I am struggling to picture this since but it seems like there are issues because $f(z)=log(z)$ isn't well defined in the same range as $1/z$.
Is it worth considering $f(z)$ as anything other than just a function? e.g setting $f(z)=log(z)$ and proving it this way?