I am reading these lecture notes and there is a converse to the Cauchy Riemann equations and it is stated as follows:
If the partial derivatives exist and are continuous then $f$ is (complex) differentiable.
My question is: Doesn't continuity imply "exist"? Meaning, we could just say if the partial derivatives are continuous then $f$ is differentiable? Or what does "exist" mean in this context? I assumed it meant "is finite".