Ahlfors says that for rational function $R(x) = \frac{P(z)}{Q(z)}$, we define $R(z)$ to be $\infty$ when $Q(z) = 0$. Then he says that $R(z)$ is clearly continuous.
To me, $R(z)$ is clearly continuous at the points where $Q(z) \not = 0$. But for continuity, you need $|R(z) - \infty| = \infty < \epsilon$ for $z$ which are close to the zero. So $R(z)$ can't be continuous in the sense that it is continuous at every point.
Is Ahlfors being informal here, or am I missing something fundamental?