Understanding Removable discontinuity of the given function: ##e^x##

[Svein]

@Svein I'm not sure how that addresses the question of whether $1/z$ is a continuous function though, which is the analogous question to $1/x$ in $\mathbb{R}$

I did not say that $1/z$ was continuous. I said that in complex analysis we do not have a problem with $1/z$. It is called a pole.