Let $f:U\subseteq \hat{\mathbb{C}}\to \hat{\mathbb{C}}$ be "holomorphic" in the manner we have previously defined. Then $f$ has an isolated singularity at $\mathrm{\infty }$ if 1;; $g(z)=f\left(\frac{1}{z}\right)$ has an isolated singularity at $0$. The type of singularity is inherited from $g$.