\begin{definition}[Definition:Real Hyperbolic Cosecant/Definition 2]
The '''real hyperbolic cosecant''' function is defined on the real numbers as:
:$\csch: \R_{\ne 0} \to \C$:
:$\forall x \in \R_{\ne 0}: \csch x := \dfrac 1 {\sinh x}$
where $\sinh$ is the real hyperbolic sine.
It is noted that at $x = 0$ we have that $\sinh x = 0$, and so $\csch x$ is not defined at that point.
\end{definition}