\begin{definition}[Definition:Inverse Hyperbolic Cosecant/Real/Definition 1]
The '''inverse hyperbolic cosecant''' $\arcsch: \R_{\ne 0} \to \R$ is a real function defined on the non-zero real numbers $\R_{\ne 0}$ as:
:$\forall x \in \R_{\ne 0}: \map \arcsch x := y \in \R: x = \map \csch y$
where $\map \csch y$ denotes the hyperbolic cosecant function of $y$.
\end{definition}