\begin{definition}[Definition:Inverse Hyperbolic Sine/Real/Definition 1]
The '''inverse hyperbolic sine''' $\arsinh: \R \to \R$ is a real function defined on $\R$ as:
:$\forall x \in \R: \map \arsinh x := y \in \R: x = \map \sinh y$
where $\map \sinh y$ denotes the hyperbolic sine function.
\end{definition}