\begin{definition}[Definition:Inverse Hyperbolic Sine/Real/Definition 2]
The '''inverse hyperbolic sine''' $\arsinh: \R \to \R$ is a real function defined on $\R$ as:
:$\forall x \in \R: \map \arsinh x := \map \ln {x + \sqrt {x^2 + 1} }$
where:
:$\ln$ denotes the natural logarithm of a (strictly positive) real number
:$\sqrt {x^2 + 1}$ denotes the positive square root of $x^2 + 1$.
\end{definition}