\begin{definition}[Definition:Inverse Hyperbolic Tangent/Real/Definition 1]
Let $S$ denote the open real interval:
:$S := \openint {-1} 1$
The '''inverse hyperbolic tangent''' $\artanh: S \to \R$ is a real function defined on $S$ as:
:$\forall x \in S: \map \artanh x := y \in \R: x = \map \tanh y$
where $\map \tanh y$ denotes the hyperbolic tangent function.
\end{definition}