\begin{definition}[Definition:Power Tower Function]
The '''power tower function''' is the real function $f: \R \to \R$ defined on the closed interval $\closedint {e^{-e} } {e^{1/e} }$ as:
:$\map f x = x^{x^{x^{x^{x^{\cdot^{\cdot^\cdot} } } } } }$
where the tower of powers tends to infinity.
\end{definition}