# Interval of Definition of Power Tower Function

## Definition

The power tower function is defined on the closed interval $\closedint {e^{-e} } {e^{1/e} }$.

## Historical Note

This result was demonstrated by Leonhard Paul Euler.

It was reported in François Le Lionnais and Jean Brette: Les Nombres Remarquables where it is pointed out that $e^{1/e}$ is, interestingly, greater than $1$.