Title: A Polylogarithm Solution to the Epsilon--Delta Problem,
Abstract: Let $f$ be a continuous real function defined in a subset of the real line.
The standard definition of continuity at a point $x$ allow us to correlate any
given epsilon with a (possibly depending of $x$) delta value. This pairing is
known as the epsilon--delta relation of $f$. In this work, we demonstrate the
existence of a privileged choice of delta in the sense that it is continuous,
invertible, maximal and it is the solution of a simple functional equation. We
also introduce an algorithm that can be used to numerically calculate this map
in polylogarithm time, proving the computability of the epsilon--delta
relation. Finally, some examples are analyzed in order to showcase the accuracy
and effectiveness of these methods, even when the explicit formula for the
aforementioned privileged function is unknown due to the lack of analytical
tools for solving the functional equation.