The equality between ε(f ) and δ(f ) proved via Newton polygons

 In this paper, we reproduce the proof given in \cite{Andrei} of the equality between ε(f ) and δ(f ), two important objects in Valuation Theory. This proof uses the notion of Newton polygons. We present some  details that were omitted in \cite{Andrei} and illustrate a step-by-step construction of a Newton Polygon associated to a specific finite set.