Let K be a field of arbitrary characteristic. Let v:K->R union {∞} be defined by the following properties: 1.v(x) = ∞⇔x = 0, 2.v(x y) = v(x) + v(y) for all x, y element K, and 3.v(x + y)>=inf{v(x), v(y)}.

Krasner's lemma | non-Archimedean geometry

Archimedes