Definition:Archimedean Property/Norm

Definition
Let $\left({S, \circ}\right)$ be a semigroup.

Let $n: S \to \R$ be a norm on $S$.

Then $n$ satisfies the Archimedean property on $S$ iff:
 * $\forall a, b \in S: n \left({a}\right) > 0 \implies \exists m \in \N_{>0}: n \left({a^m}\right) > n \left({b}\right)$

where $a^m$ denotes the $m$th power of $a$.