\begin{definition}[Definition:Non-Archimedean/Norm (Division Ring)/Archimedean]
Let $\norm {\, \cdot \,}$ be a norm on a division ring $R$ satisfying the norm axioms:
:{{:Axiom:Multiplicative Norm Axioms}}
A norm $\norm {\, \cdot \,}$ is said to be '''Archimedean''' {{iff}} it does not satisfy the {{NormAxiomNonArch|4}}.
That is, $\norm {\, \cdot \,}$ is '''Archimedean''' {{iff}}:
{{begin-axiom}}
{{axiom | n = \text N 5
        | q = \exists x, y \in R
        | ml= \norm {x + y}
        | mo= >
        | mr= \max \set {\norm x, \norm y}
}}
{{end-axiom}}
\end{definition}