# Definition:Non-Archimedean/Norm (Division Ring)/Archimedean

A norm $\norm {\, \cdot \,}$ on a division ring $R$ is Archimedean if and only if it is not non-Archimedean.
$\exists x, y \in R: \norm {x + y} > \max \set {\norm x, \norm y}$