Definition:Non-Archimedean/Norm (Vector Space)/Archimedean

Definition
A norm $\left\Vert \cdot \right\Vert$ on a space $X$ is Archimedean iff it is not non-Archimedean.

That is, iff:
 * $\exists x, y, \in X: \left\Vert {x + y} \right\Vert > \max \left\{ {\left\Vert {x} \right\Vert, \left\Vert {y} \right\Vert} \right\}$