\begin{definition}[Definition:Non-Archimedean/Norm (Vector Space)/Archimedean]
A norm $\norm {\,\cdot\,} $ on a vector space $X$ is '''Archimedean''' {{iff}} it is not non-Archimedean.
That is, {{iff}}:
:$\exists x, y \in X: \norm {x + y} > \max \set { {\norm x, \norm y} }$
Category:Definitions/Norm Theory
\end{definition}