Definition:Non-Archimedean/Norm (Vector Space)/Archimedean
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Definition
A norm $\norm {\,\cdot\,} $ on a vector space $X$ is Archimedean if and only if it is not non-Archimedean.
That is, if and only if:
- $\exists x, y \in X: \norm {x + y} > \max \set { {\norm x, \norm y} }$