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

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Definition

A norm $\norm {\, \cdot \,}$ on a division ring $R$ is Archimedean if and only if it is not non-Archimedean.


That is, if and only if:

$\exists x, y \in R: \norm {x + y} > \max \set {\norm x, \norm y}$


Sources