Definition 1.5 (Non-archimedean). An absolute value $\left|\bullet \right|$ on $K$ is said to be non-archimedean if it satisfies the ultrametric inequality:

$$\left|x+y\right|\le \max (\left|x\right|,\left|y\right|).$$

If $\left|\bullet \right|$ is not non-archimedean, then it is archimedean.