A non-Archimedean absolute value on a field $F$ is an absolute value $\vert \cdot\vert :F\to \mathbb R$ such that $\vert x+y\vert \leq\max{\vert x\vert ,\vert y\vert }$ for all $x,y\in F$. This inequality is called the ultrametric inequality and it is stronger than the triangle inequality.