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