MathGloss

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