In mathematics, a discrete valuation is an integer valuation on a field K; that is, a function: ν : K → Z ∪ { ∞ } {\displaystyle \nu :K\to \mathbb {Z} \cup \{\infty \}} satisfying the conditions: ν = ν + ν {\displaystyle \nu =\nu +\nu } ν ≥ min { ν, ν } {\displaystyle \nu \geq \min {\big \{}\nu,\nu {\big \}}} ν = ∞ ⟺ x = 0 {\displaystyle \nu =\infty \iff x=0} for all x, y ∈ K {\displaystyle x,y\in K}. Wikipedia