http://mathworld.wolfram.com/Valuation.html
absolute value satisfy triangle inequality
$p$-adic valuation satisfy ultrametric inequality
$|x+y| ≤ \max\{|x|,|y|\}$
then can we find some valuation satisfy
$0≤|x|$
$|x|=0$ iff $x=0$
$|xy|=|x||y|$
$|x+y| ≤ \min\{|x|,|y|\}?$
is it exist? not trivial valuation.