TOPICS
Search

Archimedean Valuation


An Archimedean valuation is a valuation |·| on a field K for which there is an x in K with |x|<=1 and |1+x|>1. Equivalently, the strong triangle inequality

 |x+y|<=max(|x|,|y|)

does not hold for all x,y in K. The usual absolute value on the real numbers is Archimedean, as can be seen by taking x=1.


See also

Non-Archimedean Valuation, Valuation

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Archimedean Valuation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ArchimedeanValuation.html

Subject classifications