Talk:Ostrowski's theorem
From Wikipedia, the free encyclopedia
The definition of equivalence of absolute values as given here doesn't seem to go very well with the definition given on Norm_(mathematics). Ncik 00:49, 13 December 2005 (UTC)
- I think that's because they're not the same thing. A norm is a function on a VS, and it depends on an absolute value on the field for it's definition. Sometimes one has a field extension L/K and one has an absolute value (A) on K and an absolute value (B) on L which agrees with (A) where they are both defined, i.e. on K. Then (B) will certainly be a norm on L, considered as a vector space over (K,(A)). But in general they are not comparable, and I think that's why the equivalence relation on norms doesn't look like the equivalence relation on absolute values. Please correct me if I'm wrong. Owen Jones 12:29, 2 April 2006 (UTC)
