Virgil
Posts:
8,833
Registered:
1/6/11


Re: What is the intuitive meaning of "nonArchimedean" for a valued field?
Posted:
May 13, 2013 11:17 PM


In article <bf23b5089d6c459bb7975022f1dd0e5d@tz3g2000pbb.googlegroups.com>, mike3 <mike4ty4@yahoo.com> wrote:
> Hi. > > I'm curious about this. The "Archimedean property" for an _ordered_ > field F means that given any positive elements a and b in F, with a < > b, then there exists a natural number n such that na < b.
Not quite as stated above.
Given 0 < a < b there must be some natural n such that na > b.
But if a is negative, one will have na < b for all naturals n.
The standard ordered field of reals and all of of its subfields have the property, but fields with infinitesimal elements do not. 

