In article <firstname.lastname@example.org>, mike3 <email@example.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. --