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Topic: What is the intuitive meaning of "non-Archimedean" for a valued field?
Replies: 11   Last Post: May 15, 2013 4:29 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: What is the intuitive meaning of "non-Archimedean" for a valued field?
Posted: May 13, 2013 11:17 PM

In article
mike3 <mike4ty4@yahoo.com> wrote:

> Hi.
>
> 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.
--

Date Subject Author
5/13/13 mike3
5/13/13 William Elliot
5/13/13 mike3
5/13/13 Virgil
5/13/13 Virgil
5/13/13 mike3
5/14/13 Virgil
5/14/13 mike3
5/14/13 Virgil
5/14/13 Brian Q. Hutchings
5/15/13 Brian Q. Hutchings
5/14/13 FredJeffries@gmail.com