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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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 mike3 Posts: 2,396 Registered: 12/8/04
Re: What is the intuitive meaning of "non-Archimedean" for a valued field?
Posted: May 13, 2013 11:50 PM
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On May 13, 8:17 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <bf23b508-9d6c-459b-b797-5022f1dd0...@tz3g2000pbb.googlegroups.com>,
>
>  mike3 <mike4...@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.
> --

Correct. I made a mistake/typo: it should be "na > b".

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

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