Completeness
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Completeness
Does the ordered field of the rational functions satisfy the completeness theorem : " All non-empty
sets have a supremum" .
sets have a supremum" .
- Tolaso J Kos
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Re: Completeness
I give the answer but not the solution so that I don't spoil someone's fun if he/she wants to try.Papapetros Vaggelis wrote:Does the ordered field of the rational functions satisfy the completeness theorem : " All non-empty
sets have a supremum" .
Answer
Imagination is much more important than knowledge.
Re: Completeness
Papapetros Vaggelis wrote:Does the ordered field of the rational functions satisfy the completeness theorem : " All non-empty
sets have a supremum" .
No, it does not, because the ordered field of the rational functions does not satisfy the Archimedean property. This is quite known.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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