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Does the ordered field of the rational functions satisfy the completeness theorem : " All non-empty

sets have a supremum" .

Papapetros Vaggelis wrote:Does the ordered field of the rational functions satisfy the completeness theorem : " All non-empty

sets have a supremum" .

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" .

No, it does not, because the ordered field of the rational functions does not satisfy the Archimedean property. This is quite known.