Question #14975
Construct an example of incomplete ordered field that is complete in Cauchy sense.
Expert's answer
Let H be an ordered field of rational functions.
If we extend it by
equivalence classes of fundamental sequences then we get an ordered field
where each fundamental sequence
converges. But this completion in Cauchy
sense is not complete in terms of supremum.
If we extend it by
equivalence classes of fundamental sequences then we get an ordered field
where each fundamental sequence
converges. But this completion in Cauchy
sense is not complete in terms of supremum.
