# Answer on Abstract Algebra Question for Paul

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.

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