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In: Advanced Math

Let F be an ordered field. We say that F has the Cauchy Completeness Property if...

Let F be an ordered field. We say that F has the Cauchy Completeness Property if every Cauchy sequence in F converges in F. Prove that the Cauchy Completeness Property and the Archimedean Property imply the Least Upper Bound Property.
Recall:
Least Upper Bound Property: Let F be an ordered field. F has the Least Upper Bound Property if every nonempty subset of F that is bounded above has a least upper bound.​

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Colby Messinger answered 1 year ago
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