Morgan I.

# Prove that sup(a, b)=sup[a, b]=b and inf(a, b)=inf[a, b]=a. Is completeness relevant?

Denoting, as usual, by (a, b) an ”open interval”, {x : a<x< b} and by [a, b] the corresponding ”closed interval”, {x : a≤x≤b} of real numbers, prove that sup(a, b)=sup[a, b]=b and inf(a, b)=inf[a, b]=a.
Is completeness relevant?
In other words, does the proof work for any ordered ﬁeld?

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Tutor
4.6 (10)

Mathematics/Statistics Tutor

Morgan I.

Thank you! What about the relevance of completeness? (Does the proof work with any ordered field?)
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01/31/18

Bobosharif S.

tutor
Most probably it works. I don't have a counterexample.
But I'm not sure what you mean by ordered field? If you specify definition or ordered filed, then I might tell you more.

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01/31/18

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