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Answer to Question #42285 in Real Analysis for Johny Sasameb

Question #42285
Let S⊆R be non empty . Prove that if a number u in R has the properties (i) for every n∈N the number u-1/n is not an upper bound of S, and (ii) for every number n∈N the number u + 1/n is upper bound S, then u =sup S.
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