Question: Let S R be nonempty. Show that if u = sup S, then {or every number n N the number u - 1/n

Let S ⊂ R be nonempty. Show that if u = sup S, then {or every number n ∈ N the number u - 1/n is not an upper bound of S, but the number u + 1/n is an upper bound of S. (The converse is also true.

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