Let S be a nonempty set of real numbers that is bounded from above and let x = sup S. Prove that either x belongs to S or x is an accumulation point of S.

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A: Please see the attachment

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A: Solution

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Q: Let A be a nonempty subset of R that is bounded above and let α = sup A. If α is NOT an element in…

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Q: Show that f(x) = 1/x2 is uniformly continuous on the set [1,∞) but not on the set (0, 1].

A: To show that f(x)=1x2 is uniformly continuous on the set [1,∞) but not on (0,1].