Question

Let S be a nonempty subset of ?. Prove that if a number u in ? has the properties: (i) for every n ? ? the number u - 1/n is not an upper bound of S, and (ii) for every n ? ? the number u + 1/n is an upper bound of S, then u = sup S.

          Let S be a nonempty subset of ?. Prove that if a number u in ? has the properties:
(i) for every n ? ? the number u - 1/n is not an upper bound of S, and
(ii) for every n ? ? the number u + 1/n is an upper bound of S,
then u = sup S.

Let S be a nonempty subset of ?. Prove that if a number u in ? has the properties:
(i) for every n ? ? the number u - 1/n is not an upper bound of S, and
(ii) for every n ? ? the number u + 1/n is an upper bound of S,
then u = sup S.

Added by Brandon G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/17/2022

Step 1

This means that there exists an element in S that is greater than u - CN for every CN. Show more…

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Let S be a nonempty subset of R. 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 n ∈ N the number u + 1/n is an upper bound of S, then u = sup S.