4.7 Let S and T be nonempty bounded subsets of R.(a) Prove if S≤ T, then inf T ≤ inf S ≤ sup S ≤ sup T.(b) Prove sup(SUT) = max{sup S, sup T}. Note: In part (b), do notassume SCT.

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Answered: 4.7 Let S and T be nonempty bounded…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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4.7 Let S and T be nonempty bounded subsets of R. (a) Prove if S≤ T, then inf T ≤ inf S ≤ sup S ≤ sup T. (b) Prove sup(SUT) = max{sup S, sup T}. Note: In part (b), do not assume SCT.