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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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