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Given that S,T CR are nonempty, bounded subsets of the set of real numbers. State whether True or False. Justify your answer in each case. (a) Then sup (SnT) < sup S. (b) Let U = {s+t:s€ S,t e T}, then sup U = sup S + sup T (c) Suppose that S := {1+ " : n e N}, and T := and sup T = 2. {1 - ": n e N}, then inf S = 0 (-1)"

Given that S,T CR are nonempty, bounded subsets of the set of real numbers. State whether True or False. Justify your answer in each case. (a) Then sup (SnT) < sup S. (b) Let U = {s+t:s€ S,t e T}, then sup U = sup S + sup T (c) Suppose that S := {1+ " : n e N}, and T := and sup T = 2. {1 - ": n e N}, then inf S = 0 (-1)"

Advanced Engineering Mathematics
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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Given that S, T CR are nonempty, bounded subsets of the set of real numbers. State whether True or False. Justify your answer in each case. (a) Then sup (SNT) < sup S. (b) Let U = {s +t:s € S,t ET}, then sup U = sup S + sup T {1+ " : n e N}, and T := {1 - )" : n e N}, then inf S = 0 (c) Suppose that S:= and sup T = 2.
Transcribed Image Text:Given that S, T CR are nonempty, bounded subsets of the set of real numbers. State whether True or False. Justify your answer in each case. (a) Then sup (SNT) < sup S. (b) Let U = {s +t:s € S,t ET}, then sup U = sup S + sup T {1+ " : n e N}, and T := {1 - )" : n e N}, then inf S = 0 (c) Suppose that S:= and sup T = 2.
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