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Suppose that A is a non-empty subset of R which is bounded above and that x > 0. Define x A = {xa a E A}. Prove that sup(xA) = x sup(A). Hint: Use the definition of sup to prove the two inequalities sup(xA) ≤ x sup(A) and x sup(A) ≤ sup(xA).

Suppose that A is a non-empty subset of R which is bounded above and that x > 0. Define x A = {xa a E A}. Prove that sup(xA) = x sup(A). Hint: Use the definition of sup to prove the two inequalities sup(xA) ≤ x sup(A) and x sup(A) ≤ sup(xA).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose that A is a non-empty subset of R which is bounded above and that x > 0. {xa a E A}. Prove that sup(xA) = x sup(A). Hint: Use the definition of sup to prove the two inequalities sup(xA) ≤ x sup(A) and x sup(A) ≤ sup(xA). Define x A = In each question below you must prove your answer. If the sequence converges, you need to use the definition of limit to prove that you are correct. Lumit
Transcribed Image Text:Suppose that A is a non-empty subset of R which is bounded above and that x > 0. {xa a E A}. Prove that sup(xA) = x sup(A). Hint: Use the definition of sup to prove the two inequalities sup(xA) ≤ x sup(A) and x sup(A) ≤ sup(xA). Define x A = In each question below you must prove your answer. If the sequence converges, you need to use the definition of limit to prove that you are correct. Lumit
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