*7. Let S be a nonempty bounded subset of R and let ke R. Define kS = {ks : se S}. Prove the following: (a) Ifk20, then sup (kS) = k · sup S and inf (kS) = k - inf S. (b) If k<0, then sup (kS) = k - inf S and inf (kS) = k - sup S.
*7. Let S be a nonempty bounded subset of R and let ke R. Define kS = {ks : se S}. Prove the following: (a) Ifk20, then sup (kS) = k · sup S and inf (kS) = k - inf S. (b) If k<0, then sup (kS) = k - inf S and inf (kS) = k - sup S.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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