Let A be a non-empty, bounded set of positive real numbers. Let B be the set consisting of numbers of the form b = Va +3, for a E A. Show that B is bounded above, and that sup B = Vsup A + 3.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 13E: 13. Let Z denote the set of all integers, and let Prove that .
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3 Let A be a non-empty, bounded set of positive real numbers. Let B be the set consisting of numbers
of the form
b = Va+3, for a E A.
Show that B is bounded above, and that
sup B = Vsup A+3.
Transcribed Image Text:3 Let A be a non-empty, bounded set of positive real numbers. Let B be the set consisting of numbers of the form b = Va+3, for a E A. Show that B is bounded above, and that sup B = Vsup A+3.
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