2.x+2 (i) Let x be a positive real number with x2 < 2. Prove that x < x+2 and () < 2. 2x+2 x+2 (ii) Explain why this means that the set S = {r € Q : x² < 2} has no maximal element. (iii) Does the set T = {x € Q : x² < 2} || hovo olomont? mo

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 63E
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Question
2x+2
(i) Let x be a positive real number with x? < 2. Prove that x <
x+2
and
2
(
2x+2
< 2.
x+2
(ii) Explain why this means that the set
S = {x € Q : 2² < 2}
has no maximal element.
(iii) Does the set
T = {x € Q : x² < 2}
have a maximal element?
Transcribed Image Text:2x+2 (i) Let x be a positive real number with x? < 2. Prove that x < x+2 and 2 ( 2x+2 < 2. x+2 (ii) Explain why this means that the set S = {x € Q : 2² < 2} has no maximal element. (iii) Does the set T = {x € Q : x² < 2} have a maximal element?
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