2x+2(i) Let x be a positive real number with x? < 2. Prove that x <x+2and2(2x+2< 2.x+2(ii) Explain why this means that the setS = {x € Q : 2² < 2}has no maximal element.(iii) Does the setT = {x € Q : x² < 2}have a maximal element?

Since you have posted multiple questions but according to guidelines, we will solve first question…

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

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

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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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?

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