(b) Consider the following set of real numbers: 3n² +n +3 A-3+N} CR { n³ n = :n Prove that A is bounded. (ii) Prove that inf(A) = 0. Can you replace inf by min? Justify your answer. (iii) Find sup(A) and max(A), justifying your answer in each case. [4] [4] [3]
(b) Consider the following set of real numbers: 3n² +n +3 A-3+N} CR { n³ n = :n Prove that A is bounded. (ii) Prove that inf(A) = 0. Can you replace inf by min? Justify your answer. (iii) Find sup(A) and max(A), justifying your answer in each case. [4] [4] [3]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(b) Consider the following set of real numbers:
+n +3
A
1- {3³0²2 +1 + ³ = RCN} CR
n
n
(i) Prove that A is bounded.
(ii) Prove that inf(A) 0. Can you replace inf by min? Justify your answer.
(iii) Find sup(A) and max(A), justifying your answer in each case.
=
A
[4]
[3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc33fa3ef-6a6a-465a-986f-fdde28dde808%2F5089cef3-f426-41e8-8aa9-9fd6fa9255d6%2Fnuitwl_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Consider the following set of real numbers:
+n +3
A
1- {3³0²2 +1 + ³ = RCN} CR
n
n
(i) Prove that A is bounded.
(ii) Prove that inf(A) 0. Can you replace inf by min? Justify your answer.
(iii) Find sup(A) and max(A), justifying your answer in each case.
=
A
[4]
[3]
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