EXAMPLES Classify the following subsets of R as bounded or unbounded. If it is bounded, write down its supremum and / or infimum. (i) {x: x-5 ≤ 2} (ii) { //1/2: neN} (iii) { x = R {0}} //12 :
EXAMPLES Classify the following subsets of R as bounded or unbounded. If it is bounded, write down its supremum and / or infimum. (i) {x: x-5 ≤ 2} (ii) { //1/2: neN} (iii) { x = R {0}} //12 :
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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![EXAMPLES
Classify the following subsets of R as bounded or unbounded.
If it is bounded, write down its supremum and / or infimum.
(i) {x: x - 5] ≤ 2}
(ii) {/1/2: neN}
(iii) { ½/2 : x € R\{0}}
EXAMPLES
1. Prove that sup(1, 2) = 2.
2. Prove that in f(1, 2) = 1.
3. Prove that in f[1, 2) = 1.
4. Show that (1, 2) has no maximum.
5. Show that [1,2] has a maximum.
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2b5643b-61fa-475e-a189-c90ed499689b%2Fd4694ac9-2a2d-44e2-8cbc-d35d374155fc%2F1friq9d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXAMPLES
Classify the following subsets of R as bounded or unbounded.
If it is bounded, write down its supremum and / or infimum.
(i) {x: x - 5] ≤ 2}
(ii) {/1/2: neN}
(iii) { ½/2 : x € R\{0}}
EXAMPLES
1. Prove that sup(1, 2) = 2.
2. Prove that in f(1, 2) = 1.
3. Prove that in f[1, 2) = 1.
4. Show that (1, 2) has no maximum.
5. Show that [1,2] has a maximum.
1
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