and behave according to the familiar rules of algebra. For each of the following sets of real numbers, tell whether or not the given set is bounded above. For those that are, give three different upper bounds and find the least upper bound. (a) (-1,3] (c) {1,2,3,4} (e) (-∞,0] (b) [-1,3) (d) {5} (f) (0, +∞)
and behave according to the familiar rules of algebra. For each of the following sets of real numbers, tell whether or not the given set is bounded above. For those that are, give three different upper bounds and find the least upper bound. (a) (-1,3] (c) {1,2,3,4} (e) (-∞,0] (b) [-1,3) (d) {5} (f) (0, +∞)
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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If you're not able to solve all, that is okay. I just really need help with (b), (d), (f), etc... [The problems on the right side]
Thank you so much.
Transcribed Image Text:2. For each of the sets listed in Exercise 1, tell whether or not the given set
is bounded below. For those that are, give three different lower bounds
and find the greatest lower bound.
m
163 (2)
![1. Assume that real numbers exist and behave according to the familiar rules
of algebra. For each of the following sets of real numbers, tell whether or
not the given set is bounded above. For those that are, give three different
upper bounds and find the least upper bound.
(a) (-1,3]
(c) {1,2,3,4}
(e) (-∞0,0]
(b) [-1,3)
(d) {5}
(f) (0, +∞)
(g) Ø
(1) { / 2 : * >0}
(h) { //:n=N}
{<<2}
:neN}
1
(k) { 2 - / / : neN}
n
(m) {+¹:1>2} (n) {sin ():N)
N}
x
2
(1) +
2n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b45a43a-b1fe-4bb2-b8ff-5fadce0e9d26%2F6c7838a6-8afc-41aa-b973-37dbd9cadc82%2Fcbgw2a3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Assume that real numbers exist and behave according to the familiar rules
of algebra. For each of the following sets of real numbers, tell whether or
not the given set is bounded above. For those that are, give three different
upper bounds and find the least upper bound.
(a) (-1,3]
(c) {1,2,3,4}
(e) (-∞0,0]
(b) [-1,3)
(d) {5}
(f) (0, +∞)
(g) Ø
(1) { / 2 : * >0}
(h) { //:n=N}
{<<2}
:neN}
1
(k) { 2 - / / : neN}
n
(m) {+¹:1>2} (n) {sin ():N)
N}
x
2
(1) +
2n
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