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(a) Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the following sets. Provide an explanation of your answer. i) {x : |z − 1 < 2}; iii) {zza_r_10); ii) {r: z− 1|>2}; iv) {−2, 2, −2.1, 2.1, −2.11, 2.11,...).

(a) Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the following sets. Provide an explanation of your answer. i) {x : |z − 1 < 2}; iii) {zza_r_10); ii) {r: z− 1|>2}; iv) {−2, 2, −2.1, 2.1, −2.11, 2.11,...).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 1TFE: Label each of the following statements as either true or false. The Well-Ordering Theorem implies...
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(a) Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the following sets. Provide an explanation of your answer. i) {x : x − 1 < 2}, iii) {zz3+ 1 0); hi) {r: 2-1 > 2}; iv) { 2, 2, 2.1, 2.1, -2.11, 2.11,...}. (b) Using the delta-epsilon definition of the limit, prove that #2 72 +1 lim 200 2 3 =∞.
Transcribed Image Text:(a) Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the following sets. Provide an explanation of your answer. i) {x : x − 1 < 2}, iii) {zz3+ 1 0); hi) {r: 2-1 > 2}; iv) { 2, 2, 2.1, 2.1, -2.11, 2.11,...}. (b) Using the delta-epsilon definition of the limit, prove that #2 72 +1 lim 200 2 3 =∞.
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