Helpe question 4 to question 9 (4) Let A C R be a et ith greatet element a e A Prove that sup(A)=a(5) Let A = {r € R+ : a² < 2} . Explain hy A i bounded above and below and find sup(A) and inf(A).(6) Suppose A, B C R are both non-empty subsets with a = Sup(A) and 3 = sup(B) both exist-ing. Then if A C B then a < ß .(7) Let A = {4,7, 8} and B = {–1,5}, Find and comparesup(A+B) , inf(A+B), sup(A)+sup(B),sup A - inf B, inf A-inf B(8) Prove by an example that for any set A, g.l.b(-A) = –l.u.b(A)(9) Prove and give an example that if A and B are two bounded non-empty subset of R, thenAUB is also bounded

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Description: Helpe question 4 to question 9 (4) Let A C R be a et ith greatet element a e A Prove that sup(A)=a(5) Let A = {r € R+ : a² < 2} . Explain hy A i bounded above and below and find sup(A) and inf(A).(6) Suppose A, B C R are both non-empty subsets with a

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(4) Let A CRbe a et ith greatet element a E A Prove that sup(A)=a

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 1E: Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary...

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