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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 compare sup(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, then AUB is also bounded
Transcribed Image Text:(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 compare sup(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, then AUB is also bounded
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