4 A Let A Cr Be Non Empty And Bounded Below Show That I Inf A Sup A Where A X X A Ii Inf A Sup B W 1 (20.18 KiB) Viewed 72 times
4. (a) Let A CR be non-empty and bounded below. Show that i. inf A= - sup(-A) where -A= {-x € A} ii. inf A = sup(B) where B = {b:b is a lower bound for A} (b) Let A, B CR which are non-empty, bounded above. i. Show that if ACB, then sup A <sup B. ii. Show that if sup(A)< sup(B) then there must exist a b € B that is an upper bound for A.
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€ A} ii. inf A = sup(B) where B = {b:b is a lower bound for A} (b) Let A, B CR which are non-empty, bounded above. i. Show that if ACB, then sup A <sup B. ii. Show that if sup(A)< sup(B) then there must exist a b € B that is an upper bound for A.