Question: Determine sup A and inf A where they exist: (a) A= {x R x-9>0} {n 1 EN: . (b) AnN: 1- (-1) n (c)

Determine sup A and inf A where they exist: (a) A= {x

R x-9>0} {n 1 EN: . (b) AnN: 1- (-1)" n (c)

Determine sup A and inf A where they exist: (a) A= {x R x-9>0} {n 1 EN: . (b) AnN: 1- (-1)" n (c) A = Q = (d) A No NU {0}. (e) A = {1: n=N} {MEN} (f) A = { 1 + 1 2n If b is an upper bound of A, prove that b = sup A if, and only if, for every >0 there is an element a E A such that a > b-. State and prove the corresponding result for inf A. If the sets A and B are bounded above and AC B, prove that sup A sup B. What can you say about inf A and inf B?

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