Let 0 SCR be bounded above and u R. Prove that the following two conditions are...

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Let 0 SCR be bounded above and u R. Prove that the following two conditions are equivalent: 1. u = sup S. 2. For every > 0 we have (a) u + is an upper bound for S, and (b) u-e is NOT an upper bound for S. - State and prove the analogue of the previous exercise for inf S. Let 0 SCR be bounded above and u R. Prove that the following two conditions are equivalent: 1. u = sup S. 2. For every > 0 we have (a) u + is an upper bound for S, and (b) u-e is NOT an upper bound for S. - State and prove the analogue of the previous exercise for inf S.