(*sup) : Every nonempty set A of real numbers which is bounded from above has a supremum. Prove that this property implies that every Cauchy sequence {xn} of real numbers has a limit. Please follow the steps listed below to finish the proof. (*inf) : Every nonempty set A of real numbers which is bounded from below has a infimum. Write YN sup{*n : n > N}, zN = inf{xn :n < N}. Using (*sup) and (*inf) to prove that {yN} and {zN} both have limits, and hence prove that the Cauchy sequence {xn} has a limit.

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