(a) Show that - d(m, n) = | m2 -n21 1 + \m2 – n2| defines a metric on the set of natural numbers N. Hint: use the monoto

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A Show That D M N M2 N21 1 M2 N2 Defines A Metric On The Set Of Natural Numbers N Hint Use The Monoto 1 (81.97 KiB) Viewed 18 times

(a) Show that - d(m, n) = | m2 -n21 1 + \m2 – n2| defines a metric on the set of natural numbers N. Hint: use the monotonicity of the function t t/(1 +t) fort e [0, 0). (b) Does d define a metric on the set of integers Z ? Justify your answer. a (c) Describe all bounded subsets of (N, d). = (d) Determine the largest rı > 0 and the smallest r2 > 0 such that, for all m EN, B°(m, rı) = {m} and Bºm, r2) = N. - (e) Describe all totally bounded subsets of (N, d).