(a) Show that d(m, n) = |m²-n²| 1+ m²-n²| defines a metric on the set of natural numbers N. Hint: use the monotonicity of the function tt/(1+t) for t = [0, 00). (b) Does d define a metric on the set of integers Z? Justify your answer. (c) Describe all bounded subsets of (N, d).

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