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Question: v question 5 exercise 2124 of moon and stirling 2000...

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V. QUESTION 5 Exercise 2.1-24 of [Moon and Stirling, 2000]: The fact that a sequence is Cauchy depends upon the metric employed. Let fn (t) be the sequence of functions for t <-1/n; for-1/n st s 1/n; for 1/n <t, 0, fn(t)-〈nt/2+1/2, in the metric space (Ca, b,), where doo(f,g) -sup (t) -g(t) Show that, 1 n , for m n nim 2 2mn Hence, conclude that in this metric space, fn is not a Cauchy sequence.

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