Question: Question 1. Let X = (0, 1] and define (for x, y E X) e(x, y) = la - yl+ and d(x, y) = |x

Question 1. Let X = (0, 1] and define (for x, y E X) e(x, y) = la - yl+ and d(x, y) = |x - yl. (i) Show that e is a metric on X. (ii) Let {n)n C X. Show m -+ xin (X, d) if and only if an -+ x in (X, e). (iii) Show (X, d) is not complete. (iv) Show (X, e) is complete

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