Question: If d is a metric on a vector space X = {0} which is obtained from a norm || ||, and d is defined

If d is a metric on a vector space X = {0}

If d is a metric on a vector space X = {0} which is obtained from a norm || ||, and d is defined by d(x, y) = d(x, y) + 1 (x+y). d(x,x) = 0, (a) Show that d is a metric on X. (b) Show that d cannot be obtained from a norm.

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