(f) Let V be a vector space and d be a metric on V such that (i) d(x,y) = d(x+z, y+z) for all x,y, z ϵ V, and (ii) d(λx,λy) = λd(x,y) for all x,y ϵ V and λ ϵ F Define ||.|| by ||x|| = d (x, 0). Show that ||.|| is a norm on V. Next, show that the metric induced by ||.|| is precisely d.

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