It is known that Q [0,1] is a countable set (do not prove this). Let Qn...

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It is known that Q [0,1] is a countable set (do not prove this). Let Qn [0, 1] = {1, 2, ..., rn,... .} be an arbitrary fixed ordering of the elements of Qn [0, 1] in a sequence. For any f, g = C[0, 1] define - P(f, 9) = | f (rn) 9(rn)| n=1 2n (a) Show that p(f,g) is well-defined (the above series is convergent). (b) Carefully explain whether or not p is a metric on C[0, 1]. [1 mark] [5 marks] It is known that Q [0,1] is a countable set (do not prove this). Let Qn [0, 1] = {1, 2, ..., rn,... .} be an arbitrary fixed ordering of the elements of Qn [0, 1] in a sequence. For any f, g = C[0, 1] define - P(f, 9) = | f (rn) 9(rn)| n=1 2n (a) Show that p(f,g) is well-defined (the above series is convergent). (b) Carefully explain whether or not p is a metric on C[0, 1]. [1 mark] [5 marks]