5. Let (R, p) be the metric space of the real numbers with the discrete metric....

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5. Let (R, p) be the metric space of the real numbers with the discrete metric. (p (x,y)=0 if x=y, p(x,y)=1 if x #y) Let B = [1,4]. a. Is B an open set? Why or why not? b. What are the cluster points of B? Give reasons for your answer. c. In this space (discrete metric) does the sequence (1/n) ne N) converge to 0? Why or why not? 5. Let (R, p) be the metric space of the real numbers with the discrete metric. (p (x,y)=0 if x=y, p(x,y)=1 if x #y) Let B = [1,4]. a. Is B an open set? Why or why not? b. What are the cluster points of B? Give reasons for your answer. c. In this space (discrete metric) does the sequence (1/n) ne N) converge to 0? Why or why not?