Let d denote the usual metric on R and consider the metric e on R

given by e(x, y) = |x − y|/(1 + |x − y|). (You may assume e is a

metric.)

In (R, e), show that B(0, 1) = R, and find B(0,1/3).

Can someone please explain simply what I would have to do to get 4 marks?

Thanks in advance!