If (X, d) is any metric space, show that another metric on X is defined by c(x y)= d(x,y) /1+d(x,y) and X is bounded in the metric c.

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If (X, d) is any metric space, show that another metric on X is defined by

c(x y)= d(x,y) /1+d(x,y)

and X is bounded in the metric c.

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