1(i) Show, if (X, d) is a metric space, then d∗ : X × X → [0,∞)
defined by d∗(x, y) = d(x, y) /1 + d(x, y) is a metric on X. Feel
free to use the fact: if a, b are nonnegative real numbers and a ≤
b, then a/1+a ≤ b/1+b .
1(ii) Suppose A ⊂ B ⊂ R. Show, if A is not empty and B is
bounded below, then both inf(A) and inf(B) exist and...