1(i) Show, if (X, d) is a metric space, then d∗ : X × X →...

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 moreover, inf(A) ≥ inf(B).

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Colby Messinger answered 1 year ago

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