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(III) If 0 ≤ a < ε for all ε > 0, then show that a...

(III) If 0 ≤ a < ε for all ε > 0, then show that a = 0. Using this conclude that if b ≤ a < b + ε for all ε > 0, then a = b. Hint: On contrary assume that a ≠ 0, then a > 0. Now choose your ε > 0 in a clever way to get a contraction.

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