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1. (a) Let S be a nonempty set of real numbers that is bounded above. Prove...

1. (a) Let S be a nonempty set of real numbers that is bounded above. Prove that if u and v are both least upper bounds of S, then u = v.
(b) Let a > 0 be a real number. Define S := {1 − a n : n ∈ N}. Prove that if epsilon > 0, then there is an element x ∈ S such that x > 1−epsilon.

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