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Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤...

Question 3. Let a1,...,an ∈R. Prove that
(a1 + a2 + ... + an)2 /n ≤ (a1)2 + (a2)2 + ... + (an)2.
Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T).
Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above and T is bounded below. Let U = {t−s|t ∈ T, s ∈ S}. Prove that U is bounded below and inf(U) = inf(T)−sup(S).

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