Let A and B be bounded nonempty subsets of R, and let A B fa b a 2 A b 2 Bg Prove that sup(A B) sup A sup B and inf(A B) inf A inf B

Question: Let A and B be bounded nonempty subsets of R, and let A B : fa b : a 2 A; b 2

Let A and B be bounded nonempty subsets of R, and let A þ B :¼ fa þ b : a 2 A; b 2 Bg. Prove that sup(A + B) = sup A + sup B and inf(A + B) = inf A + inf B.

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