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Real analysis, Infimum, Supremum [closed]

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Let ∅ 6= A, B ⊆ R and α∈ R. Consider the following subsets:

A + B := {a + b : a ∈ A, b ∈ B}

Show that, if A and B are bounded above, then so is A + B and sup A + B = sup A + sup B.\


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