Chapter2
from above, so sup(A+B) exists if and only if both supA and supB exist. In that case, if x ∈ A and y ∈ B, then x+y ≤ supA+supB, so supA +supB is an upper bound of A +B and therefore sup(A +B) ≤ supA+supB. To get the inequality in the opposite direction, suppose that ǫ > 0. Then there
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