I really need some help with this problem. Let A and B be sets of real numbers. Define a set A + B by A+B={a+b l a is in A and b is in B} Show that if A and B are bounded sets then, l.u.b.(A+B)=(l.u.b. A) + (l.u.b. B)
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Suppose the LUB (A+B) > LUB A + LUB B and arrive at a contradiction. Suppose the LUB (A+B) < LUB A + LUB B and arrive at a contradiction. Remember that we can find numbers in C as close to LUB C without exceeding it as we like.
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