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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- September 22nd 2008, 02:25 PMredraider8200Advanced Calculus
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) - September 22nd 2008, 02:32 PMicemanfan
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.