Thread: Advanced 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)

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.