Question

Real Analysis sup and inf question...

Answer 1

Sorry, that reads, Let A and B be non empty bounded subsets of R.
Determine a formula for inf(A+B) and sup(A+B) in terms of the infim aand suprema of A and B. Prove that your formulas are correct.

Answer 2

\[A+B={x+y:x \in A, y \in B}\]

Answer 3

We know that if A is non empity and bounded set, exist an a in A such that a<= x for all x in A, then infA =a and similarly for B: inf B = b. Therefore inf(A+B) = a+b <= sup(A+B) = sup(A) + sup(B)