Suprema

[mikedwiener]

I think the answer is Sup(A+B) = Sup(A) + Sup(B), but I need a proof. The sets do not have to be finite.
Define A + B = {x + y : x e A and y e B}.


Compute sup (A + B) in terms of sup (A) and sup (B). Repeat exercise for


inf (A + B). Justify your answer.

 

[daon2]

You need a proof, so what is stopping you? How do you prove a number is the supremum for a set?