1) Let A and B be a subsets of the real numbers with least upper bound u and v. Prove that their union has a least upper bound, and express it in terms of u and v.
2) Let A be the set of negative real numbers. Prove that 0 is equal to the least upper bound of A.
Hint: one needs to check that 0 is an upper bound and if x < 0 then 0 is not an upper bound; i.e., there is some y in A such that x < y.
I am soo sorry to keep on asking questions, but Math is reallly hard for me. Thank you very much in advance.