Hi.
Let be a bounded real set, the set of upper bounds of has always a minimal element, which is the supremum of
Now for instance, 1):
two bounded real sets.
and and
T or F:
Suppose that A and B are bounded sets in the real numbers.
1) sup (A U B) = max {sup A, sup B}
2) If the elements of A and B are positive and A.B = {ab | a is in A, b is in B}, then sup(A.B) = sup(A)sup(B)
3) The analogous problems for the greatest lower bound.
I believe all of them are true, but just wanted to make sure before I started on the proofs. Thanks!