Then, element of
Then, is an upper bound.
Thus, if the least upper bound exists.
Which is true because any negative is strictly less than a positive.
Use the completeness property. are upper bounded. Then, is upper bounded. Thus, by completeness it has a least upper bound.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.