Question

Let A and B be nonempty bounded subsets of the real numbers.
a ) Explain why the union, AUB has a supremum.

Answer 1

for supremum to exist, the sets should be bounded from above and are nonempty. Since the question said that we have 2 bounded non-empty sets and since A and B are both subsets of R (all real numbers), then we say that A U B has a supremum

hmm, I hope this made it clear for you :)

Answer 2

Moreover, no matter how many elements are found in AUB , they're still less than the Real number sequence, so that's why AUB has a supremum ^_^