(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A and B be nonempty bounded subsets of R. Show that sup(AUB)=max(sup(A),sup(B))

Or another version of this problem:

Show that if A and B are bounded subsets of R, then AUB is a bounded set. Show that sup(AUB)=sup(supA, supB)

3. The attempt at a solution

Hi! I have hard time visualizing this problem. Would you help me understand it visually? What should think of first when trying to solve this problem?

Does it matter at all if the subsets look like this or not?:

_____[ A ]______[ B ]_____

VS

_____{ A [ } B ]________

The solutions to this problem seems not to care about that. That's why I am confused.

For example, in the first version of the problem, they only care if sup A is equal, greater, or less than sup B. They somehow don't care if the subsets overlap or not.

And this bothers me a lot! :-(

Thank you in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show that sup(AUB)=max(sup(A),sup(B))

**Physics Forums | Science Articles, Homework Help, Discussion**