Let S,T be non-empty bounded subsets of the real numbers. Prove that is bounded above.
How would you start this question?
If are upper bounds for and respectively, prove that for all .
Fernando Revilla
It is right, I said
upper bounds, not minimum upper bounds.
Oryou should take max{s,t}
Fernando Revilla
I think I can see the general idea, but am having trouble writing a formal proof. Here is what I have thus far:
Let and such that are upper bounds for S and T respectively.
If we set max{ }, then:
. Therefore is bounded above.
Is this along the right lines or am I way off?