Sorry that should read and sup S[itex]\in[/itex]S
just the definitions of sup, inf, boundedness, and max
The Attempt at a Solution
I have tried a few different things, but this question is posted for advice, not just an answer. I am trying to think of a good way to start and we don't use contrapositive proofs in my class. I was thinking I could try proof by contradiction, but then I will have to do 2 cases, first assuming S is not bounded, then assuming supS is not in S. I understand the definitions of the terms, and I could explain why this is true verbally, but I am stuck trying to do it formally. Again, I am not just fishing for an answer, I really need to get these down or I wont pass anyway.