So i have to write a proof for [0,1] where 1 is the supremum (least upperbound) of [0,1]. So far this is what I have..

Pf: Claim 1 is an upperbound of [0,1] for all a in set [0,1] when a ≤ 1. Since this is true we've shown that 1 is an upperbound. For every b when b is an upperbound of [0,1] and b ≥ 1. We must prove this...

I don't know if this is right, and if it is where do I go from here???