1. If E has a supremum, prove that it has only one supremum.

'Was thinking about taking the approach: Suppose E has 2 supremums and prove that it is false. Help on ideas to approach and make this flow will help me lots.

2. Prove that if M is an upperbound of a set E and M is in E, then M is the supremum of E.

Again help on where to go and flow with this one too. I so wish I could wrap my head around these proofs and understand them more. I think having taken all the calc's 15 years ago is part of my problem.