Thread: Real Analysis-Supremum

1. Real Analysis-Supremum

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???

2. Originally Posted by ktina7447
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???
In analysis clarity is essential, so you should first improve the statement of your problem to something like:

Prove that 1 is the supremum of [0,1].

The expand on what this means:

So we need to prove that 1 is an upper bond for [0,1], and that if a is any upper bound for [0,1] then 1<=a.

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