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Math Help - Real Analysis-Supremum

  1. #1
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    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???
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  2. #2
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    Quote Originally Posted by ktina7447 View Post
    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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