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Math Help - proofs

  1. #1
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    proofs

    given that S=( 0,1), show that the max S doesnt exist.

    to show that, my notes states that:

    let M ∈ S and M= max S.

    take M* = (M+1)/2

    then we need to show that M* ∈ S and that M < M*...

    mayb i know if there is a fixed method that i can adopt whener i have to solve proving questions?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    given that S=( 0,1), show that the max S doesnt exist.
    to show that, my notes states that:
    let M ∈ S and M= max S.
    take M* = (M+1)/2
    then we need to show that M* ∈ S and that M < M*...
    This is always true.
    If a<b then a<\frac{a+b}{2}<b.
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Well suppose there was an x \in S with y<x for all y \in S. Clearly we would need to have x<1, because all elements of S are <1. Thus the open interval (x,1) is not empty, and all of its elements are in S and all of them are greater than x - this clearly contradicts the definition of x.
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