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Math Help - Show that the sequence is bounded.

  1. #1
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    Show that the sequence is bounded.

    I know that is has to be bounded because its finite, but I'm guessing there is some sort of mathematical proof for this?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by WartonMorton View Post
    I know that is has to be bounded because its finite, but I'm guessing there is some sort of mathematical proof for this?
    Bounded in what sense? That the diameter of the set is finite? This would follow since \Omega=\left\{|a_k-a_j|:a_k,a_j\in S,\text{ }j\ne k\right\} is finite and each element is a finite number and thus \text{diam }S=\max\text{ }\Omega<\infty
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    Quote Originally Posted by Drexel28 View Post
    Bounded in what sense? That the diameter of the set is finite? This would follow since \Omega=\left\{|a_k-a_j|:a_k,a_j\in S,\text{ }j\ne k\right\} is finite and each element is a finite number and thus \text{diam }S=\max\text{ }\Omega<\infty

    I think that is a little advance. We have not talked about diameters of sequences in class. I think what they mean by bounded is something along the lines of like S= {1, 2, 3, ... , 10} where it is bound by 1 and 10.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by WartonMorton View Post
    I think that is a little advance. We have not talked about diameters of sequences in class. I think what they mean by bounded is something along the lines of like S= {1, 2, 3, ... , 10} where it is bound by 1 and 10.
    Well you still haven't defined what you mean by bounded.
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  5. #5
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    Quote Originally Posted by Drexel28 View Post
    Well you still haven't defined what you mean by bounded.

    bounded in the sense of a bounded set..?
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  6. #6
    Super Member Anonymous1's Avatar
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    What Drexel28 is trying to say is...

    Assume that S is finite but not bounded above.

    Set max\{S\}=m_0, but then the set is bounded by m_0.

    Therefore, there must be some m_1\in S: m_1 > m_0, but then the set is bounded by m_1... ad infinitum.

    The set must be infinite to be unbounded.

    A similar argument shows the set is bounded below...
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