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Math Help - Proof help

  1. #1
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    Proof help

    Theorem:
    Suppose
    m,n eN are such that

    n >= m. Then n = m + b if and only if b = n - m.

    The problem:
    Suppose x,y,z e N are such that y <= x and z <= x. THen, x - y = z if and only if x - z = y.

    I must prove this problem as a consequence of the above theorem...any advice?
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  2. #2
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    Hi

    You just have to use your theorem twice.

    y,z\leq x, so you know that z=x-y\Leftrightarrow x=z+y. That was a first time, now, with the theorem and addition commutativity:


    x=z+y\Leftrightarrow ...?
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  3. #3
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    I'm still not seeing how to prove it?? Any more advice?
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  4. #4
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    Do you agree with what I've done?
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  5. #5
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    Nevermind...I figured it out. Thanks for all your help!
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  6. #6
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    Quote Originally Posted by jzellt View Post
    Nevermind...I figured it out. Thanks for all your help!
    jzelt are you sure the problem is correct??
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  7. #7
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    Yes, the problem is correct!
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