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Math Help - Test

  1. #1
    Junior Member
    Joined
    Jan 2010
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    33

    Test

    The Problem: Let S = (0,1)

    Prove for each \varepsilon > 0 there exist an x  \in S such that x < \varepsilon .

    Solution:

    For every \varepsilon > 0, 0 < \frac{\varepsilon }{2} < \varepsilon

    Consider \frac{\varepsilon }{2} and x = \frac{1}{2}
    then

    x < \varepsilon

     \Leftrightarrow \frac{1}{2} < \frac{\varepsilon }{2}

     \Leftrightarrow 1 < \varepsilon

    Thus

    \varepsilon > 0 and \varepsilon = 1 > x = \frac{1}{2}

    Therefore x <
    \varepsilon

    Q.E.D
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  2. #2
    MHF Contributor
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    Re: Test

    See my post in the other forum.
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