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Math Help - Proof with inequalities

  1. #1
    Senior Member chella182's Avatar
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    Proof with inequalities

    Sorry if this is in the wrong place, couldn't think of where to put this; the module's called The Foundations of Calculus, but yeah...

    Suppose that \epsilon>0. Prove that if x,l,y\in\mathbb{R} and |x-l|,|y-l|<\frac{\epsilon}{2} then |x-y|<\epsilon.

    I've tried a few stuff with the triangle inequalities and what not and they've lead no where

    Cheers in advance.
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  2. #2
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    |x-y|=|x-l-y+l|\leq |x-l|+|l-y|=|x-l|+|y-l|<2\frac{\epsilon}{2}=\epsilon
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  3. #3
    Senior Member chella182's Avatar
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    Thanks.
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