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Math Help - Absolute value proofs

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    Absolute value proofs

    Prove the following

    1) ||x|-|y|| is less than or equal to |x-y|.

    2) If |x-y| < E for all E > 0, then x = y.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by noles2188 View Post
    Prove the following

    1) ||x|-|y|| is less than or equal to |x-y|.
    see here

    2) If |x-y| < E for all E > 0, then x = y.
    use the contrapositive.

    that is, show that if x \ne y, then there is some \epsilon > 0 for which |x - y| \ge \epsilon

    (you need to know the definition of absolute values here)
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