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Math Help - modulo

  1. #1
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    modulo

    i was wondering, is l a-b l< lal - lbl?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    a=3, b=2
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  3. #3
    MHF Contributor Unknown008's Avatar
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    Or put a = 0, b = 1
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  4. #4
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    \displaystyle (|a-b|)^2\geq (|a|-|b|)^2

    \displaystyle (|a-b|)^2=(a-b)(a-b)=a^2-2ab+b^2=|a|^2-2ab+|b|^2\geq |a|^2-2|a||b|+|b|^2=(|a|-|b|)^2

    Now take the square root of both sides and we prove the inequality (triangle inequality).

    \displaystyle (|a-b|)^2\geq (|a|-|b|)^2\rightarrow  |a-b|\geq |a|-|b|
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