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Math Help - inequality

  1. #1
    key
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    inequality

    prove that |a+b|< |a|+|b| is true for all reall numbers
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  2. #2
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    Quote Originally Posted by key View Post
    prove that |a+b|< |a|+|b| is true for all reall numbers
    If a\geq 0 we end up with:
    |a+b|\leq a + |b|.
    Now if -a\leq b <0 we have:
    a+b\leq a + |b| \implies b\leq |b| which is true.
    And if 0\leq b we have:
    a+b\leq a+b which is true.
    Now if a<0 let a=-c where c>0 so:
    |a+b|\leq |a|+|b| \implies |c+(-b)| \leq |c|+|-b|.
    Which we established above already.
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