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Math Help - absolute value proof

  1. #1
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    absolute value proof

    let x1, x2, ..., xn-1,xn be in R and n be in N prov that |x1+x2+...+xn-1+xn| is less than or equal to |x1|+|x2|+...+|xn-1|+|xn|

    hint use induction and triangle inequality
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  2. #2
    MHF Contributor

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    Can you prove the simplest case? If a and b are real numbers, what can you say about |a+ b| and |a|+ |b|. Try cases:
    1) a and b both \ge 0.
    2) a\ge 0, b< 0.
    3) a< 0, b\ge 0.
    4) a< 0 and b< 0.

    If you can do that, think of x_1+ x_2+ \cdot\cdot\cdot+ x_{n-1}+ x_n as (x_1+ x_2+ \cdot\cdot\cdot+ x_{n-1})+ x_n
    and prove this by induction on n.
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