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Proof with real numbers

  1. Jan 5, 2009 #1
    1. The problem statement, all variables and given/known data

    For real numbers x(1), x(2), ..., x(n), prove that |x(1) + x(2) +...+x(n)| <= |x(1)|+...|(n)|

    2. Relevant equations

    3. The attempt at a solution

    Maybe begin with prooving that x <= |x| ? Im not sure how to do this though.
    Any help or hints would be great, as im really stuck on this.
  2. jcsd
  3. Jan 5, 2009 #2


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    Homework Helper

    First of all, one can prove that, for some real numbers a, b, |a + b| <= |a| + |b|. Any ideas how to generalize? Try to use this inequality to show that |a + b + c| <= |a| + |b| + |c|, for some given real numbers, a, b and c.
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