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Math Help - Using cases in proofs

  1. #1
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    Using cases in proofs

    Hi, does anybody know how to prove the following statement:

    For each real number r, -|r| r |r|.

    by using two cases in the proof.
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  2. #2
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    Quote Originally Posted by fruitcakelover View Post
    Hi, does anybody know how to prove the following statement:

    For each real number r, -|r| r |r|.

    by using two cases in the proof.
    Given x\in \mathbb{R} we define |x| = x \mbox{ if }x\geq 0 \mbox{ and }|x| = -x\mbox{ if }x<0.

    Case 1, when x\geq 0. Thus |x|=x. And so we need to prove -x\leq x\leq x. Which is true since x\leq x and -x<0\leq x.

    Case 2, when x<0. You continue.
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