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Math Help - Proof by cases

  1. #1
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    Proof by cases

    I need to use a proof by cases to show that for all real numbers :

    |xy| = |x| |y| Could someone please get me started.

    I think if x >or = to 0 and y> or = 0 then |x| = x and |y| = y so xy = |xy|= |x| |y|
    and if x< 0 and y<0 then |x| = -x and |y| = -y and since -x(-y) = xy I can go to same as above. Is this right????
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  2. #2
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    Quote Originally Posted by frostking2 View Post
    I need to use a proof by cases to show that for all real numbers :
    |xy| = |x| |y| Could someone please get me started.
    I think if x >or = to 0 and y> or = 0 then |x| = x and |y| = y so xy = |xy|= |x| |y| and if x< 0 and y<0 then |x| = -x and |y| = -y and since -x(-y) = xy I can go to same as above. Is this right????
    Yes it is correct.
    Now finish: take one nonnegative and one negative.
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