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(-a)(-b)=(ab) proof

  1. Jun 26, 2009 #1
    Hey All,
    I found this proof on the internet, but its logic seems flawed.
    Let x = (-a)(-b)
    =(-1 * a)(-1 * b)
    =-1 * a * -1 * b
    =-1 * -1 * a * b
    =(-1 * -1)(a * b)
    = ab
    So it's saying that (-a)(-b) = ab. This doesn't seem like a logical proof, or at least a satisfying one. Using what you're trying to prove in the proof itself seems wrong. It's trying to prove that two negatives multiplied together equal a positive, but it's using (-1 * -1) in the proof before it's been proven.
    I'm trying to learn proofs, and this just seemed wrong, and I wanted clarification.
    I appreciate any feedback.
  2. jcsd
  3. Jun 26, 2009 #2


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    Gold Member

    Read further back in whatever source you're using -- this was probably proven earlier. Specifically, it seems to have already proven/assumed that [itex](-x) = (-1) * x[/itex], and I bet has also shown that [itex]-(-x)=x[/itex].
  4. Jun 26, 2009 #3
    Thanks for the reply. I"ll check on what you suggested.
    BTW, Is there a software program that makes posting math symbols easier?
    Maybe a graphics program where I can just post an image?
  5. Jun 27, 2009 #4


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    Science Advisor

    On this board you can use LaTex. Just surround your code with [ tex ] and [ /tex] or [ itex] and [ /itex] (without the spaces):
    [tex]\int_{-\infty}^\infty} e^{-x^2}dx[/tex]

    Click on that to see the code. There is also a thread about LaTex on this board.
  6. Jun 27, 2009 #5
    Thanks for the info, both of you.
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