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Is there a proof od negative numbers?

  1. Sep 8, 2008 #1
    Hi everyone!

    This may be a stupid question but is there a proof of negative numbers? Specifically why does this work -a(-b)=c I was trying to explain it to someone and drew a blank.

    Thanks!
     
  2. jcsd
  3. Sep 8, 2008 #2
    Are you asking why two negatives multiplied produces a positive? If so, here's a proof I once read:


    Let x = ab + (-a)(b) + (-a)(-b)


    Then, x = ab + -a(b-b)
    = ab -a(0)
    = ab - 0
    = ab

    However, we also have x = b(a -a) + (-a)(-b)
    = (-a)(-b)

    Therefore, ab = (-a)(-b). QED.

    Hope that's what you wanted.
     
  4. Sep 8, 2008 #3
    Thanks i just couldn't logically reason it!
     
  5. Sep 9, 2008 #4
    1 is the identity and -1 can only change the sign. Since (-1) ab = -ab. Thus the absolute value of (-1)(-1) = 1. So we have only the choices (-1)(-1) = 1 or
    (-1)(-1) = -1.
     
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