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Simple Apparent contradiction?

  1. Jul 11, 2012 #1
    I came across this when doing another problem:

    Suppose we have 2 numbers, (a+b) and (c+d), which both equal 0.

    a+b=0
    c+d=0

    Then a+b=0=c+d,
    Thus, a+b=c+d

    However, a+b+c+d=0
    Thus, a+b=-c-d

    Therefore, a+b=c+d AND a+b=-(c+d)

    How is this possible?
     
  2. jcsd
  3. Jul 11, 2012 #2

    chiro

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    Science Advisor

    Hey Gamerex and welcome to the forums.

    The simple answer is that -0 = +0 = 0. That's the basic argument for a problem like this.
     
  4. Jul 11, 2012 #3

    Curious3141

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    Homework Helper

    No contradiction. The only solution to the equation x = -x is x = 0, which you can verify.
     
  5. Jul 12, 2012 #4

    Mentallic

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    Homework Helper

    Therefore,

    c+d=-(c+d)
    2(c+d)=0
    c+d=0

    No problem there.
     
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