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I need help ly asap proving that -0=0

  1. Sep 18, 2008 #1
    I need help urgently asap proving that -0=0

    1. The problem statement, all variables and given/known data
    Prove that
    0=-0

    2. Relevant equations

    We Can use only the following axioms for Real Numbers

    (x+y)+z=x+(y+z); (xy)z=x(yz)
    x+y=y+x; xy=yx
    x(y+z)=(xy)+(xz)
    The Additive Identity 0+x=x
    The Additive Inverse for all x in the real numbers there exists -x, such that x+(-x)=0
    Multipicative Identity There exists an element 1, such that x*1=x
    Mult. Inverse There exists for all x an inverse (1/x), such that x(1/x)=1
    If x is in the real numbers than one of the following is true
    x is positive
    x is 0
    -x is positive

    You can also add or multiply the same thing to both sides of the equation


    3. The attempt at a solution

    We know that x+(-x)=0
    thus, we see that -(x+(-x))=-0

    I'm not sure where i can go next. We can use the distributive property, but would we be allowed to use it in this situation with the (-).
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Sep 18, 2008
  2. jcsd
  3. Sep 18, 2008 #2
    Re: I need help urgently asap proving that -0=0

    Why not prove that any real number multiplied by 0 is 0, and so as a consequence of that, -0 = -1*0 = 0
     
  4. Sep 18, 2008 #3
    Re: I need help urgently asap proving that -0=0

    what about this

    start out with the true statement: 0=0
    using additive inverse: 0+(-0)=0
    which is an additive identity for: -0=0
     
  5. Sep 18, 2008 #4
    Re: I need help urgently asap proving that -0=0

    Another:

    Let be x de inverse additive of 0 (that is -0), then by definition:

    0+x=0

    Since 0 is the additive identity:

    x=0
     
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