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Homework Help: Prove a+b=b+a for integers

  1. Apr 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that for any two integers a and b, a+b=b+a. You may use the face that this holds for natural numbers.

    2. Relevant equations

    3. The attempt at a solution
    a=(x,y), b=(u,v)
    x,y,u,v are natural numbers
    a+b = (x,y)+(u,v) = (u,v)+ (x,y) = b+a

    I'm not sure if my attempt was correct.
  2. jcsd
  3. Apr 15, 2009 #2
    This step assumes the conclusion. You have to prove it.

    Hint: What is the definition of (x,y)+(u,v)?
  4. Apr 15, 2009 #3


    Staff: Mentor

    What do the equations above mean? a and b are integers, not ordered pairs.
  5. Apr 15, 2009 #4


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    Staff Emeritus
    Science Advisor
    Gold Member

    I suspect the opening poster forgot to tell us that he's working with a specific presentation of the integers -- represented as the set of ordered pairs of natural numbers modulo an equivalence relation -- along with the definition of + that he's using.

    (Of course, maybe that's exactly what you were prompting the opening poster to say -- if so, sorry 'bout that)
  6. Apr 15, 2009 #5


    Staff: Mentor

    Nope, I wasn't thinking that at all, so no problem.
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