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Equivalance classes and integer addition

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove: If a and b are in N the [(1,1+a)] + [(1,1+b)] = [(1,1+a+b)]


    2. Relevant equations
    Definition: We define + over Z as follows: if [(a,b)] and [(c,d)] are any two equivalence classes, we define

    [(a,b)] + [(c,d)] = [(a+c,b+d)].


    3. The attempt at a solution

    So the left hand is [(2,2+a+b)] since 2, a, b are all [tex]\in[/tex] N does this mean this is equivalent to [(1,1+a+b)]?
     
  2. jcsd
  3. Nov 20, 2009 #2

    HallsofIvy

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    What is the equivalence relation?

    One way of defining Z from N is to say that two pairs of natural numbers, (a, b) and (c, d) are equivalent if and only if a+ d= b+ c. Is that the equivalence relation you are using?
     
  4. Nov 20, 2009 #3
    ahh..yes yes it is. i didnt quit understand my notes. i got the solution, thanks for clearing it up
     
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