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Is this group associative

  1. Feb 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Im looking at this example and trying to figure out how they showed it was associative.
    They start out with x*y=x+y+1
    then they add in z to show it is associative.
    x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2
    I dont know how they go from
    this x*(y+z+1)=x+(y+z+1)+1
    and end up with the equation on the right.
    If i solved for x from x*y=x+y+1 and plugged it in I wouldn't get what they got.
    Maybe there is some trick that I am missing.
     
  2. jcsd
  3. Feb 13, 2013 #2

    haruspex

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    They're simply applying the rule for *. If the general rule is x'*y'=x'+y'+1, and you have x*(y+z+1) then you can match up x' with x and y' with (y+z+1):
    x*(y+z+1) = x'*y' = x'+y'+1 = x+(y+z+1)+1
    What do you mean you 'solved it'? The * doesn't stand for normal multiplication here. x*y=x+y+1 is defining an operation '*'.
     
  4. Feb 13, 2013 #3
    oh ok i see now, thanks for your help.
     
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