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No. of binary operations?

  1. Jan 22, 2009 #1


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    1. The problem statement, all variables and given/known data
    How many different commutative binary operations can be defined on a set of 2 elements? On a set of 3 elements?

    3. The attempt at a solution
    I do not understand the question. Seems like an infinite number.
  2. jcsd
  3. Jan 22, 2009 #2


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    If '*' is the operation and {a,b} is the set of two elements, then to define the operation you need to define a*a, a*b, b*a and b*b in the set {a,b}. That's hardly an infinite number of possibilities.
  4. Jan 23, 2009 #3


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    Got it. Just confused at the time.
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