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Closed non-commutative operation on N

  1. Mar 25, 2009 #1
    The problem statement, all variables and given/known data

    (i) Give an example of a closed non-commutative binary operation on N (the set of all natural numbers).
    (ii) Give an example of a closed non-associative binary operation on N.

    The attempt at a solution
    This has me stumped, there must be something simple that I'm missing. I was thinking divisibility ('|')...

    EDIT: Looking back at my first topic, wow, I've come a long way since when I last posted
     
    Last edited: Mar 25, 2009
  2. jcsd
  3. Mar 25, 2009 #2

    CompuChip

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    Note that a binary operation goes from N x N into N again. Divisibility is therefore not a really good example, for example, which number is 3 | 6? What does (3 | 6) | 4 mean?

    Instead, try something simpler. I think you can even use the same counterexample for both. Let me give you a hint:
    3 - 5 = - (5 - 3).
     
  4. Mar 25, 2009 #3
    Okay, that clears some things up, thanks.
    I need to use a counter-example?
    I still can't work it out, sorry. I think that your hint went clear over my head.

    I can't use subtraction (as it is not a closed operation in N), can I?
     
  5. Mar 25, 2009 #4

    HallsofIvy

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    Then define a new operation. For example, x*y= 2x+ y is clearly non-commutative.
     
  6. Mar 25, 2009 #5
    Ah, thank you very much. I wasn't looking at the questions broadly enough. :)
     
  7. Mar 26, 2009 #6

    CompuChip

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    Sorry, I meant example instead of counterexample.
    And I thought it said Z in which N is indeed closed.
    My apologies.
     
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