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Set theory

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data
    zu3x5e.png


    2. Relevant equations
    An equivalence relation on a set A, is for a,b,c in A if:
    a~a
    a~b => b~a
    a~b and b~c => a~c


    3. The attempt at a solution
    It seems uncomplicated, but I don't know how I would write down a proof. The book I'm using is Topics in Algebra, 1st Edition Herstein
     
  2. jcsd
  3. Sep 13, 2010 #2

    jgens

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    Gold Member

    What if there were some element [itex]a \in A[/itex] which wasn't related to any other member of [itex]A[/itex]?
     
  4. Sep 13, 2010 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    In other words, consider A= {1, 2, 3} and the relation is {(1, 1), (1,2), (2,1), (2,2)},
     
  5. Sep 13, 2010 #4
    I don't understand this. I think equivalence classes are generalized equal signs for some property. So (1,1) I understand, but how so for (1,2)?
     
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