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Math Help - Equivalence relation and total ordering problem

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    Equivalence relation and total ordering problem

    Let R denote a relation defined on a set A as follows: xRy iff x<=y where <= is a total ordering on A. Can R be an equivalence relation on A?
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    Quote Originally Posted by jsteel2 View Post
    Let R denote a relation defined on a set A as follows: xRy iff x<=y where <= is a total ordering on A. Can R be an equivalence relation on A?
    What if the set only contains one element.
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    So the argument is that R can only be an equivalence relation if the set A has atleast two elements?
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    Quote Originally Posted by jsteel2 View Post
    So the argument is that R can only be an equivalence relation if the set A has atleast two elements?
    The question is "Can R be an equivalence relation on A?" so if the answer is yes, you only need to find one example then you're done. I believe the one-element set is the simplest example... for example A = {1} and R = {A,A,{(1,1)}}.
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