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Math Help - equivalence relations

  1. #1
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    equivalence relations

    Is xy> 0 an equivalence relation? I cant seem to find which property isnt satisfied
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: equivalence relations

    Let's see...

    From wikipedia:

    A given binary relation ~ on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive. Equivalently, for all a, b and c in A:
    1. a ~ a. (Reflexivity)
    2. if a ~ b then b ~ a. (Symmetry)
    3. if a ~ b and b ~ c then a ~ c. (Transitivity)


    Did you check these?
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  3. #3
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    Re: equivalence relations

    Quote Originally Posted by ILikeSerena View Post
    Let's see...

    From wikipedia:

    A given binary relation ~ on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive. Equivalently, for all a, b and c in A:
    1. a ~ a. (Reflexivity)
    2. if a ~ b then b ~ a. (Symmetry)
    3. if a ~ b and b ~ c then a ~ c. (Transitivity)


    Did you check these?
    Yeah, it seems to me that all 3 are satisfied but I think Im missing something
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: equivalence relations

    Let's start with the first.

    For all a you need that a~a.
    What does that mean for your relationship?
    What are the possibilities for a?
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  5. #5
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    Re: equivalence relations

    Quote Originally Posted by ILikeSerena View Post
    Let's start with the first.

    For all a you need that a~a.
    What does that mean for your relationship?
    What are the possibilities for a?
    a would either be positive or negative, and aa > 0 regardless of whether the number is positive or negative
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  6. #6
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    Re: equivalence relations

    Quote Originally Posted by qwerty31 View Post
    a would either be positive or negative, and aa > 0 regardless of whether the number is positive or negative
    HINT: Is 0>0~?
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  7. #7
    Super Member ILikeSerena's Avatar
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    Re: equivalence relations

    Quote Originally Posted by qwerty31 View Post
    a would either be positive or negative, and aa > 0 regardless of whether the number is positive or negative
    What about a=0?
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