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Math Help - Abstract Algebra

  1. #1
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    Abstract Algebra

    Conversely if P is a partition of a set S, then there is some equivalence relation R on S such that P is the set of all equivalence classes.

    I can prove the reverse but I need help going through it with this direction.
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  2. #2
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    Quote Originally Posted by Juancd08 View Post
    Conversely if P is a partition of a set S, then there is some equivalence relation R on S such that P is the set of all equivalence classes.

    I can prove the reverse but I need help going through it with this direction.
    Define E\subseteq S\times S so that (a,b) \in E if and only if a,b lie in the same partition set.
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