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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Originally Posted by Juancd08 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 $\displaystyle E\subseteq S\times S$ so that $\displaystyle (a,b) \in E$ if and only if $\displaystyle a,b$ lie in the same partition set.
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