Two different but equivalent definitions of a partial ordering are possible. The first is a generalization of the usual ← operation in which the relation must be a transitive, antisymmetric, and reflexive relation defined on the set S. The second definition is a generalization of the usual < operation in which the relation must be a transitive, asymmetric, and irreflexive relation defined on S. A set with a partial ordering defined on it is called a partially ordered set or sometimes a poset.
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