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Def/Partial order
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Definition of Partial order: Suppose that $X$ is a set, and $R$ is a relation on $X$. Then, $R$ is called a partial order on $X$, if $R$ is reflexive, transitive, and antisymmetric.
When $R$ is a partial order on $X$, the pair $(X,R)$ is called a partially ordered set or poset.
Logical Connections
This definition logically relies on the following definitions and statements: Def/Binary relation, Def/Reflexive relation, Def/Transitive relation, Def/Antisymmetric relation
The following statements and definitions logically rely on the material of this page: Def/Maximal element, Def/Minimal element, Def/Total order, and Def/Upper bound
To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Ordered sets, Clust/Relations
