The SlugMath Wiki is under heavy development!

# Def/Partial order

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

##### Toolbox
#Google analytics tracking #End tracking code