Partial Ordering/Examples/Arbitrary Example 1

Example of Partial Ordering

Let $X = \set {x, y, z}$.

Let $\RR = \set {\tuple {x, x}, \tuple {x, y}, \tuple {x, z}, \tuple {y, y}, \tuple {z, z} }$.

Then $\RR$ is a partial ordering on $X$.

The strict partial ordering on $X$ corresponding to $\RR$ is its reflexive reduction:

$\RR^{\ne} = \set {\tuple {x, y}, \tuple {x, z} }$

Sources

• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: $(0)$