Partially Ordered Set

Definition

A partially ordered set is a set with a binary relation (usually $\le$) that is:

• reflexive - $x\le x$
• anti-symmetric: $x\le y$ and $y\le x\to x=y$
• transitive: $x\le y$ and $y\le z\to x\le z$

A partially ordered set is also often referred to as a “poset.”