Partially Ordered Sets

A partially ordered set (poset) is a collection of elements where some pairs can be compared to see which is "greater" or "smaller," but not necessarily all. Think of tasks with dependencies: some must be completed before others, but some are independent. In a poset, this relation is transitive (if A is before B and B before C, then A is before C), reflexive (each element is related to itself), and antisymmetric (if A is before B and B before A, then they are the same). Posets help model situations where not everything is directly comparable but a hierarchy or ordering exists among some elements.