A poset is a set E equipped with a partial order, that is, a binary relation L (usually given the symbol "less than or equal to") which is

- reflexive
- x L x for every x ∈ E.
- transitive
- if x L y and y L z, then x L z.
- (weakly) antisymmetric
- if x L y and y L x, then x = y.

*Ordinary differential equations in the complex domain*, "the fowl in a hen-yard are partially ordered under the pecking order."

Posets are important in several areas of mathematics and computer science, including logic, set theory, functional analysis, combinatorics, semantics and type theory, and the study of algorithms.