Contraction of "

partially

ordered

set", although in the

decades since their introduction,

posets have proven to be

fundamental enough to

deserve their own

word, and not have to be a

partial anything.

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.

As Einar Hille put it in his nice little book

*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.