", although in the decade
s since their introduction, poset
s 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
- x L x for every x ∈ E.
- 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.