In
mathematics, especially
order theory, a
partially ordered set (or
poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a
set. A poset consists of a set together with a
binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other. Such a relation is called a
partial order to reflect the fact that not every pair of elements need be related: for some pairs, it may be that neither element precedes the other in the poset. Thus, partial orders generalize the more familiar
total orders, in which every pair is related. A finite poset can be visualized through its
Hasse diagram, which depicts the ordering relation.