In the
mathematical area of
order theory, every
partially ordered set P gives rise to a
dual (or
opposite) partially ordered set which is often denoted by
Pop or
Pd. This dual order
Pop is defined to be the set with the
inverse order, i.e.
x =
y holds in
Pop if and only if y =
x holds in
P. It is easy to see that this construction, which can be depicted by flipping the
Hasse diagram for
P upside down, will indeed yield a partially ordered set. In a broader sense, two
posets are also said to be duals if they are
dually isomorphic, i.e. if one poset is
order isomorphic to the dual of the other.