then the transitivity of ≤ ensures that for all a and b in X, we have
There can be sets $S$ of cardinal number less than $X$ such that P is isomorphism to the containment order on S. The size of the smallest possible S is called the 2dimension of S.
Several important classes of poset arise as containment orders for some natural collections, like the Boolean lattice Q^{n}, which is the collection of all 2^{ n} subsets of an nelement set, the intervalcontainment orders, which are precisely the orders of order dimension at most two, and the dimension n orders, which are the containment orders on collections of nboxes anchored at the origin. Other containment orders that are interesting in their own right include the circle orders, which arise from disks in the plane, and the angle orders.

