ordered set in a sentence

Examples

1. The position of each element within the ordered set is also given by an ordinal number.
2. Every non-empty well-ordered set has a least element.
3. The set of all Dedekind cuts is itself a linearly ordered set ( of sets ).
4. An abstract polytope is a partially ordered set of elements or members, which obeys certain rules.
5. This proof is similar to the proof that an order embedding between partially ordered sets is injective.
6. A totally ordered set ( with its order topology ) which is a complete lattice is compact.
7. Replace each well-ordered set with its ordinal.
8. Every non-empty totally ordered set is directed.
9. As ordered sets, they are quite different.
10. It begins by defining well-ordered sets.