Directed sets are a generalization of nonempty totally ordered sets, that is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed).
That is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed). Directed sets are a generalization of nonempty totally ordered sets.
Directed sets are a generalization of nonempty totally ordered sets. That is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed).
Directed sets are a generalization of nonempty totally ordered sets. That is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed).