31. A sequence is usually indexed by the natural numbers, which are a totally ordered set . 32. These concepts generalize respectively those of preordered set, partially ordered set and totally ordered set. 33. One can also glue together different linearly ordered sets to form a circularly ordered set. 34. This theorem provides, for example, a technique to characterize elements and gaps in ordered sets . 35. These concepts generalize respectively those of preordered set, partially ordered set and totally ordered set . 36. Join and meet are symmetric totally ordered set is simply its maximal / minimal element. 37. The lexicographic order of totally ordered sets is however a linear extension of their product order. 38. As mentioned before, domain theory deals with partially ordered sets to model a domain of computation. 39. Subsets of partially ordered sets inherit the order. 40. Let P be a finite partially ordered set .
