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