| 41. | The position of each element within the ordered set is also given by an ordinal number.
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| 42. | Every non-empty well-ordered set has a least element.
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| 43. | The set of all Dedekind cuts is itself a linearly ordered set ( of sets ).
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| 44. | An abstract polytope is a partially ordered set of elements or members, which obeys certain rules.
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| 45. | This proof is similar to the proof that an order embedding between partially ordered sets is injective.
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| 46. | A totally ordered set ( with its order topology ) which is a complete lattice is compact.
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| 47. | Replace each well-ordered set with its ordinal.
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| 48. | Every non-empty totally ordered set is directed.
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| 49. | As ordered sets, they are quite different.
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| 50. | It begins by defining well-ordered sets.
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