| 11. | *An example comes from reversing the direction of inequalities in a partial order.
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| 12. | Below are four different Hasse diagrams for this partial order.
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| 13. | Not every partial order obeys the transitive law for incomparability.
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| 14. | When a partial order is negative, the overall order is usually considered as undefined.
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| 15. | The specialization order yields a tool to obtain a partial order from every topology.
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| 16. | The permutations for which this partial order is series-parallel are exactly the separable permutations.
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| 17. | A group " G " with a partial order is called an ordered group.
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| 18. | The defining axioms of effect algebras guarantee that d " is a partial order.
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| 19. | In the following, partial orders will usually just be denoted by their carrier sets.
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| 20. | It follows that the relation defined in this way is only a partial order.
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