| 1. | Natural language word definitions do have a mathematical transitive relation ."
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| 2. | The complement of a transitive relation is not always transitive.
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| 3. | Accordingly, thermal equilibrium between systems is a transitive relation.
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| 4. | The union of two transitive relations need not be transitive.
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| 5. | Every relation can be extended in a similar way to a transitive relation.
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| 6. | The second section talks about analogies and transitive relations.
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| 7. | No general formula that counts the number of transitive relations on a finite set is known.
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| 8. | The basic idea is to maximize the amount of transitive relations in a given data set due to game outcomes.
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| 9. | If a transitive relation is also total, it is a partial order is also total, it is a total order.
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| 10. | Each preference relation belongs to the set " Rel ( X ) " of all total and transitive relations on " X ".
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