vault backup: 2025-03-18 16:10:04
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@ -49,7 +49,7 @@ We now show that $\to$ is acyclic.
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3. It cannot have cycles with more than 2 edges:
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3. It cannot have cycles with more than 2 edges:
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- by contradiction, consider a shortest cycle
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- by contradiction, consider a shortest cycle
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- adjacent edges cannot belong to the same order (otw. the cycle would be shortable, because of transitivity)
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- adjacent edges cannot belong to the same order (not both $\to_X$ ), otw. the cycle would be shortable, because of transitivity of the total order!
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> [!PDF|red] class 6, p.6> we would have a cycle of length
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> [!PDF|red] class 6, p.6> we would have a cycle of length
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