Patent val/Properties: Difference between revisions
→Adjacent GPVs property: correction |
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\mathrm {N} = \bigcap_{i = 1}^{\pi (p)} \mathrm {N}_i </math> | \mathrm {N} = \bigcap_{i = 1}^{\pi (p)} \mathrm {N}_i </math> | ||
Then v is a GPV of every edo in N if N is not | Then v is a GPV of every edo in N if N is non-empty and not a single point; otherwise it is not a GPV. | ||
== Cardinality == | == Cardinality == | ||
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This property states that, for example, if it is known that {{val| 12 19 28 }} is a GPV, then the next GPV is one of {{val| 13 19 28 }}, {{val| 12 20 28 }}, or {{val| 12 19 29 }}. | This property states that, for example, if it is known that {{val| 12 19 28 }} is a GPV, then the next GPV is one of {{val| 13 19 28 }}, {{val| 12 20 28 }}, or {{val| 12 19 29 }}. | ||
This also holds for any rationally independent subgroups, such as 2.3.7 and 2.9.7. It does not hold, however, for rationally dependent subgroups, such as 2.3. | This also holds for any rationally independent subgroups, such as 2.3.7 and 2.9.7, and even ''some'' rationally dependent subgroups, such as 2.3.9.7. It does not hold, however, for other rationally dependent subgroups, such as 2.3.27.7, where at certain points of edo number ''N'', both the mappings for 3 and 27 increment. | ||
=== Proof === | === Proof === | ||