Superpartient ratio: Difference between revisions

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<math>\displaystyle \prod_{i \mathop = 1}^{P \mathop - 1} \dfrac {i + 1} {i} = P</math>

When considering ratios, and particularly when they are ratios for [[comma]]s, it can be useful to introduce the notion of the '''degree of epimoricity''' (not to be confused with ''epimericity'' – see link below). In terms of ''p''/''q'' reduced to lowest terms it is ''p'' - ''q''. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[Wikipedia:Størmer's theorem|Størmer's theorem]] can be extended to show that for each prime limit p and each degree of ~~epimoricity~~ n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.

When considering ratios, and particularly when they are ratios for [[comma]]s, it can be useful to introduce the notion of the '''degree of epimoricity''' (not to be confused with ''epimericity'' – see link below). In terms of ''p''/''q'' reduced to lowest terms it is ''p'' - ''q''. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[Wikipedia:Størmer's theorem|Størmer's theorem]] can be extended to show that for each prime limit p and each degree of epimericity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.

== See also ==

@@ Line 5: / Line 5: @@
 <math>\displaystyle \prod_{i \mathop = 1}^{P \mathop - 1} \dfrac {i + 1} {i} = P</math>
-When considering ratios, and particularly when they are ratios for [[comma]]s, it can be useful to introduce the notion of the '''degree of epimoricity''' (not to be confused with ''epimericity'' – see link below). In terms of ''p''/''q'' reduced to lowest terms it is ''p'' - ''q''. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[Wikipedia:Størmer's theorem|Størmer's theorem]] can be extended to show that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.
+When considering ratios, and particularly when they are ratios for [[comma]]s, it can be useful to introduce the notion of the '''degree of epimoricity''' (not to be confused with ''epimericity'' – see link below). In terms of ''p''/''q'' reduced to lowest terms it is ''p'' - ''q''. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[Wikipedia:Størmer's theorem|Størmer's theorem]] can be extended to show that for each prime limit p and each degree of epimericity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.
 == See also ==