S-expression: Difference between revisions
→Equivalent S-expressions: section, clarify |
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: For example: S''k'' = [''k''-1, ''k'', ''k''+1]^[-1, 2, -1] because S''k'' = (''k''-1)<sup>-1</sup>''k''<sup>2</sup>(''k''+1)<sup>-1</sup>. | : For example: S''k'' = [''k''-1, ''k'', ''k''+1]^[-1, 2, -1] because S''k'' = (''k''-1)<sup>-1</sup>''k''<sup>2</sup>(''k''+1)<sup>-1</sup>. | ||
; | ; S-comma | ||
: | : Any comma within one of the infinite families of commas discussed here, excluding 1/n-square-particulars for n>5 (so square-particulars, triangle-particulars, 1/3-square-particulars, 1/4-square-particulars and 1/5-square-particulars are included, but not anything beyond; this bound is used for exclusion (rather than n>3) to allow the utility of 1/5-square-particulars in avoiding twin primes by equating superparticular intervals on either side of the twin primes). | ||
; Indirect S-comma | |||
: Any comma that is the product or ratio of two S-commas. These appear frequently as S-expressions for commas that are more challenging/nontrivial to represent from the perspective of S-expressions, for example the [[schisma]] admits at least three such representations! | |||
== Mathematical derivation == | == Mathematical derivation == | ||