Generator-offset property: Difference between revisions

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 '''Claim 2''': If a scale ''U'' has ''b'' X's and ''b'' Y's, gcd(''j'', 2''b'') = 1, and consecutively stacked ''j''-steps occur in 2 alternating sizes, the ''b'' Y's and ''b'' Z's alternate.
-Proof: write η and ζ for the two sizes of ''j''-steps. Since gcd(''j'', 2''b'') = 1 there exists ''m'' such that stacking ''m''-many ''j''-steps yields scale steps of ''U'', and ''m'' is odd. Hence the scale steps of ''U'' are ηζ…ζη mod e and ζη…ηζ mod e, and the step sizes clearly alternate.
+Proof: Write η and ζ for the two sizes of ''j''-steps. Since gcd(''j'', 2''b'') = 1 there exists ''m'' such that stacking ''m''-many ''j''-steps yields scale steps of ''U'', and ''m'' is odd. Hence the scale steps of ''U'' are ηζ…ζη mod e and ζη…ηζ mod e, and the step sizes clearly alternate.
 These two claims prove that ''E''<sub>X</sub>(S) = (YZ)<sup>''b''</sup>, which also proves that the two alternants' sizes differ by replacing one Y for a Z.