Neutral and interordinal intervals in MOS scales: Difference between revisions

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 === Lemma 1 ===
-For positive integers n and k and for real x, floor((n+k)x) - floor(nx) >= floor(kx).
+Let n and k be positive integers and x be a real number such that kx is not an integer. Then floor((n+k)x) - floor(nx) >= floor(kx).
 ==== Proof ====
-This is trivially true for integer x, so assume kx is not an integer. Then:
 floor((n+k)x) - floor(nx) = -1 + ceil((n+k)x) + ceil(-nx) >= ceil((n+k)x - nx) - 1 = ceil(kx) - 1 = floor(kx).