Rank-3 scale theorems: Difference between revisions

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 Since M_b is a mos mode, there is a k-step within [0, n_0] that has the slope which is just smaller than (F(n_0)-1)/n_0 (1). Similarly, there is a k-step within [n_0, n] that has the slope which is just bigger than (F(n_0)+1)/(n-n_0). These slopes are "two or more steps away" from each other, which is a contradiction. (State this more formally)
-===== LQ is equivalent to floor-LQ in case of 2-step scales =====
+===== LQ is equivalent to floor-LQ in case of 2-step scales (WIP) =====
-A floor-LQ scale ''S'' is LQ since the graph of F(x) = floor(b/a*x) has the desired lattice points: the lattice points are
-floor({(a,b)t : 0 <= t <= 1}) = floor_x(floor_y({(a,b)t : 0 <= t <= 1})) = floor_x([graph of floor(b/a*x)]) (*).
-Conversely, if a 2-step scale ''S'' is LQ, floor({(a,b)t : 0 <= t <= 1}) gives you the graph of floor(b/a*x) (plus the vertical lines) when you connect the dots. This follows from the same equation (*).
 ==== MV3 Theorem 1 (WIP) ====