Rank-3 scale theorems: Difference between revisions
| Line 39: | Line 39: | ||
Suppose that some r-step comes in 3 sizes, in x-coordinates | Suppose that some r-step comes in 3 sizes, in x-coordinates | ||
(m11, m12), (m21, m22), (m31, m32). This means that there are three numbers of small steps and there are three numbers of y-gridline crossings in the r-step. But this is impossible since it requires either floor((b/a)mi1) < (b/a)mi1 - 1 or floor((b/a)mi2) > (b/a)mi2 for some i. | (m11, m12), (m21, m22), (m31, m32). This means that there are three numbers of small steps and there are three numbers of y-gridline crossings in the r-step. But this is impossible since it requires either floor((b/a)mi1) < (b/a)mi1 - 1 or floor((b/a)mi2) > (b/a)mi2 for some i (why?). | ||
M_b >= F: (bc it's a mos) Suppose there is an x-value x_0 where M_b(x_0) < F(x_0). Let m = min(n_0, n-n_0), n = scale size. Then find three different m-mossteps by taking one interval before n_0, one interval containing n_0 and one interval after n_0. | M_b >= F: (bc it's a mos) Suppose there is an x-value x_0 where M_b(x_0) < F(x_0). Let m = min(n_0, n-n_0), n = scale size. Then find three different m-mossteps by taking one interval before n_0, one interval containing n_0 and one interval after n_0. | ||