Rank-3 scale theorems: Difference between revisions
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F(m') - F(m) - 1 <= b/a(m'-m) <= F(m') - F(m) + 1 | F(m') - F(m) - 1 <= b/a(m'-m) <= F(m') - F(m) + 1 | ||
But F(m') -F(m) = #s and m'-m = #L. So #s -1 <= b/a*#L <= #s+1. Do the same thing for the "bad" interval [r', r] and you get | But F(m') -F(m) = #s and m'-m = #L. So #s -1 <= b/a*#L <= #s+1. Do the same thing for the "bad" interval [r', r] and you get #s+t-1 <= b/a(#L-t) <= #s+t+1. | ||
#s+t-1 <= b/a(#L-t) <= #s+t+1. | |||
Thus b/a#L <= b/a(#L-t), a contradiction. | Thus b/a#L <= b/a(#L-t), a contradiction. | ||