A devil's staircase from rotations and irrationality measures for Liouville numbers
From Sturmian and Christoffel words we derive a strictly increasing function $Δ:[0,\infty)\to\mathbb{R}$. This function is continuous at every irrational point, while at rational points, left-continuous but not right-continuous. Moreover, it assumes algebraic integers at rationals, and transcendental numbers at irrationals. We also see that the differentiation of $Δ$ distinguishes some irrationality measures of real numbers.
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