Huh — the left-hand portion of the expression is the same as the formula for the error ε of approximating r using a rational fraction a / b. In other words, the inequality seems to be saying that, as a consequence of the pigeonhole principle, we can pick any r and any K 0, and there’s always some integer a / b that approximates r with an error of less than 1 / (K · b).
the core DFA algorithm is also very simple. now i know, coming from someone who’s been doing years of PhD research on this topic, but it really is simple. you got 4 things:
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