Continued Fraction - Comparison of Continued Fractions

Comparison of Continued Fractions

Consider x = and y = . If k is the smallest index for which ak is unequal to bk then x < y if (−1)k(ak − bk) < 0 and y < x otherwise.

If there is no such k, but one expansion is shorter than the other, say x = and y = with ai = bi for 0 ≤ i ≤ n, then x < y if n is even and y < x if n is odd.

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