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.
Read more about this topic: Continued Fraction
Famous quotes containing the words comparison and/or continued:
“Clay answered the petition by declaring that while he looked on the institution of slavery as an evil, it was ‘nothing in comparison with the far greater evil which would inevitably flow from a sudden and indiscriminate emancipation.’”
—State of Indiana, U.S. public relief program (1935-1943)
“Along the journey we commonly forget its goal. Almost every vocation is chosen and entered upon as a means to a purpose but is ultimately continued as a final purpose in itself. Forgetting our objectives is the most frequent stupidity in which we indulge ourselves.”
—Friedrich Nietzsche (1844–1900)