关于Farey序列的一个研究

A Reseach on Farey Sequence

早在一百多的年前,人们就发现了Farey序列,它是介于0和1之间满足一定的性质的一个有理数列。但一直到近代才被得到真正的应用,特别是在近代数论中,也逐渐受到人们的重视。这里对于这个序列的性质进行了初步探讨研究,并根据这个性质得到关于有理数和无理数一些有趣的命题。

Farey sequence has been found one hundred years ago, they are the rational number sequence between 0 and 1. But they only got real application until today, especial in numbers theory. People pay more attention to them. In this paper, we make basic research on their proportion, and got some interesting property of rational number and irrational number.