A theorem of Erdos states:

"There exists an absolute constant c such that, if n>ck, and if a<sub>1</sub>/b<sub>1</sub>, a<sub>2</sub>/b<sub>2</sub>, ... are the Farey fractions of order n, then a<sub>x</sub>/b<sub>x</sub> and a<sub>x+k</sub>/b<sub>x+k</sub> are similarly ordered."

Can someone provide a definition of "similarly ordered" as used here?

Thanks for any insight.

Cheers, Scott 


@ARTICLE{Erdos:1943,
  author={Erd{\"o}s, Paul},
  title={A note on {F}arey series},
  journal={Quart. J. Math., Oxford Ser.},
  fjournal={The Quarterly Journal of Mathematics. Oxford. Second Series},
  volume={14},
  year={1943},
  pages={82--85},
  issn={0033-5606},
  mrclass={40.0X},
  mrnumber={MR0009999 (5,236b)},
  mrreviewer={G. Szeg{\"o}}