1
$\begingroup$

Recall the irrationality measure of a real number $r$ is $$ \mu(r)= \inf \left\{ \lambda\colon \left\lvert r-\frac{x}{y}\right\rvert\lt \frac{1}{y^{\lambda}} \text{ has only finitely many solutions} \right\}$$

Does anyone have a reference or proof?

  • 2
    Would you mind terribly accepting answers to some of the other questions you have asked?2012-08-20
  • 0
    Concerning accepting answers - please see http://meta.math.stackexchange.com/questions/3399/why-should-we-accept-answers2012-08-20
  • 0
    I think it will not be $0$, more like (in the interval $[0,1]$ measure $1$.2012-08-20
  • 0
    Andre, yes youre right. Sorry, I meant the set of real numbers that have irrationality measure larger than 2.2012-08-21

1 Answers 1