3
$\begingroup$

given an irrational number is it possible to find the closest rational number to the irrational number? If so, how?

  • 7
    No: if $x$ is any irrational number, and $q$ is any rational number, there is another rational number between $x$ and $q$.2012-12-13
  • 0
    On the other hand, Liouville's theorem on irrational algebraic numbers says there is an upper bound on how well you can approximate such numbers by rationals.2012-12-13
  • 0
    The [continued fraction](http://en.wikipedia.org/wiki/Continued_fraction) of your irrational number will allow you to get fractions as near as you want from your irrational (in some way the bests possible).2012-12-13

2 Answers 2