given an irrational number is it possible to find the closest rational number to the irrational number? If so, how?
is it possible to find the closest rational number to an irrational number?
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real-analysis
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7No: if $x$ is any irrational number, and $q$ is any rational number, there is another rational number between $x$ and $q$. – 2012-12-13
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0On 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
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0The [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