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Approximation by Rationals
This Demonstration illustrates that any real number can be approximated by a rational number to within an error equal to half its denominator. In symbols, for any real and natural number , there is a natural number such that .
This can be seen by partitioning the real line into the half-open intervals of length , . The number must fall into such an interval.




"Approximation by Rationals" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ApproximationByRationals/
Contributed by: Izidor Hafner
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