Common
Liouville number
Class of irrational numbers
Liouville number
In number theory, a Liouville number is a real number x {\displaystyle x} with the property that, for every positive integer n {\displaystyle n} , there exists a pair of integers ( p , q ) {\displaystyle (p,q)} with q > 1 {\displaystyle q>1} such that 0 < | x − p q | < 1 q n . {\displaystyle 0<\left|x-{\frac {p}{q}}\right|<{\frac {1}{q^{n}}}.} The inequality implies that Liouville numbers possess...
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