Definition:Liouville Number

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A real number $x$ is a Liouville number if for all $n \in \N$, there exist $p, q \in \Z$ (which may depend on $n$) with $q > 1$ such that:

$0 < \size {x - \dfrac p q} < \dfrac 1 {q^n}$

Also see

  • Results about Liouville numbers can be found here.

Source of Name

This entry was named for Joseph Liouville.