Introduction to Liouville Numbers

  title={Introduction to Liouville Numbers},
  author={Adam Grabowski and Artur Kornilowicz},
  journal={Formalized Mathematics},
  pages={39 - 48}
Summary The article defines Liouville numbers, originally introduced by Joseph Liouville in 1844 [17] as an example of an object which can be approximated “quite closely” by a sequence of rational numbers. A real number x is a Liouville number iff for every positive integer n, there exist integers p and q such that q > 1 and It is easy to show that all Liouville numbers are irrational. Liouville constant, which is also defined formally, is the first transcendental (not algebraic) number. It is… 
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