A Liouville number is a Transcendental Number which has very close Rational Number approximations. An Irrational
Number is a Liouville number if, for any , there exist an infinite number of pairs of Integers
and such that

Mahler (1953) proved that is not a Liouville number.

**References**

Mahler, K. ``On the Approximation of .'' *Nederl. Akad. Wetensch. Proc. Ser. A.* **56**/*Indagationes Math.* **15**,
30-42, 1953.

© 1996-9

1999-05-25