Liouville Number
A Liouville number is a Transcendental Number which has very close Rational Number approximations. An IrrationalNumber 
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.See also Liouville's Constant, Liouville's Rational Approximation Theorem, Roth's Theorem, TranscendentalNumber
References
Mahler, K. ``On the Approximation of .'' Nederl. Akad. Wetensch. Proc. Ser. A. 56/Indagationes Math. 15, 30-42, 1953.
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