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.
- Euler-Poincaré Characteristic
- Euler Polyhedral Formula
- Euler Polynomial
- Euler Polynomial Identity
- Euler Power Conjecture
- Euler Product
- Euler Pseudoprime
- Euler Quartic Conjecture
- Euler's 6n+1 Theorem
- Euler's Addition Theorem
- Euler's Circle
- Euler's Conjecture
- Euler's Criterion
- Euler's Displacement Theorem
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem
- Euler's Phi Function
- Euler's Polygon Division Problem