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.
- Regular Prime
- Regular Ring
- Regular Sequence
- Regular Singularity
- Regular Singular Point
- Regular Surface
- Regular Triangle Center
- Regulus
- Reidemeister Moves
- Reidemeister's Theorem
- Reinhardt Domain
- Relation
- Relative Error
- Relative Extremum
- Relatively Prime
- Relative Maximum
- Relative Minimum
- Relaxation Methods
- Remainder
- Remainder Theorem
- Rembs' Surfaces
- Removable Crossing
- Removable Singularity
- Rencontres Number
- Rendezvous Values