For any Algebraic Number of degree , a Rational approximation must satisfy

for sufficiently large . Writing leads to the definition of the Liouville-Roth Constant of a given number.

**References**

Courant, R. and Robbins, H. ``Liouville's Theorem and the Construction of Transcendental Numbers.'' §2.6.2 in
*What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.*
Oxford, England: Oxford University Press, pp. 104-107, 1996.

© 1996-9

1999-05-25