“Liouville's Rational Approximation Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Liouville's Rational Approximation Theorem

释义

Liouville's Rational Approximation Theorem

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

for sufficiently large

. Writing

leads to the definition of the Liouville-Roth Constantof a given number.

See also Lagrange Number (Rational Approximation), Liouville's Constant, Liouville Number, Liouville-RothConstant, Markov Number, Roth's Theorem, Thue-Siegel-Roth Theorem

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.

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