论文信息 - Formalizing a Proof that e is Transcendental - 字舞流文

Formalizing a Proof that e is Transcendental

We describe a HOL Light formalization of Hermite's proof that the base of the natural logarithm e is transcendental. This is the first time a proof of this fact has been formalized in a theorem prover.

Jesse D. Bingham | Jesse Bingham

[1] H. Cantor. Ueber eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen. , 1984 .

[2] John Harrison,et al. HOL Light: An Overview , 2009, TPHOLs.

[3] John Harrison. Verifying the Accuracy of Polynomial Approximations in HOL , 1997, TPHOLs.

[4] Robert Gray,et al. Georg Cantor and Transcendental Numbers , 1994 .

[5] Alonzo Church,et al. A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[6] Len Berggren,et al. Sur la Fonction Exponentielle , 2004 .

[7] John Harrison,et al. A formalized proof of Dirichlet's theorem on primes in arithmetic progression , 2010, J. Formaliz. Reason..

[8] Charles Hermite,et al. Œuvres de Charles Hermite: Sur la fonction exponentielle , 1874 .

[9] J. Liouville. Sur des classes très-étendues de quantités dont la valeur n'est ni algébrique, ni même réductible à des irrationnelles algébriques. , 1851 .

[10] MA John Harrison PhD. Theorem Proving with the Real Numbers , 1998, Distinguished Dissertations.

[11] Freek Wiedijk,et al. The Seventeen Provers of the World , 2006 .

[12] Freek Wiedijk,et al. The De Bruijn Factor , 2000 .

[13] K. R. Pearson,et al. Transcendence of e and π , 1991 .