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J. Liouville’s Construction of a Transcendental Number We now construct a Transcendental number using an idea of Liouville. Recall a number is said to be Algebraic if and only if there exists a polynomial f(x) with integer coffits aj, f(x) = ∑n j=0 ajx j (1) such that is a root of f(x), that is f( ) = 0: Thus because p 7 is a root of f(x ...
Liouville showed that all Liouville numbers are transcendental. The first number to be proven transcendental without having been specifically constructed for the purpose of proving transcendental numbers' existence was e, by Charles Hermite in 1873.
22 de mar. de 2024 · In 1844 Liouville was the first to prove the existence of transcendental numbers, and he constructed an infinite class of such numbers. Liouville’s theorem, concerning the measure-preserving property of Hamiltonian dynamics (conservation of total energy), is now known to be basic to statistical mechanics and measure theory.
- The Editors of Encyclopaedia Britannica
Joseph Liouville demostró por primera vez la existencia de números trascendentales en 1844, y en 1851 dio los primeros ejemplos decimales como la constante de Liouville. en el que el n ésimo dígito después del punto decimal es 1 si n es igual a k! ( k factorial) para algunos k y 0 de lo contrario.
Such numbers are named for the French mathematician Joseph Liouville, who first proved the existence of transcendental numbers in 1844 and constructed the first proven transcendental number, known as Liouville’s constant, in 1850.
- William L. Hosch
Joseph Liouville’s construction of a transcendental number Legal information: Creative Commons Attribution‑NonCommercial‑ShareAlike 3.0 License You are free: to Share – to copy, distribute, display, and perform the work to Remix – to make derivative works Under the following conditions: Attribution.
24 March 1809. Saint-Omer, France. Died. 8 September 1882. Paris, France. Summary. Joseph Liouville is best known for his work on transcendental numbers. He constructed an infinite class of such numbers. View two larger pictures. Biography.
