Liouville number
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exist infinitely many pairs of integers (p, q) with q > 1 such that Liouville numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers. They are precisely the transcendental numbers that can be more closely approximated by rational numbers than any algebraic irrational number. In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence of transcendental numbers for the first time.
0.11000100...Approximation exponentIrrationality exponentIrrationality measureLiouville's Approximation TheoremLiouville's approximation theoremLiouville's constantLiouville's numberLiouville's theorem (transcendence theory)Liouville's theorem on diophantine approximationLiouville-Roth constantLiouville approximation theoremLiouville constantLiouville numbersLiouville theorem on diophantine approximationLiouvilles ConstantLiouville–Roth constantLiouvillian numberMeasure of irrationality
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Liouville number
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exist infinitely many pairs of integers (p, q) with q > 1 such that Liouville numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers. They are precisely the transcendental numbers that can be more closely approximated by rational numbers than any algebraic irrational number. In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence of transcendental numbers for the first time.
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Em teoria dos números, um núme ...... úmero transcendente conhecido.
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En mathématiques, et plus préc ...... ence de nombres transcendants.
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En teoría de números, un númer ...... r aproximados" por racionales.
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In de getaltheorie, een deelge ...... an van transcendente getallen.
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In number theory, a Liouville ...... d e are not Liouville numbers.
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Liczba Liouville’a – liczba rz ...... jący algorytm ich uzyskiwania.
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Un numero di Liouville è un nu ...... ta dimostrata la trascendenza.
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Лиувиллево число — иррациональ ...... ая Лиувилля, определяемая как:
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عدد ليوفيل (بالإنجليزية: Liouv ...... ى وجود الأعداد المتسامية ذاته.
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リウヴィル数（リウヴィルすう、Liouville numbe ...... ∞ (k → ∞) を満たすとき、 はリウヴィル数である。
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Em teoria dos números, um núme ...... úmero transcendente conhecido.
@pt
En mathématiques, et plus préc ...... tels que 0 < |x – p/q| < A/qn.
@fr
En teoría de números, un númer ...... r aproximados" por racionales.
@es
In de getaltheorie, een deelge ...... an van transcendente getallen.
@nl
In number theory, a Liouville ...... al numbers for the first time.
@en
Liczba Liouville’a – liczba rz ...... jący algorytm ich uzyskiwania.
@pl
Un numero di Liouville è un nu ...... ionali, ma anche trascendenti.
@it
Лиувиллево число — иррациональ ...... ая Лиувилля, определяемая как:
@ru
عدد ليوفيل (بالإنجليزية: Liouv ...... ى وجود الأعداد المتسامية ذاته.
@ar
リウヴィル数（リウヴィルすう、Liouville numbe ...... ∞ (k → ∞) を満たすとき、 はリウヴィル数である。
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label
Liczba Liouville’a
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Liouville number
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Liouville-getal
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Liouvillesche Zahl
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Nombre de Liouville
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Numero di Liouville
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Número de Liouville
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Números de Liouville
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Лиувиллево число
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عدد ليوفيل
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