transcendental number oor Sjinees
transcendental number
en
(mathematics) any irrational number that is not an algebraic number
Vertalings in die woordeboek Engels - Sjinees
超越数
zh
irrational nonalgebraic number
无理数
超越數
en
number that cannot be found as a result of an algebraic equation with integer coefficients
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Like both e and π, this constant is a transcendental number.
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The best-known transcendental numbers are π and e.
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Also, π is a transcendental number; that is, it is not the root of any polynomial having rational coefficients.
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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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It was the first number to be proved transcendental without having been specifically constructed for this purpose (compare with Liouville number); the proof was given by Charles Hermite in 1873.
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Eight years ago, in this same place, representatives of # countries undertook a crucial commitment, possibly one of the most transcendental commitments that such a large number of nations ever made
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Eight years ago, in this same place, representatives of 189 countries undertook a crucial commitment, possibly one of the most transcendental commitments that such a large number of nations ever made.
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Indeed, virtually all the transcendental numbers cannot even be specified.
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In particular he gave an example of a transcendental number, the number now named the Liouvillian number
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In 1873 Hermite published the first proof that e is a transcendental number.
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These papers by Gelfond represent a major step forward in the study of transcendental numbers .
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Returning to Gelfond's contributions to transcendental numbers which we mentioned above, in 1929 he conjectured that:
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Another important area which Liouville is remembered for today is that of transcendental numbers.
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Gelfond addressed the Second All-Union Mathematics Congress in Leningrad in 1934) on Transcendental numbers.
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Liouville established in 1851 that transcendental numbers exist.
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A transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients.
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However his contributions were great and led him to prove the existence of a transcendental number in 1844 when he constructed an infinite class of such numbers using continued fractions .
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From this work he generated a large category of transcendental numbers not previously identified and showed how the underlying theory could be used to solve a wide range of Diophantine problems.
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In addition to his important work in the number theory of transcendental numbers, Gelfond made significant contributions to the theory of interpolation and the approximation of functions of a complex variable.
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The above suggests a consideration of all transcendental numbers which have a representation in terms of the Gelfond-Schneider Theorem; i.e., all numbers x such that there exists α and β such that x=αβ .
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Lindemann had proved that π is transcendental in 1882, and in a lecture given in 1886 Kronecker complimented Lindemann on a beautiful proof but, he claimed, one that proved nothing since transcendental numbers did not exist.
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During 1929-30 he taught mathematics at Moscow Technological College but already he had published some important papers: The arithmetic properties of entire functions (1929); Transcendental numbers (1929); and An outline of the history and the present state of the theory of transcendental numbers (1930).
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... to show the contemporary state of the theory of transcendental numbers, to exhibit the fundamental methods of this theory, to present the historical course of development of these methods, and to show the connections which exist between this theory and other problems in the theory of numbers.
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These topics are: prime numbers; congruences and the quadratic reciprocity law; continued fractions; irrational, algebraic and transcendental numbers; quadratic fields; arithmetical functions, their order of magnitude and the Dirichlet or power series which generate them; partitions and representations of numbers as sums of squares, cubes and higher powers; Diophantine approximation; and the geometry of numbers.
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Hence, complex numbers are notable enough for Wikipedia. On the other hand, transcendental numbers containing only 3s and 7s in their hexadecimal representations lack a commonly accepted name, in part because the description is so long, but mainly because hardly anyone, professional or amateur, has cared to study these numbers, much less publish anything about them.
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30 sinne gevind in 15 ms. Hulle kom uit baie bronne en word nie nagegaan nie.