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Related to algebraic number: Algebraic number field, Algebraic number theory

INDEFINITE, NUMBER. A number which may be increased or diminished at pleasure.
     2. When a corporation is composed of an indefinite number of persons, any number of them consisting of a majority of those present may do any act unless it be otherwise regulated by the charter or by-laws. See Definite number.

NUMBER. A collection of units.
     2. In pleading, numbers must be stated truly, when alleged in the recital of a record, written instrument, or express contract. Lawes' PI. 48; 4 T. R. 314; Cro. Car. 262; Dougl. 669; 2 Bl. Rep. 1104. But in other cases, it is not in general requisite that they should be truly stated, because they are not required to be strictly proved. If, for example, in an action of trespass the plaintiff proves the wrongful taking away of any part of the goods duly described in his declaration, he is entitled to recover pro tanto. Bac. Ab. Trespass, I 2 Lawes' PI. 48.
     3. And sometimes, when the subject to be described is supposed to comprehend a multiplicity of particulars, a general description is sufficient. A declaration in trover alleging the conversion of "a library of books"' without stating their number, titles, or quality, was held 'to be sufficiently certain; 3 Bulst. 31; Carth. 110; Bac. Ab. Trover, F 1; and in an action for the loss of goods, by burning the plaintiff's house, the articles may be described by the simple denomination of "goods" or "divers goods." 1 Keb. 825; Plowd. 85, 118, 123; Cro. Eliz. 837; 1 H. Bl. 284.

References in periodicals archive ?
Also, if [[alpha].sub.1], [[alpha].sub.2] are distinct algebraic numbers conjugate over Q then
Since [[beta].sup.2]+ [[bar.[beta]].sup.2], [[beta].sup.2][[epsilon].sup.m.sub.0] + [[bar.[beta]].sup.2][[bar.[epsilon].sub.0].sup.m], and [[epsilon].sup.m.sub.0] + [[bar.[epsilon].sub.0].sup.m] are all rational integers and [beta][bar.[beta]] = [square root of -5], then clearly A is an algebraic number. Thus, the lemma is proven.
As already mentioned, it is proved in [BFK12] that any algebraic number is computable for k = 2 and q > 2 colors, but with the significant difference that the 2 balls may be turned into two different colors.
Let a, b, c > 0 and x, y [member of] R, n [greater than or equal to] 0 and u be a real algebraic number, then
All coefficient sequences grow like [kappa][n.sup.[alpha]][[rho].sup.n] for some constants [kappa], [alpha], [rho], where [rho] is an integer or an algebraic number of degree 2 and [alpha] is a non-positive number.
Those irrational numbers that cannot serve as solutions are called transcendental numbers (from Latin words meaning "to climb beyond," since they climb beyond the algebraic numbers to further heights).
Among their topics are designs, introducing difference sets, multipliers, necessary group conditions, representation theory, using algebraic number theory, and applications.
The proof of the theorem "in full generality represents a milestone in algebraic number theory," mathematician Jonathan Rogawski of the University of California, Los Angeles remarks in the January NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY.
Hoffman and Wakatsuki study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank two over any algebraic number field.
Furuta, The genus field and genus number in algebraic number fields, Nagoya Math.
For example, he describes how Fermat's last theorem, first posited in the year 1630, remained unsolved until Andrew Wiles published his solution in 1995 while also explaining how work on Fermat's theorem led to the development of algebraic number theory and complex analysis.
This mathematics textbook for graduate students covers the fundamentals of abstract algebra including fields and Galois theory, algebraic number theory, algebraic geometry and groups, rings and modules.

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