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1. Asymptotics of arithmetic functions: asymptotics of number-theoretical functions Approximate representations of arithmetic functions (functions defined for all natural number values of the argument) by means of comparatively simple expressions with arbitrary small error terms. More precisely, for an arithmetic function $f(x)$ there ... (Mathematics) [100%] 2023-10-17

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1. Arithmetic function: number-theoretic function A complex-valued function, the domain of definition of which is one of the following sets: the set of natural numbers, the set of rational integers, the set of integral ideals of a given algebraic number field ... (Mathematics) [100%] 2023-11-04
2. Arithmetic function: In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition ... (Function whose domain is the positive integers) [100%] 2023-09-15 [Arithmetic functions] [Functions and mappings]...
3. Arithmetic function: In number theory, an arithmetic function is a function defined on the set of positive integers, usually with integer, real or complex values. Arithmetic functions which have some connexion with the additive or multiplicative structure of the integers are of ... [100%] 2023-06-13
4. Arithmetic: Arithmetic, the art of dealing with numerical quantities in their numerical relations. Arithmetic is usually divided into Abstract Arithmetic and Concrete Arithmetic, the former dealing with numbers and the latter with concrete objects. In stating that the sum of 11d. [82%] 2022-09-02
5. Arithmetic: This must have been familiar to the ancient Hebrews. The sacred books mention large amounts, showing that the people were acquainted with the art of computation. Expressions are found even for fractions (see Gesenius, "Lehrgebäude," 704). (Jewish encyclopedia 1906) [82%] 1906-01-01 [Jewish encyclopedia 1906]
6. Arithmetic: ARITHMETIC a-rith'-me-tik. See NUMBER. a-rith'-me-tik. See NUMBER. [82%] 1915-01-01
7. Arithmetic: Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. (Elementary branch of mathematics) [82%] 2024-01-13 [Arithmetic] [Mathematics education]...
8. Arithmetic: Arithmetic is an elementary branch of mathematics in which real numbers and relations among real numbers are studied and used to solve quantitative problems in finance, engineering, geometry (mensuration), and such fields. The basic arithmetic operations are addition, subtraction, multiplication ... [82%] 2023-10-19
9. Arithmetic: Arithmetic (from grc ἀριθμός (arithmós) 'number', and τική [τέχνη] (tikḗ [tékhnē]) 'art, craft') is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ... (Elementary branch of mathematics) [82%] 2023-10-19 [Arithmetic] [Mathematics education]...
10. Arithmetic: The science of numbers and operations on sets of numbers. Arithmetic is understood to include problems on the origin and development of the concept of a number, methods and means of calculation, the study of operations on numbers of different ... (Mathematics) [82%] 2023-10-19
11. Arithmetic: Arithmetic or arithmetics (from the Greek word αριθμός, meaning "number") is the oldest and most fundamental branch of mathematics. It is used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. Some have called ... [82%] 2023-02-03
12. Arithmetic (song): "Arithmetic" is a single by Brooke Fraser released in 2004. The song is the first track of Fraser's debut album What to Do with Daylight. (Song) [82%] 2024-08-13 [2004 singles] [Brooke Fraser songs]...
13. Arithmetic (book): Arithmetic (Russian: Арифметика, romanized: Arifmetika) is a 1703 mathematics textbook by the Russian educator and mathematician Leonty Magnitsky. The book served as the standard Russian mathematics textbook until the mid-18th century. (Book) [82%] 2024-08-13 [1703 non-fiction books] [Mathematics textbooks]...
14. Multiplicative arithmetic function: $\def\Epsilon{\mathrm{E}}$ An arithmetic function of one argument, $f(m)$, satisfying the condition \begin{equation} f(mn) = f(m) f(n) \label{mult} \end{equation} for any pair of coprime integers $m,n$. It is usually assumed that ... (Mathematics) [81%] 2023-10-11
15. Elementary function arithmetic: In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, x, together with induction for formulas with ... (System of arithmetic in proof theory) [81%] 2023-01-15 [Conjectures] [Formal theories of arithmetic]...
16. Additive arithmetic function: An arithmetic function of one argument that satisfies the following conditions for two relatively prime integers $m,n$ $$ f(mn) = f(m) + f(n) \ . $$ An additive arithmetic function is said to be strongly additive if $f(p^a) = f(p ... (Mathematics) [81%] 2023-10-01
17. Elementary function arithmetic: In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, \displaystyle{ x^y }[/math], together with induction ... (System of arithmetic in proof theory) [81%] 2024-08-15 [Conjectures] [Formal theories of arithmetic]...
18. Arithmetica: La Arithmetica es un tratado de 13 libros del que solo se conocen los seis primeros, que fueron escritos por el matemático griego Diofanto de Alejandría alrededor del año 250. Hallado en Venecia por el matemático alemán Johann Müller Regiomontano ... [74%] 2023-11-10
19. Functions (mathematics): This page is about mathematical functions. For functions in the context of computer programming, see functions. (Mathematics) [67%] 2024-01-03 [Pre-Calculus]