Branches of Mathematic

Arithmetic

Number Theory

Arithmetic is an elementary branch of mathematics that deals with numerical operations such as addition, subtraction, multiplication and division. In a wider sense it also covers exponentiation, the extraction of roots and the taking of logarithms. Its practice reaches back to antiquity: the Egyptians and the Sumerians had already invented numeral systems to solve practical arithmetic problems by about 3000 BCE. Arithmetic is often distinguished from the related field of number theory, which narrows its focus to the integers and their properties, such as divisibility, factorization and primality.

Facts
Central Question
Arithmetic asks how quantities can be represented as numbers and combined by the basic operations of addition, subtraction, multiplication and division, and, more broadly, what structural and axiomatic properties those operations have. 1
Key Debate
Scholars disagree on how broadly to define arithmetic's own scope: a narrow characterization restricts it to computation with natural numbers, while the more common view extends it to integers, rational numbers, real numbers and sometimes complex numbers, and some definitions restrict it further to numerical calculation alone. 1
Classification
Pure or Applied
Pure Mathematics 1
Arithmetic
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Includes

0.999..., Theorems
Source 0.999..., Wikipedia
Source Abraham Fletcher (Wikipedia)
Source Addition (Wikipedia)
Source Albert Girard (MacTutor)
Source André Tacquet (Wikipedia)
Source Baha al-Din al-Amili (Wikipedia)
Source Bhāskara II, Biography (MacTutor History of Mathematics)
Source Brahmagupta (MacTutor)
Source Charles Étienne Louis Camus (Wikipedia)
Source Cheng Dawei (Wikipedia)
Source Christian Wurstisen (Wikipedia)
Source Christoffer Dybvad (Wikipedia)
Source Commutative Property (Wikipedia)
Source Division by Zero (Wikipedia)
Source Euclidean Division (Wikipedia)
Source Farey Sequence, from Wolfram MathWorld
Source François Barrême (Wikipedia)
Source Gilles-François de Gottignies (Wikipedia)
Source Giuseppe Maria Figatelli (Wikipedia)
Source Wikipedia: Henry Briggs
Source Jean-Joseph Rallier des Ourmes (Wikipedia)
Source Jerónimo Cortés (Wikipedia)
Source Joan Francés Fulcònis (Wikipedia)
Source Johann Lantz (Wikipedia)
Source John Collins (mathematician) (Wikipedia)
Source John Colson (Wikipedia)
Source Jonas Moore (Wikipedia)
Source Juan Caramuel y Lobkowitz (Wikipedia)
Source Leonty Magnitsky (Wikipedia)
Source Lowest Common Denominator (Wikipedia)
Source Luca Pacioli, Biography (MacTutor History of Mathematics)
Source María Andrea Casamayor (Wikipedia)
Source Wolfram MathWorld: Midy's Theorem
Source Mihalj Šilobod Bolšić (Wikipedia)
Source Wolfram MathWorld: Minus Sign
Source Number (Wikipedia)
Source Pedro Chacón (Wikipedia)
Source Pietro De Martino (Wikipedia)
Source Wolfram MathWorld: Radix
Source Robert Recorde (MacTutor)
Source Sigismundus Suevus (Wikipedia)
Source Simon Stevin, Biography (MacTutor History of Mathematics)
Source Successor Function (Wikipedia)
Source Thomas Harriot (Wikipedia)
Source Yoshida Mitsuyoshi (Wikipedia)
Sources
1. Arithmetic (Wikipedia)
Wikimedia Foundation
  • Lead section
    Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division.
  • Definition, etymology, and related fields section
    There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers. However, the more common view is to include operations on integers, rational numbers, real numbers, and sometimes also complex numbers in its scope.
  • Lead section, ancient numeral systems sentence
    Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE.
  • In Group: Elementary and General Number Theory, lead paragraph
    Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division.
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Brahmagupta (MacTutor)
Includes: Brahmagupta, Biography, number systems
Quote, Includes: Brahmagupta, Biography, number systems
Brahmagupta's understanding of the number systems went far beyond that of others of the period.
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Baha al-Din al-Amili (Wikipedia)
Includes: Baha al-Din al-Amili, Lead, field of work
Quote, Includes: Baha al-Din al-Amili, Lead, field of work
A prolific author in both Arabic and Persian, Sheikh Bahaʾī composed over one hundred treatises spanning jurisprudence, logic, astronomy, mathematics, and theology-primarily in his mother tongue, Arabic.
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Cheng Dawei (Wikipedia)
Includes: Cheng Dawei, Lead, field of work
Quote, Includes: Cheng Dawei, Lead, field of work
Cheng Dawei (程大位, 1533-1606), also known as Da Wei Cheng or Ch'eng Ta-wei, was a Chinese mathematician and writer who was known mainly as the author of Suanfa Tongzong (算法統宗) (General Source of Computational Methods).
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Christian Wurstisen (Wikipedia)
Includes: Christian Wurstisen, Lead, field of work
Quote, Includes: Christian Wurstisen, Lead, field of work
Christian Wurstisen (Latin: Christianus Urstisius; 23 December 1544-29 March 1588) was a mathematician, theologian, historian from Basel.
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Albert Girard (MacTutor)
Includes: Albert Girard, Biography, fields of work
Quote, Includes: Albert Girard, Biography, fields of work
Girard worked on algebra, trigonometry and arithmetic.
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Robert Recorde (MacTutor)
Includes: Robert Recorde, Biography, Grounde of Artes
Quote, Includes: Robert Recorde, Biography, Grounde of Artes
Recorde published The Grounde of Artes in 1543 which was a very successful commercial arithmetic book
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Joan Francés Fulcònis (Wikipedia)
Includes: Joan Francés Fulcònis, Lead, field of work
Quote, Includes: Joan Francés Fulcònis, Lead, field of work
Joan Francés Fulcònis (in classical Occitan; Johan Frances Fulconis, as written in his original edition) was a mathematician born in Lieusola (today and in French Isola) ca 1520 and who lived in Nice.
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Pedro Chacón (Wikipedia)
Includes: Pedro Chacón, Lead, field of work
Quote, Includes: Pedro Chacón, Lead, field of work
Pedro Chacón (b. c.1526 in Toledo, 1581 in Rome) was a Spanish mathematician and theologian. == Life == He worked as professor of Greek at the University of Salamanca, whose history, consulting ancient documents in the library, he published in 1569.
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Thomas Harriot (Wikipedia)
Includes: Thomas Harriot, Lead, field of work
Quote, Includes: Thomas Harriot, Lead, field of work
Thomas Harriot (; c. 1560-2 July 1621), also spelled Harriott, Hariot or Heriot, was an English astronomer, mathematician, ethnographer and translator to whom the theory of refraction is attributed.
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Jerónimo Cortés (Wikipedia)
Includes: Jerónimo Cortés, Lead, field of work
Quote, Includes: Jerónimo Cortés, Lead, field of work
Jerónimo Cortés (c. 1560 - c. 1611) was a Spanish mathematician, astronomer, naturalist and Valencian compiler. == Works == Many of Cortés works involved compilations of knowledge and writings of other authors.
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Sigismundus Suevus (Wikipedia)
Includes: Sigismundus Suevus, Lead, field of work
Quote, Includes: Sigismundus Suevus, Lead, field of work
Sigismund Schwabe, known by his Latin name Sigismundus Suevus (Freistadt, 1526-1596), was a German mathematician and Evangelical theologian.
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Johann Lantz (Wikipedia)
Includes: Johann Lantz, Lead, field of work
Quote, Includes: Johann Lantz, Lead, field of work
Johann Lantz or Lanz (1564-20 September 1638) was a German mathematician and Jesuit. == Biography == Born in Tettnang on Lake Constance in 1564, he was admitted as novice in Landsberg in 1589.
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Yoshida Mitsuyoshi (Wikipedia)
Includes: Yoshida Mitsuyoshi, Lead, field of work
Quote, Includes: Yoshida Mitsuyoshi, Lead, field of work
Yoshida Mitsuyoshi (吉田 光由; 1598, January 8, 1672), also known as Yoshida Kōyū, was a Japanese mathematician in the Edo period.
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Christoffer Dybvad (Wikipedia)
Includes: Christoffer Dybvad, Study abroad, first work
Quote, Includes: Christoffer Dybvad, Study abroad, first work
på dansk udgav sit første matematiske skrift
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Abraham Fletcher (Wikipedia)
Includes: Abraham Fletcher, Article text
Quote, Includes: Abraham Fletcher, Article text
applying himself particularly to the study of arithmetic
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François Barrême (Wikipedia)
Includes: François Barrême, Lead, field of work
Quote, Includes: François Barrême, Lead, field of work
Les Comptes faits : ou Le Tarif général de toutes les monnoyes (1669) Le Livre facile pour apprendre l’arithmétique de soy-même & sans maître (1672) La géométrie servant au mesurage et à l'arpentage : ,ouvrage si facile & si commode, que par la seule
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Juan Caramuel y Lobkowitz (Wikipedia)
Includes: Juan Caramuel y Lobkowitz, Mathematics
Quote, Includes: Juan Caramuel y Lobkowitz, Mathematics
thus making a significant contribution to the development of the binary numeral system
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Jonas Moore (Wikipedia)
Includes: Jonas Moore, Mathematician and surveyor, arithmetic
Quote, Includes: Jonas Moore, Mathematician and surveyor, arithmetic
published his first book, Moores Arithmetick
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Giuseppe Maria Figatelli (Wikipedia)
Includes: Giuseppe Maria Figatelli, Lead, field of work
Quote, Includes: Giuseppe Maria Figatelli, Lead, field of work
Ristretto aritmetico (in Italian).
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John Collins (mathematician) (Wikipedia)
Includes: John Collins, Life, merchants accounts
Quote, Includes: John Collins, Life, merchants accounts
In 1652 he published An Introduction to Merchants' Accounts
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Jean-Joseph Rallier des Ourmes (Wikipedia)
Includes: Jean-Joseph Rallier des Ourmes, Lead, field of work
Quote, Includes: Jean-Joseph Rallier des Ourmes, Lead, field of work
His numerous writings are scattered in various collections, in particular in the Encyclopédie, where he provided 14 articles on arithmetics, and in the Mémoires des savants étrangers of the Académie des sciences.
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Pietro De Martino (Wikipedia)
Includes: Pietro De Martino, Lead, field of work
Quote, Includes: Pietro De Martino, Lead, field of work
He authored various works; his Nuove istituzioni di aritmetica pratica, published originally in 1739 in Naples, had many reprints (the better known of the 1758; one also in Turin in 1762).
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María Andrea Casamayor (Wikipedia)
Includes: María Andrea Casamayor, Lead, field of work
Quote, Includes: María Andrea Casamayor, Lead, field of work
She stood out for her mathematical thinking and work with numbers and made significant contributions to arithmetic, which at the time was considered the exclusive domain of men.
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Mihalj Šilobod Bolšić (Wikipedia)
Includes: Mihalj Šilobod Bolšić, Lead, field of work
Quote, Includes: Mihalj Šilobod Bolšić, Lead, field of work
Mihalj Šilobod Bolšić (1 November 1724-4 April 1787) was a Croatian Roman Catholic priest, mathematician, writer, and musical theorist primarily known for writing the first Croatian arithmetics textbook Arithmetika Horvatzka (published in Zagreb, 1758).
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John Colson (Wikipedia)
Includes: John Colson, Lead, field of work
Quote, Includes: John Colson, Lead, field of work
In 1726 he published his "Negativo-Affirmativo Arithmetik", which advocated a modified decimal system of numeration.
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Gilles-François de Gottignies (Wikipedia)
Includes: Gilles-François de Gottignies, Lead, field of work
Quote, Includes: Gilles-François de Gottignies, Lead, field of work
Arithmetica introductio ad logisticam universae mathesi servientem continens vulgo usitatam arithmeticam practicam.
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Charles Étienne Louis Camus (Wikipedia)
Includes: Charles Étienne Louis Camus, Lead, field of work
Quote, Includes: Charles Étienne Louis Camus, Lead, field of work
Part 1: Élémens d'arithmétique (1749).
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Leonty Magnitsky (Wikipedia)
Includes: Leonty Magnitsky, Lead, field of work
Quote, Includes: Leonty Magnitsky, Lead, field of work
From 1701 and until his death, he taught arithmetic, geometry and trigonometry at the Moscow School of Mathematics and Navigation, becoming its director in 1716.
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André Tacquet (Wikipedia)
Includes: André Tacquet, Lead, field of work
Quote, Includes: André Tacquet, Lead, field of work
1651: Cylindricorum et annularium libri IV (Antwerp) full text 1654: Elementa geometriae (Antwerp) 1656: Arithmeticae theoria et praxis (Louvain) 1659: Cylindricorum et annularium liber V (Antwerp) full text 1669: Opera mathematica (in Latin).
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Euclidean Division (Wikipedia)
Includes: Euclidean Division, Lead section
Quote, Includes: Euclidean Division, Lead section
In arithmetic, Euclidean division - or division with remainder - is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor.
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Addition (Wikipedia)
Includes: Addition, Lead sentence
Quote, Includes: Addition, Lead sentence
us sign +, is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division.
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Wikipedia: Henry Briggs
Includes: Henry Briggs, Lead
Quote, Includes: Henry Briggs, Lead
The specific algorithm for long division in modern use was introduced by Briggs c. 1600 AD.
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Commutative Property (Wikipedia)
Includes: Commutative property, Lead paragraph
Quote, Includes: Commutative property, Lead paragraph
Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings.
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Division by Zero (Wikipedia)
Includes: Division by Zero, Lead paragraph
Quote, Includes: Division by Zero, Lead paragraph
The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor.
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Number (Wikipedia)
Includes: Number, Lead paragraph
Quote, Includes: Number, Lead paragraph
Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers.
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Wolfram MathWorld: Midy's Theorem
Wolfram MathWorldIncludes: Midy's Theorem, Subject classifications
Quote, Includes: Midy's Theorem, Subject classifications
Number Theory Arithmetic
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Wolfram MathWorld: Radix
Wolfram MathWorldIncludes: Radix, Subject classifications
Quote, Includes: Radix, Subject classifications
Number Theory Arithmetic
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Wolfram MathWorld: Minus Sign
Wolfram MathWorldIncludes: Minus Sign, Subject classifications
Quote, Includes: Minus Sign, Subject classifications
Number Theory Arithmetic
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Farey Sequence, from Wolfram MathWorld
Includes: Farey Sequence, Subject classifications
Quote, Includes: Farey Sequence, Subject classifications
Number Theory Arithmetic
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0.999..., Wikipedia
Includes: 0.999..., Lead section
Quote, Includes: 0.999..., Lead section
0.999... is a repeating decimal that represents the number 1. The three dots
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Successor Function (Wikipedia)
Includes: Successor Function, Lead section
Quote, Includes: Successor Function, Lead section
natural number to the next one
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Lowest Common Denominator (Wikipedia)
Includes: Lowest Common Denominator, Lead section
Quote, Includes: Lowest Common Denominator, Lead section
or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It
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Bhāskara II, Biography (MacTutor History of Mathematics)
Includes: Bhāskara II, Summary
Quote, Includes: Bhāskara II, Summary
Bhaskara II or Bhaskaracharya was an Indian mathematician and astronomer who extended Brahmagupta's work on number systems.
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Luca Pacioli, Biography (MacTutor History of Mathematics)
Includes: Luca Pacioli, Biography
Quote, Includes: Luca Pacioli, Biography
In 1477 Pacioli began a life of travelling, spending time at various universities teaching mathematics, particularly arithmetic.
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Simon Stevin, Biography (MacTutor History of Mathematics)
Includes: Simon Stevin, Summary
Quote, Includes: Simon Stevin, Summary
Simon Stevin was a Flemish mathematician who presented the first elementary and thorough account of decimal fractions and introduced their use in mathematics.
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