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 QuestionArithmetic 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 DebateScholars 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 Arithmetic
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Source 0.999..., Wikipedia
Source Addition (Wikipedia)
Source Bhāskara II, Biography (MacTutor History of Mathematics)
Source Commutative Property (Wikipedia)
Source Division by Zero (Wikipedia)
Source Euclidean Division (Wikipedia)
Source Farey Sequence, from Wolfram MathWorld
Source Wikipedia: Henry Briggs
Source Lowest Common Denominator (Wikipedia)
Source Luca Pacioli, Biography (MacTutor History of Mathematics)
Source Wolfram MathWorld: Midy's Theorem
Source Wolfram MathWorld: Minus Sign
Source Number (Wikipedia)
Source Wolfram MathWorld: Radix
Source Simon Stevin, Biography (MacTutor History of Mathematics)
Source Successor Function (Wikipedia)
Sources
1. Arithmetic (Wikipedia)
Wikimedia FoundationLead 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.
View the Source Euclidean Division (Wikipedia)
Includes: Euclidean Division, Lead sectionQuote, 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.
Addition (Wikipedia)
Includes: Addition, Lead sentenceQuote, Includes: Addition, Lead sentence
us sign +, is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division.
Wikipedia: Henry Briggs
Includes: Henry Briggs, LeadQuote, Includes: Henry Briggs, Lead
The specific algorithm for long division in modern use was introduced by Briggs c. 1600 AD.
Commutative Property (Wikipedia)
Includes: Commutative property, Lead paragraphQuote, 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.
Division by Zero (Wikipedia)
Includes: Division by Zero, Lead paragraphQuote, 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.
Number (Wikipedia)
Includes: Number, Lead paragraphQuote, 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.
Wolfram MathWorld: Midy's Theorem
Wolfram MathWorldIncludes: Midy's Theorem, Subject classificationsQuote, Includes: Midy's Theorem, Subject classifications
Number Theory Arithmetic
Wolfram MathWorld: Radix
Wolfram MathWorldIncludes: Radix, Subject classificationsQuote, Includes: Radix, Subject classifications
Number Theory Arithmetic
Wolfram MathWorld: Minus Sign
Wolfram MathWorldIncludes: Minus Sign, Subject classificationsQuote, Includes: Minus Sign, Subject classifications
Number Theory Arithmetic
Farey Sequence, from Wolfram MathWorld
Includes: Farey Sequence, Subject classificationsQuote, Includes: Farey Sequence, Subject classifications
Number Theory Arithmetic
0.999..., Wikipedia
Includes: 0.999..., Lead sectionQuote, Includes: 0.999..., Lead section
0.999... is a repeating decimal that represents the number 1. The three dots
Successor Function (Wikipedia)
Includes: Successor Function, Lead sectionQuote, Includes: Successor Function, Lead section
natural number to the next one
Lowest Common Denominator (Wikipedia)
Includes: Lowest Common Denominator, Lead sectionQuote, 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
Bhāskara II, Biography (MacTutor History of Mathematics)
Includes: Bhāskara II, SummaryQuote, Includes: Bhāskara II, Summary
Bhaskara II or Bhaskaracharya was an Indian mathematician and astronomer who extended Brahmagupta's work on number systems.
Luca Pacioli, Biography (MacTutor History of Mathematics)
Includes: Luca Pacioli, BiographyQuote, Includes: Luca Pacioli, Biography
In 1477 Pacioli began a life of travelling, spending time at various universities teaching mathematics, particularly arithmetic.
Simon Stevin, Biography (MacTutor History of Mathematics)
Includes: Simon Stevin, SummaryQuote, 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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