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Overview

arithmetic

The study of the natural numbers, which are 0, 1, 2, 3…and their successors. Arithmetic is characterized by Peano's postulates. Philosophical questions include the nature of our knowledge ...

arithmetic

arithmetic   Quick reference

The Oxford Dictionary of Philosophy (3 ed.)

Reference type:
Subject Reference
Current Version:
2016
Subject:
Philosophy
Length:
62 words

... The study of the natural numbers, which are 0, 1, 2, 3…and their successors. Arithmetic is characterized by Peano ’s postulates. Philosophical questions include the nature of our knowledge of those postulates; the nature of the numbers, which are apparently the objects of which arithmetic treats; and the relation of arithmetic to empirical science. See also abstract/concrete ; conventionalism ; formalism , logical ; logicism...

arithmetic

arithmetic   Quick reference

World Encyclopedia

Reference type:
Subject Reference
Current Version:
2004
Subject:
Encyclopedias
Length:
80 words

... Calculations and reckoning using numbers and operations such as addition, subtraction, multiplication and division. The study of arithmetic traditionally involves procedures for operations such as long division and extractiing square roots. The procedures of arithmetic were put on a formal axiomatic basis ( see axiom ) by Guiseppe Peano in the late 19th century. Using such statements (including that there is a unique natural number, 1) one can give formal definitions of the set of natural numbers and the arithmetical...

arithmetic

arithmetic   Quick reference

The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

... The area of mathematics relating to numerical calculations involving only the basic operations of addition, subtraction, multiplication, division and simple...

arithmetic

arithmetic   Quick reference

A Dictionary of Weights, Measures, and Units

Reference type:
Subject Reference
Current Version:
2004

... mathematics . The arithmetic value of a number is the number stripped of any negative sign. For number x it is expressed as | x |, termed the modulus of x ; compare algebraic . The arithmetic mean of n numbers is their collective algebraic sum (i.e. respectful of signs) divided by n ; compare geometric . Applied to a series of numbers, ‘arithmetic’ indicates that adjacent members differ by a constant additive increment, the ‘common difference’ (any finite number). The arithmetic series with difference b has the form a ,  a + b ,  a ...

arithmetic

arithmetic   Reference library

The Oxford Dictionary of the Renaissance

Reference type:
Subject Reference
Current Version:
2005
Subject:
History, Early Modern History (1500 to 1700)
Length:
431 words

... . In universities arithmetic, one of the sciences of the quadrivium ( see liberal arts ), was taught from the treatise of Nicomachus of Gerasa ( fl. ad 100 ), which is a simplified and expanded version of the arithmetical books of Euclid 's Elements , books 7 to 9. There is much emphasis on the correct naming of ratios, which is perhaps partly understandable since the principal application of arithmetic was in the theory of music . There was also an interest in numbers with special properties, such as ‘perfect numbers’, which are equal to the sum...

Arithmetic

Arithmetic   Reference library

Glen Van Brummelen

The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam

Reference type:
Subject Reference
Current Version:
2014
Subject:
Religion, Science and technology
Length:
514 words

... Berggren, J. L. Episodes in the Mathematics of Medieval Islam . New York: Springer-Verlag, 1986. The chapter on arithmetic in this volume describes in some detail certain arithmetic procedures found in the works of Kūshyār ibn Labbān and Jamshīd al-Kāshī. Rashed, Roshdi . The Development of Arabic Mathematics: Between Arithmetic and Algebra . Dordrecht, Netherlands: Kluwer, 1994. A collection of studies on Arabic arithmetic and algebra, including the extraction of n -th roots and amicable numbers. Glen Van...

residue arithmetic

residue arithmetic   Quick reference

A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

...arithmetic Another name for modular arithmetic...

arithmetic unit

arithmetic unit   Quick reference

A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

... unit ( AU ) Short for arithmetic and logic unit. See ALU...

arithmetic instruction

arithmetic instruction   Quick reference

A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

... instruction An instruction that specifies an arithmetic operation to be carried out by the...

arithmetic operator

arithmetic operator   Quick reference

A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

... operator A type of operator appearing in an expression denoting one of the operations of arithmetic, e.g. +, −, * (multiplication), /...

clock arithmetic

clock arithmetic   Quick reference

The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...arithmetic Arithmetic base n where increasing values return to 1 after they reach the clock limit which is the value of n . So in clock arithmetic base 8, 5+6 will come to...

serial arithmetic

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A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

...arithmetic Operation upon one bit or digit of a number at a...

arithmetic mean

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A Dictionary of Finance and Banking (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

... mean ( arithmetic average ) An average obtained by adding together the individual numbers concerned and dividing the total by their number. For example, the arithmetic mean of 7, 20, 107, and 350 is 484/4 = 121. This value, however, gives no idea of the spread of numbers. Compare geometric mean ; median ; weighted average...

arithmetic scale

arithmetic scale   Reference library

The Handbook of International Financial Terms

Reference type:
Subject Reference
Current Version:
2005

... scale . A method of representing price movements where the vertical (price) axis uses an arithmetic scale (for instance, divided into units of 20). An alternative approach is to use a semi-logarithmic scale, where the intervals represent equivalent value...

arithmetic mean

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A Dictionary of Genetics (8 ed.)

Reference type:
Subject Reference
Current Version:
2014
Subject:
Science and technology, Life Sciences
Length:
22 words

... mean an average; the number found by dividing the sum of a series by the number of items in the...

arithmetic progression

arithmetic progression   Quick reference

A Dictionary of Genetics (8 ed.)

Reference type:
Subject Reference
Current Version:
2014
Subject:
Science and technology, Life Sciences
Length:
24 words

... progression a series of numbers in which each number is larger (or smaller) than the number that precedes it by a constant...

political arithmetic

political arithmetic   Quick reference

A Concise Oxford Dictionary of Politics and International Relations (4 ed.)

Reference type:
Subject Reference
Current Version:
2018
Subject:
Social sciences, Politics
Length:
25 words

...arithmetic Term coined by Sir William Petty ( 1623–87 ) to denote vital and economic statistics, of which he was the first systematic...

parallel arithmetic

parallel arithmetic   Quick reference

A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

...arithmetic Operation upon more than one bit or digit of a number at the same time. See parallel adder...

Peano arithmetic

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A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016
Subject:
Science and technology, Mathematics and Computer Science
Length:
162 words
Illustration(s):
1

...arithmetic An axiomatic theory, based on first-order logic, about the natural numbers. Its axioms are first-order statements about the simple arithmetic operations of successor n +1, addition n + m , and multiplication n . m , together with the principle of induction . A great variety of facts in mathematics and computer science can be reduced to, or can be coded as, statements about natural numbers, and Peano arithmetic is a strong enough theory to express and prove formally the majority of basic results. However, Gödel’s incompleteness theorems show...

arithmetic mean

arithmetic mean   Quick reference

A Dictionary of Accounting (5 ed.)

Reference type:
Subject Reference
Current Version:
2016
Subject:
Social sciences, Business and Management
Length:
68 words

... mean ( arithmetic average ) An average obtained by adding together the individual quantities and dividing the total by their number. For example, the average of 6, 7, and 107 is (6 + 7 + 107)/3 = 40. This value, however, gives no idea of the spread of numbers and may prove misleading where there are a small number of extreme values. Compare geometric mean ; weighted average...

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