## ::Number

### ::concepts

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A **number** is a mathematical object used to count, measure and label. The original examples are the natural numbers , , , and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, the term *number* may refer to a symbol, a word or a mathematical abstraction.

In mathematics, the notion of number has been extended over the centuries to include , negative numbers, rational numbers such as <math>\frac{1}{2}</math> and <math>-\frac{2}{3}</math>, real numbers such as <math>\sqrt{2}</math> and <math>\pi</math>, complex numbers, which extend the real numbers by including <math>\sqrt{-1}</math>, and sometimes additional objects. Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of the natural numbers.

Besides their practical uses, numbers have cultural significance throughout the world.<ref name="Gilsdorf">Gilsdorf, Thomas E. *Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas*, John Wiley & Sons, Feb 24, 2012.</ref><ref name="Restivo">Restivo, S. *Mathematics in Society and History*, Springer Science & Business Media, Nov 30, 1992.</ref> For example, in Western society the number 13 is regarded as unlucky, and "a million" may signify "a lot."<ref name="Gilsdorf" /> Though it is now regarded as pseudoscience, numerology, or the belief in a mystical significance of numbers, permeated ancient and medieval thought.<ref name="Ore">Ore, Oystein. *Number Theory and Its History*, Courier Dover Publications.</ref> Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.<ref name="Ore" />

During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Today, number systems are considered important special examples of much more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.<ref>Gouvea, Fernando Q. *The Princeton Companion to Mathematics, Chapter II.1, "The Origins of Modern Mathematics"*, p. 82. Princeton University Press, September 28, 2008. ISBN 978-0691118802.</ref>

**Number sections**

Intro Numerals [[Number?section={{safesubst:#invoke:anchor|main}}Main_classification|{{safesubst:#invoke:anchor|main}}Main classification]] Subclasses of the integers Subclasses of the complex numbers Extensions of the concept History See also Notes References External links

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Numbers::**number** Complex::negative System::first Which::natural Numerals::theory Rational::decimal

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{{#invoke:Hatnote|hatnote}}
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A **number** is a mathematical object used to count, measure and label. The original examples are the natural numbers , , , and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, the term *number* may refer to a symbol, a word or a mathematical abstraction.

In mathematics, the notion of number has been extended over the centuries to include , negative numbers, rational numbers such as <math>\frac{1}{2}</math> and <math>-\frac{2}{3}</math>, real numbers such as <math>\sqrt{2}</math> and <math>\pi</math>, complex numbers, which extend the real numbers by including <math>\sqrt{-1}</math>, and sometimes additional objects. Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of the natural numbers.

Besides their practical uses, numbers have cultural significance throughout the world.<ref name="Gilsdorf">Gilsdorf, Thomas E. *Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas*, John Wiley & Sons, Feb 24, 2012.</ref><ref name="Restivo">Restivo, S. *Mathematics in Society and History*, Springer Science & Business Media, Nov 30, 1992.</ref> For example, in Western society the number 13 is regarded as unlucky, and "a million" may signify "a lot."<ref name="Gilsdorf" /> Though it is now regarded as pseudoscience, numerology, or the belief in a mystical significance of numbers, permeated ancient and medieval thought.<ref name="Ore">Ore, Oystein. *Number Theory and Its History*, Courier Dover Publications.</ref> Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.<ref name="Ore" />

During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Today, number systems are considered important special examples of much more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.<ref>Gouvea, Fernando Q. *The Princeton Companion to Mathematics, Chapter II.1, "The Origins of Modern Mathematics"*, p. 82. Princeton University Press, September 28, 2008. ISBN 978-0691118802.</ref>

**Number sections**

Intro Numerals [[Number?section={{safesubst:#invoke:anchor|main}}Main_classification|{{safesubst:#invoke:anchor|main}}Main classification]] Subclasses of the integers Subclasses of the complex numbers Extensions of the concept History See also Notes References External links

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