Number

A number is a <a href="/facts/Mathematical_object/Juhyow9M">mathematical object</a> used to count, measure, and label. The most basic examples are the <a href="/facts/Natural_number/u65og8JE">natural numbers</a> 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a <a href="/facts/Numeral_system/1KKlG4nd">numeral system</a>, which is an organized way to represent any number. The most common numeral system is the <a href="/facts/Hindu%25E2%2580%2593Arabic_numeral_system/z73KvotW">Hindu–Arabic numeral system</a>, which allows for the representation of any <a href="/facts/Integer/PUwwrawx">non-negative integer</a> using a combination of ten fundamental numeric symbols, called <a href="/facts/Numerical_digit/JJdLBoGT">digits</a>. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with <a href="/facts/Serial_number/2XUENAvJ">serial numbers</a>), and for codes (as with <a href="/facts/ISBN/15AdSPa9">ISBNs</a>). In common usage, a numeral is not clearly distinguished from the number that it represents.
In mathematics, the notion of number has been extended over the centuries to include zero (0), <a href="/facts/Negative_number/LzErzCmI">negative numbers</a>, <a href="/facts/Rational_number/VJQmyY05">rational numbers</a> such as <a href="/facts/One_half/wKqmu9HK">one half</a> 
 
 
 
 
 (
 
 
 
 1
 2
 
 
 
 )
 
 
 
 {\displaystyle \left({\tfrac {1}{2}}\right)}
 
, <a href="/facts/Real_number/R02gw5Pb">real numbers</a> such as the <a href="/facts/Square_root_of_2/SD0sag94">square root of 2</a> 
 
 
 
 
 (
 
 
 2
 
 
 )
 
 
 
 {\displaystyle \left({\sqrt {2}}\right)}
 
 and <a href="/facts/Pi/vC0UBj1q">π</a>, and <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a> which extend the real numbers with a <a href="/facts/Imaginary_unit/1SCllQlU">square root of −1</a> (and its combinations with real numbers by adding or subtracting its multiples). <a href="/facts/Calculation/MHq42Sjw">Calculations</a> with numbers are done with arithmetical operations, the most familiar being <a href="/facts/Addition/apFWJBFB">addition</a>, <a href="/facts/Subtraction/dEUrp6k0">subtraction</a>, <a href="/facts/Multiplication/VtcUjpNv">multiplication</a>, <a href="/facts/Division_(mathematics)/FqLKNkmq">division</a>, and <a href="/facts/Exponentiation/pac6QY2g">exponentiation</a>. Their study or usage is called <a href="/facts/Arithmetic/hvHwkbMV">arithmetic</a>, a term which may also refer to <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, the study of the properties of numbers.
Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the <a href="/facts/13_(number)/HmJtz4cb">number 13</a> is often regarded as <a href="/facts/Unlucky/QocIMUhE">unlucky</a>, and "<a href="/facts/One_million/RMGVIm1j">a million</a>" may signify "a lot" rather than an exact quantity. Though it is now regarded as <a href="/facts/Pseudoscience/kdNzoLeS">pseudoscience</a>, belief in a mystical significance of numbers, known as <a href="/facts/Numerology/xsUjpADK">numerology</a>, permeated ancient and medieval thought. Numerology heavily influenced the development of <a href="/facts/Greek_mathematics/ealke3z8">Greek mathematics</a>, stimulating the investigation of many problems in number theory which are still of interest today.
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 <a href="/facts/Hypercomplex_number/BwKwTBF2">hypercomplex numbers</a>, which consist of various extensions or modifications of the <a href="/facts/Complex_number/2w7mqI7e">complex number</a> system. In modern mathematics, number systems are considered important special examples of more general algebraic structures such as <a href="/facts/Ring_(mathematics)/JnCUXz63">rings</a> and <a href="/facts/Field_(mathematics)/xAjAS4ko">fields</a>, and the application of the term "number" is a matter of convention, without fundamental significance.

Number open-in-new

Number