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Number

A ** number ** is a [mathematical object] used in [counting] and [measuring] . A notational symbol which represents a number is called a [numeral] , but in common usage the word number is used for both the abstract object and the symbol, as well as for the [word] for the number. In addition to their use in counting and measuring, numerals are often used for labels ( [telephone number] s), for ordering ( [serial number] s), and for codes ( [ISBN] s). In [mathematics] , the definition of number has been extended over the years to include such numbers as [0] , [negative numbers] , [rational numbers] , [irrational numbers] , and [complex numbers] .

Certain procedures which take one or more numbers as input and produce a number as output are called numerical [operations] . [Unary operations] take a single input number and produce a single output number. For example, the [successor] operation adds one to an integer, thus the successor of 4 is 5. More common are [binary operations] which take two input numbers and produce a single output number. Examples of binary operations include [addition] , [subtraction] , [multiplication] , [division] , and [exponentiation] . The study of numerical operations is called [arithmetic] .

The branch of mathematics that studies structure in number systems, by means of topics such as [groups] , [rings] and [fields] , is called [abstract algebra] .

** Types of numbers **

Different types of numbers are used in different cases. Numbers can be classified into [sets] , called [number system] s. (For different methods of expressing numbers with symbols, such as the [Roman numerals] , see [numeral system] s.)

** Natural numbers **

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