Definition of Numbers
A number is an abstract entity that represents a count or measurement. A symbol for a number is called a numeral. In common usage, numerals are often used as labels (road and telephone numbers), as indicators of order (serial numbers), and as codes (ISBN). In mathematics, the definition of a number has extended to include abstractions such as fractions, negative, irrational, transcendental and complex numbers.

The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.
Numbers should be distinguished from numerals, the symbols used to represent numbers. The number five can be represented by both the base ten numeral 5 and by the Roman numeral V. Notations used to represent numbers are discussed in the article numeral systems. An important development in the history of numerals was the development of a positional system, like modern decimals, which can represent very large numbers. The Roman numerals require extra symbols for larger numbers.
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