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 (e.g. road, telephone and house numbering), as indicators of order (serial numbers), and as codes (ISBN). more...

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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.

Types of numbers

Numbers can be classified into sets called number systems. For different methods of expressing numbers with symbols, see numeral systems.

Natural numbers

The most familiar numbers are the natural numbers, which to some mean the non-negative integers and to others mean the positive integers. In everyday parlance the non-negative integers are commonly referred to as whole numbers, the positive integers as counting numbers.

In the base ten number system, in almost universal use, the symbols for natural numbers are written using ten digits, 0 through 9. An implied place value system, one that increments in powers of ten, is used for numbers greater than nine. Thus, numbers greater than nine have numerals formed with two or more digits. The symbol for the set of all natural numbers is

Integers

Negative numbers are numbers which are less than zero. They are usually written by indicating their opposite, which is a positive number, with a preceding minus sign. For example, if a positive number is used to indicate distance to the right of a fixed point, a negative number would indicate distance to the left. Similarly, if a positive number indicates a bank deposit, then a negative number indicates a withdrawal. When the negative whole numbers are combined with the positive whole numbers and zero, one obtains the integers

Rational numbers

A rational number is a number that can be expressed as a fraction with an integer numerator and a non-zero natural number denominator. The fraction m/n represents the quantity arrived at when a whole is divided into n equal parts, and m of those equal parts are chosen. Two different fractions may correspond to the same rational number; for example ½ and 2/4 are the same. If the absolute value of m is greater than n, the absolute value of the fraction is greater than one. Fractions can be positive, negative, or zero. The set of all fractions includes the integers, since every integer can be written as a fraction with denominator 1. The symbol for the rational numbers is a bold face Read more at Wikipedia.org