From The Art and Popular Culture Encyclopedia
A number is an abstract object, tokens of which are symbols used in counting and measuring. A 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. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (ISBNs). In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. As a result, there is no one encompassing definition of number and the concept of number is open for further development.
Certain procedures which input one or more numbers and output a number are called numerical operations. Unary operations input a single number and output a single number. For example, the successor operation adds one to an integer: the successor of 4 is 5. More common are binary operations which input two numbers and output a single number. Examples of binary operations include addition, subtraction, multiplication, division, and exponentiation. The study of numerical operations is called arithmetic.