Number systems

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, number may refer to a symbol, a word, or a mathematical abstraction.

In mathematics, the notion of number has been extended over the centuries to include 0, negative numbers, rational numbers such as $1 / 2$ and $- 2 / 3$ , real numbers such as $\sqrt 2$ and $π$ , and complex numbers, which extend the real numbers by adding a square root of $-1$ . Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers.