# Integer

An **integer** is the number zero (0), a positive natural number (1, 2, 3, etc.) or a **negative integer** with a minus sign (−1, −2, −3, etc.).[1] The negative numbers are the additive inverses of the corresponding positive numbers.[2] In the language of mathematics, the set of integers is often denoted by the boldface **Z** or blackboard bold .[3][4][5]

Algebraic structure → Group theoryGroup theory |
---|

The set of natural numbers is a subset of , which in turn is a subset of the set of all rational numbers , itself a subset of the real numbers .[lower-alpha 1] Like the natural numbers, is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.[9]

The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as **rational integers** to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.