# Integer

## Number in {..., –2, –1, 0, 1, 2, ...} / From Wikipedia, the free encyclopedia

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An **integer** is the number zero (0), a positive natural number (1, 2, 3, etc.) or a **negative integer** (−1, −2, −3, etc.).^{[1]} The negative numbers are the additive inverses of the corresponding positive numbers.^{[2]} The set of all integers is often denoted by the boldface **Z** or blackboard bold $\mathbb {Z}$.^{[3]}^{[4]}

The set of natural numbers $\mathbb {N}$ is a subset of $\mathbb {Z}$, which in turn is a subset of the set of all rational numbers $\mathbb {Q}$, itself a subset of the real numbers $\mathbb {R}$.^{[lower-alpha 1]} Like the set of natural numbers, the set of integers $\mathbb {Z}$ 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.^{[8]}

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.