An

**integer** (from the Latin

*integer* meaning "whole") is a 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.

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An **integer** (from the Latin *integer* meaning "whole") is a 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.

The set of integers consists of zero (0), the natural numbers (1, 2, 3, …), also called *whole numbers* or *counting numbers*, and their additive inverses (the **negative integers**, i.e., −1, −2, −3, …). This is often denoted by a boldface Z ("**Z**") or blackboard bold $\mathbb {Z}$ (Unicode U+2124 ℤ) standing for the German word *Zahlen* ([ˈtsaːlən], "numbers"). ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite.

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

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