**Integer**

The **integers** (from the Latin *integer,* literally "untouched," hence "whole": the word *entire* comes from the same origin, but via French) are formed by the natural numbers (including 0) (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as a subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {..., −2, −1, 0, 1, 2, ...}. For example, 21, 4, and −2048 are integers; 9.75, 5½, and √2 are not integers.

The set of all integers is often denoted by a boldface **Z** (or blackboard bold, Unicode U+2124 ℤ), which stands for *Zahlen* (German for *numbers*, pronounced ).

The integers (with addition as operation) form the smallest group containing the additive monoid of the natural numbers. Like the natural numbers, the integers form a countably infinite set.

In algebraic number theory, these commonly understood integers, embedded in the field of rational numbers, are referred to as **rational integers** to distinguish them from the more broadly defined algebraic integers.

Read more about Integer: Algebraic Properties, Order-theoretic Properties, Construction, Integers in Computing, Cardinality

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