An Integer (from the Latin 'integer' meaning "whole") is colloquially defined as 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 sq. rt. 2 are not.

The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers, add their additive inverses (the negative integers, i.e., -1, -2, -3, ...). The set of integers is often denoted by the boldface (Z) or blackboard (Z) letter "Z" standing originally for the German word 'Zahlen' (numbers).

"Z" is a subset of the set of all rational numbers Q, which in turn is a subset of the real numbers R. Like the natural numbers, Z is countably infinite.

The integers form the smallest group and the smallest ring containing the real numbers. In the 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.