# Integer

nummer that can be written wioot a fractional or decimal component
(Reguidit frae Integers)

An integer is a nummer that can be written wioot a fractional or decimal component. For example, 21, 4, an −2048 are integers; 9.75, 5½, an 2 are nae integers. The set o integers is a subset o the real nummers, an consists o the naitural nummers (1, 2, 3, ...), zero (0) an the negatives o the naitural nummers (−1, −2, −3, ...).

The name derives frae the Laitin integer (meanin leeterally "untouched," hence "whole": the wird entire comes frae the same origin, but via French). The set o aw integers is eften denotit bi a bauldface Z (or blackboard bold $\mathbb {Z}$ , Unicode U+2124 ℤ), which stands for Zahlen (German for nummers, pronoonced [ˈtsaːlən]).

The integers (wi addeetion as operation) furm the smawest group containin the additive monoid o the naitural nummers. Lik the naitural nummers, the integers furm a coontably infinite set. In algebraic nummer theory, these commonly unnerstuid integers, embeddit in the field o rational nummers, are referred tae as rational integers tae distinguish them frae the mair broadly defined algebraic integers.

The integers (wi addeetion an multiplication addition) furm a unital ring which is the maist basic ane, in the follaein sense: for ony unital ring, thare is a unique ring homomorphism frae the integers intae this ring. This universal property characterize the integers.