# Integer

nummer that can be written wioot a fractional or decimal component

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, ...).

Seembol eften uised tae denote the set o integers (see Leet o mathematical seembols)

The name derives frae the Laitin integer (meanin leeterally "untouched," hence "whole": the wird entire comes frae the same origin, but via French[1]). The set o aw integers is eften denotit bi a bauldface Z (or blackboard bold ${\displaystyle \mathbb {Z} }$, Unicode U+2124 ℤ), which stands for Zahlen (German for nummers, pronoonced [ˈtsaːlən]).[2][3]

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.

## References

1. Evans, Nick (1995). "A-Quantifiers and Scope". In Bach, Emmon W (ed.). Quantification in Natural Languages. Dordrecht, The Netherlands; Boston, MA: Kluwer Academic Publishers. p. 262. ISBN 0-7923-3352-7.
2. Miller, Jeff (2010-08-29). "Earliest Uses of Symbols of Number Theory". Retrieved 2010-09-20.
3. Peter Jephson Cameron (1998). Introduction to Algebra. Oxford University Press. p. 4. ISBN 978-0-19-850195-4.