The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus tangere ("to touch"). "Entire" derives from the same origin via the 展开

Traditional development
In elementary school teaching, integers are often intuitively defined as the union of the (positive) natural … 展开

The set of integers is countably infinite, meaning it is possible to pair each integer with a unique natural number. An example of such a pairing is
(0, 1), (1, 2), (−1, 3), (2, 4), (−2, 5), (3, 6), . . . ,(1 − k, 2k − 1), (k, 2k ), . . .
More technically, the 展开

Like the natural numbers, $${\displaystyle \mathbb {Z} }$$ is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers (and importantly, 展开

$${\displaystyle \mathbb {Z} }$$ is a totally ordered set without upper or lower bound. The ordering of $${\displaystyle \mathbb {Z} }$$ is given by: :... −3 < −2 < −1 < 0 < 1 < 2 < 3 < ... An integer is positive if it is greater than zero, and negative if it is less than zero. Zero is … 展开

An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in … 展开

1. ^ More precisely, each system is embedded in the next, isomorphically mapped to a subset. The commonly-assumed set-theoretic … 展开