An integer is the number zero (0), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). The negations or additive inverses of the positive natural numbers are referred to as … See more

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

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. … See more

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 See more

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, See more

$${\displaystyle \mathbb {Z} }$$ 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 … See more

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 See more