What is integer?

An integer is a number that can be written without a fractional component. It is often a primitive data type in computer languages. However, integer data types can only embody a subset of all integers, since practical computers are of finite capacity — integers from the smallest group containing natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to classify them from the more general algebraic integers.

The integers are the algebraic integers, which are also rational numbers. Integers can be formally assembled as the equivalence classes of ordered pairs of natural numbers. Integers are the only non- trivial ordered abelian group whose positive elements are well ordered. Also, the addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers.