Integer If the domain is restricted to then each and every member of has one and only one corresponding member of N and by the definition of cardinal equality the two sets have equal cardinality. Integer An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The set of integers consists of zero (), the positive natural numbers (, , , …), also called "whole numbers" or "counting numbers", and their additive inverses (the negative integers, i.e.,
Gaussian integer to 3 modulo 4 (that is, it may be written , with a nonnegative integer) . The other prime numbers are not Gaussian primes, but each is the product of two conjugate Gaussian primes. A Gaussian integer is a Gaussian prime if and only if either: In other words, a Gaussian integer is a Gaussian prime if and only if either its norm is a prime number, or it is the product of a unit () and a prime number of the form . It follows that there are three cases for the factorization of a prime number in the