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 form a commutative ring, which is a subring of the field of complex numbers. It is thus an integral domain. When considered within the complex plane, the Gaussian integers constitute the -dimensional integer lattice. The "conjugate" of a Gaussian integer is the Gaussian integer . The "norm" of a Gaussian integer is its product with its conjugate. The norm of a Gaussian integer is thus the square of its absolute value as a complex number. The norm of a Gaussian integer is a nonnegative integer, which is a sum of two squares. Thus a norm cannot be of the form