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.,
Eisenstein integer integer is said to be an Eisenstein prime if its only non-unit divisors are of the form , where is any of the six units. There are two types of Eisenstein primes. First, an ordinary prime number (or "rational prime") which is congruent to is also an Eisenstein prime. Second, 3 and any rational prime congruent to is equal to the norm of an Eisentein integer . Thus, such a prime may be factored as , and these factors are Eisenstein primes: they are precisely the Eisenstein integers whose norm is a rational prime. The ring of Eisenstein integers forms