Integer 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., −1, −2, −3, …). The set of integers is often denoted by a boldface Z ("") or blackboard bold formula_1 (Unicode U+2124 ℤ) standing for the German word "Zahlen" (, "numbers"). The integers form
Quadratic integer examples of most studies of algebraic number fields. The quadratic integer rings divide in two classes depending on the sign of . If , all elements of formula_22 are real, and the ring is a "real quadratic integer ring". If , the only real elements of formula_22 are the ordinary integers, and the ring is a "complex quadratic integer ring". For real quadratic integer rings, the ideal class number, which measures the failure of unique factorization, is given in OEIS A003649; for the imaginary case, they are given in OEIS A000924. For < 0, ω is a complex (imaginary or