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
Integer matrix not become excessively large (see condition number). Theorems from matrix theory that infer properties from determinants thus avoid the traps induced by ill conditioned ("nearly" zero determinant) real or floating point valued matrices. The inverse of an integer matrix formula_3 is again an integer matrix if and only if the determinant of formula_3 is exactly formula_5 or formula_6. Integer matrices of determinant formula_5 form the group formula_8, which has far-reaching applications in arithmetic and geometry. For formula_9, it is closely related to the modular group. The intersection of the integer matrices with the orthogonal group is the group of signed