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 relation algorithm is an integer relation between any two real numbers "x" and "x". The algorithm generates successive terms of the continued fraction expansion of "x"/"x"; if there is an integer relation between the numbers then their ratio is rational and the algorithm eventually terminates. Integer relation algorithms have numerous applications. The first application is to determine whether a given real number "x" is likely to be algebraic, by searching for an integer relation between a set of powers of "x" {1, "x", "x", ..., "x"}. The second application is to search for an integer relation between a real number "x" and