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 sorting the square root of their previous magnitude. Repeating this range reduction until the keys are small enough to bucket sort leads to an algorithm with running time . A complicated randomized algorithm of in the word RAM model of computation allows these time bounds to be reduced even farther, to . An integer sorting algorithm is said to be "non-conservative" if it requires a word size that is significantly larger than . As an extreme instance, if , and all keys are distinct, then the set of keys may be sorted in linear time by representing it as a bitvector,