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
Comparison sort An identical upper bound follows from the existence of the algorithms that attain this bound in the worst case. The above argument provides an "absolute", rather than only asymptotic lower bound on the number of comparisons, namely formula_8 comparisons. This lower bound is fairly good (it can be approached within a linear tolerance by a simple merge sort), but it is known to be inexact. For example, formula_9, but the minimal number of comparisons to sort 13 elements has been proved to be 34. Determining the "exact" number of comparisons needed to sort a given number of entries is a