Integer If the domain is restricted to then each and every member of has one and only one corresponding member of N and by the definition of cardinal equality the two sets have equal cardinality. 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.,
Counting sort the sets of items within each bucket, whereas counting sort instead stores a single number (the count of items) per bucket. In the most general case, the input to counting sort consists of a collection of items, each of which has a non-negative integer key whose maximum value is at most . In some descriptions of counting sort, the input to be sorted is assumed to be more simply a sequence of integers itself, but this simplification does not accommodate many applications of counting sort. For instance, when used as a subroutine in radix sort, the keys for each call