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.,
Integer complexity this way was originally considered by . They asked for the largest number with a given complexity ; later, Selfridge showed that this number is For example, when , and the largest integer that can be expressed using ten ones is . Its expression is Thus, the complexity of an integer is at least . The complexity of is at most (approximately ): an expression of this length for can be found by applying Horner's method to the binary representation of . Almost all integers have a representation whose length is bounded by a logarithm with a smaller constant factor,