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.,
Radical of an integer no known polynomial-time algorithm for computing the square-free part of an integer. The definition is generalized to the largest "t"-free divisor of "n", formula_5, which are multiplicative functions which act on prime powers as The cases "t"=3 and "t"=4 are tabulated in and . The notion of the radical occurs in the abc conjecture, which states that, for any "ε" > 0, there exists a finite "K" such that, for all triples of coprime positive integers "a", "b", and "c" satisfying "a" + "b" = "c", For any integer formula_8, the nilpotent elements of the finite ring formula_9 are all