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.,
Transposable integer permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits from the repeating decimal starting from different digits. This illustrates that cyclic permutations are somehow related to repeating decimals and the corresponding fractions. The greatest common divisor (gcd) between any cyclic permutation of an "m"-digit integer and 10 − 1 is constant. Expressed as a formula, where "N" is an "m"-digit integer; and "N" is any cyclic permutation of "N". For example, If "N" is an "m"-digit integer, the number "N", obtained by shifting "N" to the left cyclically, can be obtained from: where