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.,
Kaprekar number Kaprekar numbers are named after D. R. Kaprekar. Let "X" be a non-negative integer and "n" a positive integer. "X" is an "n"-Kaprekar number for base "b" if there exist non-negative integer "A", and positive integer "B" satisfying: If "d" is any divisor of "n", then "X" is also a "d"-Kaprekar number for base "b". A Kaprekar number for base "b" is one which is an "n"-Kaprekar number for that base and some positive integer "n". More generally, we can define the set "K"("N") for a given integer "N" as the set of integers "X" for which An "n"-Kaprekar number