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 triangle longest side is shorter than the sum of the other two sides. Each such triple defines an integer triangle that is unique up to congruence. So the number of integer triangles (up to congruence) with perimeter "p" is the number of partitions of "p" into three positive parts that satisfy the triangle inequality. This is the integer closest to when "p" is even and to when "p" is odd. It also means that the number of integer triangles with even numbered perimeters "p" = 2"n" is the same as the number of integer triangles with odd numbered perimeters "p" =