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.,
Algebraic integer . Each algebraic integer belongs to the ring of integers of some number field. A number is an algebraic integer if and only if the ring is finitely generated as an Abelian group, which is to say, as a -module. The following are equivalent definitions of an algebraic integer. Let be a number field (i.e., a finite extension of , the set of rational numbers), in other words, for some algebraic number by the primitive element theorem. Algebraic integers are a special case of integral elements of a ring extension. In particular, an algebraic integer is an integral element of