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.,
Non-integer representation field extension of the rationals containing β. Then any real number in [0,1) having a periodic β-expansion must lie in Q(β). On the other hand, the converse need not be true. The converse does hold if β is a Pisot number , although necessary and sufficient conditions are not known. Non-integer representation A non-integer representation uses non-integer numbers as the radix, or bases, of a positional numbering system. For a non-integer radix β > 1, the value of is The numbers "d" are non-negative integers less than β. This is also known as a β-expansion, a notion introduced by and