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 integer "k" such that . Set and For , put In other words, the canonical β-expansion of "x" is defined by choosing the largest "d" such that , then choosing the largest "d" such that , etc. Thus it chooses the lexicographically largest string representing "x". With an integer base, this defines the usual radix expansion for the number "x". This construction extends the usual algorithm to possibly non-integer values of β. Base behaves in a very similar way to base 2 as all one has to do to convert a number from binary into base is put a zero