Let be an Archimedean ordered integral domain and let be the unit interval in . The infinite decimal representation of is a function from the unit interval in to the type of sequences in the natural numbers that are bounded below by and bounded above by , such that is equal to the limit of the following sequence
The infinite decimal representation of the rational numbers consist of all the eventually periodic sequences in the natural numbers that are bounded below by and bounded above by .
The infinite decimal representation of the decimal numbers consist of all the sequences such that there is a natural number such that for all decimal number and natural numbers , or .