Finite Automata and the Writing of Numbers

Abstract

Numbers do exist, independently of the way we represent them, of the way we write them. And there are many ways to write them: integers as finite sequence of digits once a base is fixed, rational numbers as a pair of integer or as an ultimately periodic infinite sequence of digits, or reals as an infinite sequence of digits but also as a continued fraction, just to quote a few. Operations on numbers are defined, independently of the way they are computed. But when they are computed they amounts to be algorithms that work on the representations of numbers.