(untitled) (The São Paulo Journal of Mathematical Sciences, 2008)
It is well-known that stable Cantor sets are topologically conjugate to adding machines. In this work we show are also conjugate to an algebraic object, the ring of P−adic integers with respect to group tramnslation. This ring is closely related to the field of p-adic numbers; connections and distintions are explored. The inverse limit construction provides a purely dynamical proof of an algebraic result: the classification of adding machines, or P−adic integers, up to group isomorphism.