Re: [math-fun] 0.9999... = 1 and all that

A colleague who's an algebraist in the UC-Berkeley math dept. assures me that for N any integer >= 2, "multiplication is certainly continuous in the standard topology on the N-adic integers, since this is the inverse limit of the discrete topologies on the rings Z/N^k, under which multiplication is certainly continuous." So as I had read somewhere, there is indeed a natural multiplication on the N-adic integers which is continuous relative to the topology induced by the N-adic metric. Even though for N composite the N-adic integers do have zero-divisors. --Dan Daniel Asimov Visiting Scholar Department of Mathematics University of California Berkeley, California