If there's no need to restrict the coefficients to a finite set, then my favorite "base" system is factorial base, where a positive real number q is written as q = Sum_{k=0 to n} C_k K! + Sum{k=1 to oo} d_k / k!, where 0 <= C_k <= k and 0 <= d_k <= k-1 (so the second sum may as well be from k = 2 to oo) As long as the first sum is chosen to equal the floor of q, and the second sum uses the greedy algorithm, the representation is unique. --Dan Jim wrote: << For those of you who haven't seen the Faltin et al. article, let me mention just one of their tricks: Allow the digits in a base r expansion to be arbitrary non-negative integers, not just elements of {0,1,...,r-1}, and then introduce real numbers as equivalence classes of such expansions.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele