Using factorial base (which I'd also thought of) I can show that for any real x whose factorial base expansion is x = integer + a_2/2! + . . . + a_n/n! + . . . (0 <= a_n <= n-1) with a *bounded* set of coefficients {a_n}, the set {frac(n!*x)} cannot be dense in ([0,1). This is an uncountable set of reals {x}, but it has measure 0. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele