Continued Radicals To appear in The Ramanujan Journal.

If a1, a2, . . . , an are nonnegative real numbers and fj(x) = √ aj + x, then f1 ◦ f2 ◦ · · · ◦ fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n → ∞ of such an expression is a continued radical. We consider the set of real numbers S(M) representable as a continued radical whose terms a1, a2, . . . are all from a finite set M . We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.