Every real function continuous on a closed interval is representable as a convergent sequence of step functions defined by an R-converter. Deterministic and nondeterministic R-converters are considered with the corresponding classes of operators that they define in the Cantor space. It is shown that the problem of finding the roots of the equation f(x) = 0 for a continuous and sign-constant function on [0, 1] cannot be solved by a deterministic R-converter, while a nondeterministic R-converter produces a solution of this problem.