Published online by Cambridge University Press: 26 February 2010
Write ‖θ‖ for the distance from the real number θ to the nearest integer. An n-tuple of real numbers (β1, …, βn) will be called badly approximable, if there is constant C > 0 such that
for all positive integers q. As is well known, a single number β is badly approximable if and only if the partial quotients in its continued fraction are bounded.