Degree of independence of numbers

Abstract

Abstract A new concept of independence of real numbers, called degree independence, which contains those of linear and algebraic independences, is introduced. A sufficient criterion for such independence is established based on a 1988 result of Bundschuh, which in turn makes use of a generalization of Liouville’s estimate due to Feldman in 1968. Applications to numbers represented by Cantor series and product expansions are derived.