A degree structure on representations of irrational numbers

We study a degree structure on representations of irrational numbers. (Typical examples of representations are Cauchy sequences, Dedekind cuts and base-10 expansions.) We prove that the structure is a distributive lattice with a least and a greatest element. The maximum degree is the degree of the representation by continued fractions. The minimum degree is the degree of the representation by Weihrauch intersections.