As mentioned, Exponentiation implies recursion principles and so in formula_201, one can reason about sequences formula_202 or about shrinking intervals in formula_203 and this also enables speaking of Cauchy sequences and their arithmetic. Any Cauchy real number is a collection of sequences, i.e. subset of a set of functions on formula_204. More axioms are required to always grant completeness of equivalence classes of such sequences and strong principles need to be postulated to imply the existence of a modulus of convergence for all Cauchy sequences. Weak countable choice is generally the context for proving uniqueness of the Cauchy reals as complete (pseudo-)ordered field. "Pseudo-" here highlights that the order will, in any case, constructively not always be decidable.