 The existence of a modulus for a Cauchy sequence follows from the well-ordering property of the natural numbers (let formula_10 be the smallest possible formula_11 in the definition of Cauchy sequence, taking formula_12 to be formula_13).The existence of a modulus also follows from the principle of dependent choice, which is a weak form of the axiom of choice, and it also follows from an even weaker condition called AC00.