9. one of the first things that we did in our work with analysis was provide axioms for r and one of our axioms was the axiom of completeness. it is possible to use the monotone convergence theorem as an axiom instead (and then to derive the axiom of completeness from it). our proof of the nested interval property in class relied on the axiom of completeness. provide an alternate proof of the nested interval property that does not use the axiom of completeness but instead uses the monotone convergence theorem.