1. The problem statement, all variables and given/known data Use the Monotone convergence theorem to give a proof of the Nested interval property. 2. Relevant equations Monotone convergence theorem: If a sequence is increasing or decreasing and bounded then it converges. Nested Interval property: If we have a closed interval [a,b] and we keep making intervals inside this and they keep getting smaller the union of all these intervals is non-empty and contains one element. 3. The attempt at a solution If we started at the left endpoint of some closed interval and we had a monotonically increasing sequence and it continued on the to right with equally spaced steps, and we had a decreasing sequence that started from the right endpoint, eventually these 2 sequences will be heading towards each other and eventually reach the same common point. I think I need to be careful about how I pick the spacing between the terms in the sequence. Am I headed in the right direction with this.