1. The problem statement, all variables and given/known data Let E be nonempty subset of R which is bounded above (thus, a = sup E exists) Does there exist a strictly monotone sequence in E which converges to a? 2. Relevant equations 3. The attempt at a solution I've been thinking about just taking a monotone bounded (this must be true by condition of E) sequence of rationals in E(an interval on the real line) which converges to the supremum (endpoint of the interval). I'm not sure how to formally construct this.