The discussion focuses on the existence of a monotone increasing sequence {an} within a nonempty subset A of R that is bounded above, demonstrating that α=supA can be approached as the limit of this sequence. It is established that for every positive integer n, the set \{ a_i | |a_i - α| < 1/n \} is non-empty, allowing for the selection of elements to form the subsequence. The question of whether the sequence can be strictly increasing is raised, but the discussion does not provide a definitive conclusion on this aspect.
PREREQUISITESMathematics students, particularly those studying real analysis, educators teaching sequence convergence, and researchers exploring properties of monotone sequences.