real analysis - intuition behind Monotone convergence theorem . . . Step 3: Finally, I propose the utilization of a diagonalization argument to establish the Monotone Convergence Theorem conclusively Your guidance and feedback would be greatly appreciated in refining this approach to the Monotone Convergence Theorem
Every bounded monotone sequence converges - Mathematics Stack Exchange If you want to prove the statement, if a sequence is monotone and bounded then it converges, the logically equivalent contrapositive would be, if a sequence is divergent then either it is not monotone or it is not bounded So, your idea would only get you halfway there You would also need to prove that divergent bounded sequences cannot be