Self learner here. This is the typical proof for the Monotone Convergence Theorem. Typically the pattern I've seen for proving convergence is based on the epsilon delta definition of a limit L of an infinite sequence where the trick is to find the right value of N and then use that to prove that $|a_n - L| < \epsilon$. This proof doesn't seem to follow this approach to me because N is never really defined in the proof, so that's why I am confused. Thank you in advance for your answer.
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