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They worked through the incomplete proof together, starting at the base case and following the inductive step as if it were a narrow bridge. Conversation flickered: a student proposed a lemma, another countered with a tighter bound. At the critical step, one of them, a doctoral candidate named Karim, paused and said, “This is only valid if we assume the function is uniformly continuous on that interval.” one of them

A thorough study of limits, convergence, divergence, and convergence tests (e.g., Cauchy’s convergence criterion, D’Alembert’s ratio test).