A Cauchy sequence detects convergence from inside the sequence: sufficiently late terms become arbitrarily close to one another without first knowing the limit. This complete Woody Calculus lesson develops the formal epsilon-N definition, proves that every convergent sequence is Cauchy, explains why ℚ is incomplete and ℝ is complete, and connects completeness to metric spaces, compactness, function spaces, and Banach fixed-point theory.