MIT's 18.100B Real Analysis course continues with Tobias Holck Colding on the Cauchy criterion for convergence. The lecture addresses a practical problem in analysis: proving a sequence converges without knowing its limit in advance. Colding defines a Cauchy sequence, shows the equivalence between being Cauchy and being convergent in the real numbers, and works through the proof carefully, building on earlier lectures about sequences and limits. He then turns to applications, demonstrating where this criterion does real work in analysis, particularly in settings where an explicit limit is hard or impossible to write down. The session runs 77 minutes and is delivered chalkboard-style, in the standard MIT OpenCourseWare lecture format, with Colding developing each step of the argument at the board rather than through slides.