Cauchy Completeness and existence of limits.
Sometimes it is useful to have criterion for when a sequence of real or complex numbers exists. In this video, we talk about one such criterion, the Cauchy completeness theorem which can be considered, a "feature" of the real numbers. We'll use it to show any decreasing sequence of real numbers which is bounded below has a limit. As an application, we show that the Newton-Raphson method for approximating square roots of numbers converges to the correct value.