Chapter 4 Sec. 5: Discontinuities [Principles of Mathematical Analysis]

Welcome back to Chapter 4 of Principles of Mathematical Analysis. So far we have studied continuous functions and the beautiful ways continuity interacts with compactness and connectedness. In this short but important section we turn the question around and ask: when a function fails to be continuous at a point, what does that failure look like? It turns out that not all discontinuities are alike. We will introduce one-sided limits, use them to sort discontinuities into two clean categories, and then walk through four carefully chosen examples that show how wild a discontinuity can get. Let's begin. Slides: https://github.com/petercerno/princip...