Chapter 4 Sec. 6: Monotonic Functions [Principles of Mathematical Analysis]
Welcome back to Chapter 4 on continuity. In this section we study monotonic functions, that is, functions which never decrease, or never increase, on a given interval. These functions are remarkably well behaved. We will see that their one-sided limits always exist, that they can only be discontinuous in the mildest possible way, and that they can have at most countably many discontinuities. Let's get started. Slides: https://github.com/petercerno/princip...
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Chapter 4 Sec. 2: Continuous Functions [Principles of Mathematical Analysis]
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Chapter 4 Sec. 3: Continuity and Compactness [Principles of Mathematical Analysis]
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