26 Volume 5 — Analysis and proof
The central move of this volume is taming the infinite.
Up until now, you’ve relied on assumptions about how numbers behave between points. This volume strips away those assumptions and rebuilds mathematics on a rigorous foundation of limits, instantaneous rates of change, and continuous accumulation.
By the end of this volume, you will understand how to freeze a changing system precisely at a moment in time, how to add up an infinite number of infinitely small pieces, and how to construct a rock-solid logical argument that proves why something must guaranteeably be true.
26.1 Chapters
| Chapter | Title | Core move |
|---|---|---|
| 1 | Limits and continuity | Approaching the boundary |
| 2 | Differential calculus | Measuring instantaneous change |
| 3 | Integral calculus | Accumulating continuous amounts |
| 4 | Proof and reasoning | Establishing absolute certainty |