# Episode 4: The Domino Effect

**Objective:** To master mathematical induction in all its forms—ordinary, strong, and structural—and understand how the Well-Ordering Principle provides the logical foundation for these techniques [Part III, 8].

### I. Introduction: Turning the Infinite into the Finite

* **The Problem of "Forever":** How to prove a pattern holds for all natural numbers without checking each case individually.

* **The Domino Analogy:** Understanding the two steps required to start a chain reaction—knocking over the first domino (base case) and ensuring each falling domino knocks over the next (inductive step).

### II. Segment 1: Ordinary Mathematical Induction (Chapter 10)

* **The Principle of Mathematical Induction (PMI):**

* **The Base Case:**

* **Th ...