This is a beta course, so its structure, chapters, and examples may continue to change.
Mathematical Induction
Mathematical induction is a powerful tool for proving propositions related to natural numbers. It is like toppling a row of dominoes—as long as you prove that the first one falls, and that each falling domino causes the next to fall, then all the dominoes will fall.
The Inspiration of Dominoes
Imagine an infinitely long row of dominoes. To make all the dominoes fall, two conditions must be satisfied:
- The first domino falls (the base case)
- Whenever any domino falls, it causes the next one to fall (the recurrence relation)
This is the core idea of mathematical induction!