Mathematical Induction
📋 What it is
Induction proves a statement for ALL whole numbers by proving step 1, then proving each step forces the next.
🗣️ Coach says
Careful — this “induction” is a PROOF (certain), not the guessing kind. Show it works for the first case, then show “if it works for n, it works for n+1.” Like dominoes: knock the first, and every one falls.
🧠 Memory hook
Base case + the domino step. First domino falls + each knocks the next = ALL fall.
😂 Giggle
Why did proof by exhaustion need a nap?
Because it tested EVERY. SINGLE. CASE.
😲 Whoa!
Mathematical induction lets you prove something about infinitely many numbers with just two finite steps — one of the most efficient ideas in all of math.
✅ Quick check: You prove a formula works for n = 1, and prove “if it works for n, it works for n+1.” Which numbers is it now proven for?
Say your answer out loud first — then reveal.
All whole numbers from 1 up — the base case starts the chain and the step carries it forever.
The base plus the inductive step together cover every natural number, like falling dominoes.
🧪 Try it! (2 minutes)
Line up real dominoes (or books). Push the first and explain out loud why the whole row falling matches the two steps of induction.