Proof by Contradiction
📋 What it is
You assume the opposite of what you want, then show it forces an impossibility — so the opposite must be false.
🗣️ Coach says
This is the sneaky-powerful tool. Pretend the claim is FALSE, follow the logic, and watch it crash into nonsense. If assuming “not true” breaks reality, then “true” it is.
🧠 Memory hook
Assume the opposite. If it explodes into nonsense, the original was true all along.
😂 Giggle
Why was the theorem so respected?
Because it had been proven beyond all doubt!
😲 Whoa!
The proof that √2 is irrational is a famous proof by contradiction — it assumes √2 IS a fraction, then shows that fraction can’t exist.
✅ Quick check: You assume “there IS a largest prime,” and that assumption lets you build an even bigger prime. What have you shown?
Say your answer out loud first — then reveal.
There is NO largest prime — the assumption led to a contradiction, so it must be false.
If assuming a statement produces an impossibility, the statement is false.
🧪 Try it! (2 minutes)
Try it in words: assume “I have the tallest possible tower of blocks,” then add one block. What does the contradiction prove?