Misconceptions & Reasoning
📋 What it is
Common traps: “it worked for examples so it’s proven,” and “I can’t find a proof so it’s false.”
🗣️ Coach says
Two mistakes trip everyone up. First: examples are NOT a proof (they only support a conjecture). Second: failing to find a proof doesn’t make something false — maybe you just haven’t found it yet. Spot these and you’re ahead.
🧠 Memory hook
Examples ≠ proof. And “I couldn’t prove it” ≠ “it’s false.”
😂 Giggle
Why did the mathematical induction feel infinite?
Because it proved the base case and then said "and the next one, and the next one, forever!"
😲 Whoa!
Fermat’s Last Theorem resisted proof for 358 years — “nobody has proven it” never meant it was false; it was finally proven in 1994.
✅ Quick check: A friend says “this rule works for the first 100 numbers, so it’s definitely true forever.” What’s the flaw?
Say your answer out loud first — then reveal.
Checking 100 cases supports the conjecture but doesn’t prove it — the 101st (or millionth) could still break it.
No finite number of confirming examples proves a statement about infinitely many cases.
🧪 Try it! (2 minutes)
Find a claim that’s true for small numbers but you’re not sure holds forever. Notice the itch to call it “proven” — and resist it.