Three Counterexamples
Definitions are easy; boundaries only show up in counterexamples
I'm learning [concept] and I already know the definition plus two typical examples. Give me three counterexamples, one per case: 1) looks like it fits the definition but doesn't; 2) counts only while a certain condition holds, and stops counting when it doesn't; 3) often used as a textbook example but is really a boundary case. For each, say which element of the definition it violates and what goes wrong if I misclassify it.
How to use
Case 2 earns its keep — it hands you a boundary condition instead of a single point.
Good for
- You know the definition cold and still hesitate on real cases
- Your team needs one shared line for what counts — an incident, an active user — and definitions alone won't settle it
Not for
- You need a single fast judgment, such as whether this contract counts as a breach; a boundary discussion wastes the time
- The concept itself is contested (consciousness, intelligence), where counterexamples surface the disagreement instead of resolving it
Example
Input
Compound interest. I know the definition: interest earns interest.
What you get
It should produce all three: a lookalike (simple interest with annual top-ups, which grows fast but never compounds), a conditional case (negative returns, where compounding magnifies the loss and flips the sign), and a boundary case (per-second accrual in high-frequency trading, real in the math but eaten by costs). Each one should point back to whether the interest base includes interest already earned.
Common mistakes
- Mistaking 'doesn't apply to me' for a counterexample; a counterexample sits on the boundary of the concept, it isn't just irrelevant
- Supplying three versions of the same type (all numeric extremes), which draws no boundary at all
Try tweaking it like this
- Ask for 'three counterexamples plus who is most likely to misclassify each', which suits training and checklists
- Add 'if I exclude all three, is the definition still usable?', which tests the definition rather than the examples