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Counterexample

Foundations and logic

A single case satisfying a claim’s hypotheses but failing its conclusion, which is enough to disprove the claim outright.

What is usually left out

The asymmetry is the point: proving a universal statement requires an argument covering every case, while refuting it requires exactly one. This is why a conjecture can accumulate overwhelming numerical support and still be false, and why the smallest known counterexample to a statement is sometimes astronomically large.

Related terms