Linked from

The 23 pages that link to Counterexample, each with the reason it gives.

• Proof by contradictionCompared with: A single counterexample refutes a universal statement directly, without an indirect proof.

• Reductio ad absurdumCompared with: Unlike reductio, a counterexample can refute a universal claim without deriving a contradiction.

• Existence theoremCompared with: A single counterexample can refute a related universal claim, unlike proving one instance exists.

• Erdős–Straus conjectureCompared with: One integer n with no valid decomposition would refute the conjecture.

• Littlewood conjectureCompared with: Finding a pair with positive limit inferior would refute the conjecture.

• Herzog–Schönheim conjectureCompared with: No counterexample to the conjecture is known, despite extensive searches.