Counterexample
- Category
- STANDARD MATHEMATICS
- Definition
- A legitimate example that shows a universal claim is false.
- Math Level
- GENERAL
A counterexample is a legitimate example that shows a universal mathematical statement is false.
One counterexample is enough because the original claim says every permitted case must work. Riemann Console treats counterexamples as useful progress when they eliminate an over-strong conjecture or research route.
See also: universal statement, exact counterexample, numerical counterexample, hostile testing..