hasCounterexample
P64864
predicate
Indicates that there exists at least one specific case or instance that disproves or violates a given claim, rule, or general statement.
Observed surface forms (6)
- disproofMethod ×3
- counterexampleInvolves ×2
- hasCounterexampleProvidedBy ×1
- hasCounterexamples ×1
- isCounterexampleTo ×1
- isUsedAsCounterexampleTo ×1
Sample triples (13)
| Subject | Object |
|---|---|
| Fermat's theorem on sums of two squares | 3 ≡ 3 (mod 4) and 3 is not a sum of two squares ⓘ |
| Fermat's theorem on sums of two squares | 7 ≡ 3 (mod 4) and 7 is not a sum of two squares ⓘ |
| Hilbert’s fourteenth problem | Masayoshi Nagata via predicate surface "hasCounterexampleProvidedBy" ⓘ |
| Hilbert’s fourteenth problem | non-finitely generated ring of invariants via predicate surface "counterexampleInvolves" ⓘ |
| Hilbert’s fourteenth problem | action of an algebraic group on affine space via predicate surface "counterexampleInvolves" ⓘ |
| Whitney umbrella | naive generalizations of manifold properties to singular varieties via predicate surface "isUsedAsCounterexampleTo" ⓘ |
| Connes embedding problem | construction of non-hyperlinear II₁ factors via predicate surface "disproofMethod" ⓘ |
| Connes embedding problem | use of nonlocal games and quantum correlations via predicate surface "disproofMethod" ⓘ |
| Szekeres snark | 3-edge-colorability of bridgeless cubic graphs via predicate surface "isCounterexampleTo" ⓘ |
| Pólya’s conjecture | existence of counterexamples for large x via predicate surface "disproofMethod" ⓘ |
| Pólya’s conjecture | values of x for which M(x) > 0 via predicate surface "hasCounterexamples" ⓘ |
| Hilbert's third problem | pairs of polyhedra of equal volume that are not equidecomposable ⓘ |
| Hilbert's third problem | cube and regular tetrahedron of equal volume ⓘ |