Examples of using A counterexample in English and their translations into Russian
{-}
-
Official
-
Colloquial
Now Ubuntu GNU/Linux has become a counterexample.
A counterexample was proposed by Diestel and Leader in 2001.
The ZetaGrid project was set up to search for a counterexample to the Riemann hypothesis.
Show with a counterexample that the Hückel rule is not a necessary condition for aromaticity.
In Corollary 1.4 the arc I cannot be replaced by S1:the standard 3-winding is a counterexample 8.
However, in a 1904 paper he described a counterexample to this claim, a space now called the Poincaré homology sphere.
A counterexample near 1018 would require a prime gap fifty million times the size of the average gap.
The court does not always look at the auto-examination already done andprefers to do a counterexample.
Computational experiments have shown that, if a counterexample exists, it would have to have more than 177 vertices.
If a counterexample is being sought or a large-scale proof by exhaustion is being attempted, distributed computing techniques may be used to divide the calculations between multiple computers.
He showed that the conjecture has a counterexample, which he estimated to be around 1.845× 10361.
Therefore, if a counterexample to the Erdős-Straus conjecture exists, the smallest n forming a counterexample would have to be a prime number, and it can be further restricted to one of six infinite arithmetic progressions modulo 840.
Tait conjectured that all amphichiral knots had even crossing number, but a counterexample was found by Morwen Thistlethwaite et al. in 1998.
Therefore, it is a counterexample to Tait's conjecture that every 3-regular polyhedron has a Hamiltonian cycle.
The Kittell graph is named after Irving Kittell,who used it as a counterexample to Alfred Kempe's flawed proof of the four-color theorem.
This publication marks the first known appearance of the Petersen graph in the mathematical literature,12 years before Julius Petersen's use of the same graph as a counterexample to an edge coloring problem.
In the other directions, Kelmans showed that a counterexample could be transformed into a counterexample to the original Barnette conjecture.
One way of proving a statement about the objects of S is to assume the existence of a counterexample and deduce a contradiction.
Published in 1973, it provides a counterexample to the Crispin Nash-Williams conjecture that every 4-regular 4-vertex-connected graph is Hamiltonian.
It was proposed by P. G. Tait(1884) and disproved by W. T. Tutte(1946),who constructed a counterexample with 25 faces, 69 edges and 46 vertices.
Using the same reasoning,they show that a counterexample to Albertson's conjecture for the chromatic number n(if it exists) must have fewer than 4n vertices.
In a classical CEGAR algorithm a path in a program to be explored is called a counterexample and it means a path to the error state.
It can thus be used as a counterexample against the idea that every Artinian module is Noetherian whereas every Artinian ring is Noetherian.
In 1980 the authors Pomerance, Selfridge, andWagstaff offered $30 for the discovery of a counterexample, that is, a composite number that passed this test.
Robertson, Seymour& Thomas(1993a) used this fact in their proof of the case k 6 of the Hadwiger conjecture, the statement that every 6-chromatic graph has the complete graph K6 as a minor: they showed that any minimal counterexample to the conjecture would have to be an apex graph, butsince there are no 6-chromatic apex graphs such a counterexample cannot exist.
If an analyzed property is violated during the verification process and a counterexample is generated, then an error can be localized inside the verified MSC.
At one time it was unclear whether a complex surface such that q andP1 both vanish is rational, but a counterexample(an Enriques surface) was found by Federigo Enriques.
For k 8, this is not true: a graph found by Catlin(1979) as a counterexample to Hajós's conjecture that k-chromatic graphs contain a subdivision of Kk,also serves as a counterexample to this problem.
Francisco(Paco) Santos Leal(born May 28, 1968) is a Spanish mathematician at the University of Cantabria,known for finding a counterexample to the Hirsch conjecture in polyhedral combinatorics.
Moreover, it is even not necessarily a closed set: a counterexample is a sphere passing through the origin, with the conical hull being an open half-space plus the origin.