Примеры использования Counterexamples на Английском языке и их переводы на Русский язык
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Counterexamples in analysis.
Jordan M. Stoyanov: Counterexamples in Probability.
This topology is used to provide interesting examples and counterexamples.
Other counterexamples may be found among the rank one symmetric spaces.
However, if false,it has only finitely many counterexamples.
Other counterexamples were found later, in many cases based on Grinberg's theorem.
Generalized to directed graphs, the conjecture has simple counterexamples, as observed by Poljak& Rödl 1981.
These counterexamples are translated to functional tests that can be simulated by the HDL simulator.
However, a heuristic argument by Pomerance suggests that there are infinitely many counterexamples.
These two graphs provide counterexamples to the conjecture of W. T. Tutte that every cubic 3-connected bipartite graph is Hamiltonian.
However, a heuristic argument by Carl Pomerance andHendrik W. Lenstra suggests there are infinitely many counterexamples.
This applies only to connected graphs;disconnected counterexamples include disjoint unions of odd cycles, or of copies of K2k+1.
However, counterexamples to the Hajós conjecture are now known, so this connection does not provide an avenue for proof of the Albertson conjecture.
However, Gompf, Scharlemann& Thompson(2010) suggested that the conjecture might not be true, andprovided a family of knots that could be counterexamples to it.
As Grünbaum writes, simplicial arrangements“appear as examples or counterexamples in many contexts of combinatorial geometry and its applications.”.
The two known counterexamples to the Dirac-Motzkin conjecture(which states that any n-line arrangement has at least n/2 ordinary points) are both simplicial.
Moreover, Chen and Greene have constructed a set S of 1248 primes such that, among the nearly 21248 products ofdistinct primes in S, there may be about 740 counterexamples.
Counterexamples to his proof were found in 1890 and 1896(the Poussin graph), and later, the Fritsch graph and Soifer graph provided two smaller counterexamples.
Sun and his twin brother Sun Zhiwei proved a theorem about what are now known as the Wall-Sun-Sun primes that guided the search for counterexamples to Fermat's last theorem.
While there are some counterexamples, such as Arabic,"prestigious and standard varieties coincide to the extent that the two terms can be used interchangeably.
While topology has mainly been developed for infinite spaces, finite topological spaces are often used to provide examples of interesting phenomena or counterexamples to plausible sounding conjectures.
Ol'shanskii found some striking counterexamples for sufficiently large odd exponents(greater than 1010), and supplied a considerably simpler proof based on geometric ideas.
Kempe's(incorrect) proof is based on alternating chains, andas those chains prove useful in graph theory mathematicians remain interested in such counterexamples.
Counterexamples to this conjecture were later discovered, but the possibility that a finite bound on toughness might imply Hamiltonicity remains an important open problem in graph theory.
This conjecture is false if topological manifolds andhomeomorphisms are replaced by smooth manifolds and diffeomorphisms; counterexamples can be constructed by taking a connected sum with an exotic sphere.
In particular, the heuristic shows that such counterexamples have asymptotic density greater than 1 n ε{\displaystyle{\tfrac{1}{n^{\varepsilon}}}} for any ε> 0{\displaystyle\varepsilon>0.
To support his position that methodological rules generally do not contribute to scientific success,Feyerabend provides counterexamples to the claim that(good) science operates according to a certain fixed method.
In the case of borderline cases of art and prima facie counterexamples, open concepts“call for some sort of decision on our part to extend the use of the concept to cover this, or to close the concept and invent a new one to deal with the new case and its new property” p.
Thus, beyond their obvious application to problems of symmetry in the plane, these groups are among the simplest examples of non-abelian groups, andas such arise frequently as easy counterexamples to theorems which are restricted to abelian groups.
One must try to identify faulty reasoning in the opponent's argument, to attack the reasons/premises of the argument,to provide counterexamples if possible, to identify any fallacies, and to show why a valid conclusion cannot be derived from the reasons provided for his/her argument.