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this idea further by classifying various principles in terms of "how nonconstructive" they are, by showing they are equivalent to various fragments of the...

a single set, again showing that the two expressions are equal. A nonconstructive proof establishes that a mathematical object with a certain property...

In mathematics, the probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence...

proofs, not every school of mathematical thought accepts this kind of nonconstructive proof. This argument form traces back to Ancient Greek philosophy and...

axioms that are nonconstructive but are weaker than the full law of the excluded middle. They are used to gauge the amount of nonconstructivity required for...

Wikipedia's openness, with individuals vandalizing or modifying articles in nonconstructive ways. Others feature individuals using Wikipedia as a reference work...

importantly, she has repudiated categorization within feminism as "nonconstructive to specific problems", saying: "I've turned up in every category. So...

from proofs that, when expressed in natural language, appear to be nonconstructive. This research has led to improved results in analysis obtained from...

which exhibits an object satisfying the "some" statement, or by a nonconstructive proof, which shows that there must be such an object without concretely...

helpful even if it is proved, because such a proof will almost surely be nonconstructive. A proof of P ≠ NP would lack the practical computational benefits...

drawn line will have. Though nearly all modern mathematicians consider nonconstructive proofs just as sound as constructive ones, they are often considered...

mathematics in Hungary Minimum overlap problem Probabilistic method – Nonconstructive method for mathematical proofs Probabilistic number theory – Subfield...

for the drop off zones. The changes have been seen as unwelcome and nonconstructive by passengers and taxi drivers, with some saying they will boycott...

above, the proof requires the axiom of choice and so is in general nonconstructive, though again, if X is not complete, there are constructible examples...

clarifies the extent and manner in which classical mathematics is nonconstructive. The language of second-order arithmetic is two-sorted. The first sort...

ultrafilters, which are filters that cannot be enlarged, and describe nonconstructive techniques in mathematical logic. Filters on sets were introduced by...

determining whether a graph has a given graph as a minor. This yields a nonconstructive proof that there is a polynomial-time algorithm for determining if...

actual infinity stems from fundamental disagreement with the idea that nonconstructive proofs such as Cantor's diagonal argument are sufficient proof that...

the Disquisitiones contains two proofs: The one in Article 54 is a nonconstructive existence proof, while the proof in Article 55 is constructive. An...

AC only matters for certain infinite sets. AC is characterized as nonconstructive because it asserts the existence of a choice function but says nothing...

graph is a fundamental task in computational graph theory. There are nonconstructive characterization theorems for the size of a maximum matching. This...

general, concrete rule by which the choice can be made renders the axiom nonconstructive. Stefan Banach and Alfred Tarski showed that the axiom of choice can...

function on Rn\{0}. The original 1983 proof by Zvi Artstein proceeds by a nonconstructive argument. In 1989 Eduardo D. Sontag provided a constructive version...

desired properties with positive probability. Consequently, they are nonconstructive — they don't explicitly describe an efficient method for computing...

Journal of Symbolic Logic, 33:452–457, 1968. William W. Tait, 1966. A nonconstructive proof of Gentzen's Hauptsatz for second order predicate logic. In Bulletin...

the sense of cardinality most real numbers are not algebraic. This nonconstructive proof that not all real numbers are algebraic was first published by...

for all finite types. The motivation for accepting these seemingly nonconstructive principles is the intuitionistic understanding of the proof that "for...

sexual drive during negative mood states. Negative moods are labeled as nonconstructive because they can affect a person's ability to process information,...

above, in the classical theory of ZFC, the axiom of choice enables nonconstructive proofs in which the existence of a type of object is proved without...

com". www.dictionary.com. Retrieved 2019-11-29. See the section on nonconstructive proofs of the entry "Constructive proof". Weisstein, Eric W. "Existence...

first player always has a winning strategy (although this theorem is nonconstructive, and explicit strategies have not been fully developed for board sizes...

Carlo as their principal simulation approach. The definition of VaR is nonconstructive; it specifies a property VaR must have, but not how to compute VaR...

from a mathematical logic perspective since it can only be proved nonconstructively. Kruskal also applied his work in linguistics, in an experimental...

generally smaller. The proof that M∗ is (usually) not the same as M* is nonconstructive and uses the axiom of choice in an essential way; it is very hard to...

As is often the case with probabilistic arguments, this theorem is nonconstructive and gives no method of determining an explicit element of the probability...

to Japanese tastes. Kurita disagrees but when Niki says she's being nonconstructive, Kurita becomes upset and leaves. The supreme side presents garlic...

Springer, pp. 326–367. Fellows, Michael R.; Langston, Michael A. (1988), "Nonconstructive tools for proving polynomial-time decidability", Journal of the ACM...

the field of nonstandard analysis. Robinson developed his theory nonconstructively, using model theory; however it is possible to proceed using only...

proof Reductio ad absurdum Proof by exhaustion Constructive proof Nonconstructive proof Tautology Consistency proof Arithmetization of analysis Foundations...

expected to pass.) A nonjump bid in a new suit is a nonforcing and nonconstructive attempt to improve the contract. Finally, 2NT or a raise of the opening...

choice or its equivalents, such as Zorn's lemma. They are therefore nonconstructive. The subject of divergent series, as a domain of mathematical analysis...

complexity) is given in. Fellows, M. R.; Langston, M. A. (1988). "Nonconstructive tools for proving polynomial-time decidability". Journal of the ACM...

the field of rational numbers. Note, however, that this method is nonconstructive, relying as it does on the existence of a (Hamel) basis for any vector...

"direct"). A corollary of this characterization is that one can (nonconstructively) prove the existence of a universal Horn axiomatization of a class...

Velupillai, K. Vela (2012). "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics" (PDF). New...

S2CID 3976355. Fellows, Michael R.; Langston, Michael A. (1988), "Nonconstructive tools for proving polynomial-time decidability", Journal of the ACM...

existence arguments invoking the Baire category theorem, this proof is nonconstructive. It shows that the family of continuous functions whose Fourier series...

European ideas and institutions, and he was against thoughtless and nonconstructive criticism of the administration. However, although Williams in many...

this verifies the mass formula in this case. Smith originally gave a nonconstructive proof of the existence of an even unimodular lattice of dimension 8...

time for all people, most of this new time is passed in "passive" (or nonconstructive) recreation. The introduction of the radio and automobile are considered...

S2CID 3172160. Fellows, Michael R.; Langston, Michael A. (1988), "Nonconstructive tools for proving polynomial-time decidability", Journal of the ACM...

optimization problems and zero-sum games. Usual proofs of these results are nonconstructive: they establish only the existence of the representation, but do not...

1002/jgt.3190070410. Fellows, Michael R.; Langston, Michael A. (1988), "Nonconstructive tools for proving polynomial-time decidability", Journal of the ACM...

mathematics, which includes Robinson's approach to nonstandard analysis, was nonconstructive and therefore deficient in numerical meaning (Feferman 2000). Bishop...