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- Constructive_proof abstract "In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem) which proves the existence of a particular kind of object without providing an example.Some non-constructive proofs show that if a certain proposition is false, a contradiction ensues; consequently the proposition must be true (proof by contradiction). However, the principle of explosion (ex falso quodlibet) has been accepted in some varieties of constructive mathematics, including intuitionism.Constructivism is a mathematical philosophy that rejects all but constructive proofs in mathematics. This leads to a restriction on the proof methods allowed (prototypically, the law of the excluded middle is not accepted) and a different meaning of terminology (for example, the term "or" has a stronger meaning in constructive mathematics than in classical). Constructive proofs can be seen as defining certified mathematical algorithms: this idea is explored in the Brouwer–Heyting–Kolmogorov interpretation of constructive logic, the Curry–Howard correspondence between proofs and programs, and such logical systems as Per Martin-Löf's Intuitionistic Type Theory, and Thierry Coquand and Gérard Huet's Calculus of Constructions.".
- Constructive_proof wikiPageExternalLink weakcounterex.html.
- Constructive_proof wikiPageExternalLink proofs.html.
- Constructive_proof wikiPageID "360113".
- Constructive_proof wikiPageRevisionID "576841845".
- Constructive_proof hasPhotoCollection Constructive_proof.
- Constructive_proof subject Category:Constructivism_(mathematics).
- Constructive_proof subject Category:Mathematical_proofs.
- Constructive_proof type Abstraction100002137.
- Constructive_proof type Argument106648724.
- Constructive_proof type Communication100033020.
- Constructive_proof type Evidence106643408.
- Constructive_proof type Indication106797169.
- Constructive_proof type MathematicalProof106647864.
- Constructive_proof type MathematicalProofs.
- Constructive_proof type Proof106647614.
- Constructive_proof comment "In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object.".
- Constructive_proof label "Bewijs door constructie".
- Constructive_proof label "Constructive proof".
- Constructive_proof label "Demonstração construtiva".
- Constructive_proof label "Dowód niekonstruktywny".
- Constructive_proof label "Démonstration constructive".
- Constructive_proof label "构造性证明".
- Constructive_proof sameAs Démonstration_constructive.
- Constructive_proof sameAs Bewijs_door_constructie.
- Constructive_proof sameAs Dowód_niekonstruktywny.
- Constructive_proof sameAs Demonstração_construtiva.
- Constructive_proof sameAs m.01_bk0.
- Constructive_proof sameAs Q3044470.
- Constructive_proof sameAs Q3044470.
- Constructive_proof sameAs Constructive_proof.
- Constructive_proof wasDerivedFrom Constructive_proof?oldid=576841845.
- Constructive_proof isPrimaryTopicOf Constructive_proof.