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- Conditional_proof abstract "A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent. The assumed antecedent of a conditional proof is called the conditional proof assumption (CPA). Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows. The validity of a conditional proof does not require that the CPA is actually true, only that if it were true it would lead to the consequent.Conditional proofs are of great importance in mathematics. Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others. It can be much easier to show a proposition's truth to follow from another proposition than to prove it independently.A famous network of conditional proofs is the NP-complete class of complexity theory. There are a large number of interesting tasks, and while it is not known if a polynomial-time solution exists for any of them, it is known that if such a solution exists for any of them, one exists for all of them. Similarly, the Riemann hypothesis has a large number of consequences already proven.".
- Conditional_proof wikiPageID "6562".
- Conditional_proof wikiPageRevisionID "563094496".
- Conditional_proof hasPhotoCollection Conditional_proof.
- Conditional_proof subject Category:Conditionals.
- Conditional_proof subject Category:Logic.
- Conditional_proof subject Category:Mathematical_proofs.
- Conditional_proof subject Category:Methods_of_proof.
- Conditional_proof type Ability105616246.
- Conditional_proof type Abstraction100002137.
- Conditional_proof type Argument106648724.
- Conditional_proof type Cognition100023271.
- Conditional_proof type Communication100033020.
- Conditional_proof type Evidence106643408.
- Conditional_proof type Indication106797169.
- Conditional_proof type Know-how105616786.
- Conditional_proof type MathematicalProof106647864.
- Conditional_proof type MathematicalProofs.
- Conditional_proof type Method105660268.
- Conditional_proof type MethodsOfProof.
- Conditional_proof type Proof106647614.
- Conditional_proof type PsychologicalFeature100023100.
- Conditional_proof comment "A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent. The assumed antecedent of a conditional proof is called the conditional proof assumption (CPA). Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows.".
- Conditional_proof label "Conditional proof".
- Conditional_proof sameAs m.01xs6.
- Conditional_proof sameAs Q5159270.
- Conditional_proof sameAs Q5159270.
- Conditional_proof sameAs Conditional_proof.
- Conditional_proof wasDerivedFrom Conditional_proof?oldid=563094496.
- Conditional_proof isPrimaryTopicOf Conditional_proof.