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- Direct_proof abstract "In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established facts, usually existing lemmas and theorems, without making any further assumptions. In order to directly prove a conditional statement of the form "If p, then q", it suffices to consider the situations in which the statement p is true. Logical deduction is employed to reason from assumptions to conclusion. The type of logic employed is almost invariably first-order logic, employing the quantifiers for all and there exists. Common proof rules used are modus ponens and universal instantiation.In contrast, an indirect proof may begin with certain hypothetical scenarios and then proceed to eliminate the uncertainties in each of these scenarios until an inescapable conclusion is forced. For example instead of showing directly p ⇒ q, one proves its contrapositive ~q ⇒ ~p (one assumes ~q and shows that it leads to ~p). Since p ⇒ q and ~q ⇒ ~p are equivalent by the principle of transposition (see law of excluded middle), p ⇒ q is indirectly proved. Proof methods that are not direct include proof by contradiction, including proof by infinite descent. Direct proof methods include proof by exhaustion and proof by induction.".
- Direct_proof wikiPageID "238676".
- Direct_proof wikiPageRevisionID "547264707".
- Direct_proof hasPhotoCollection Direct_proof.
- Direct_proof subject Category:Logical_truth.
- Direct_proof subject Category:Mathematical_proofs.
- Direct_proof type Abstraction100002137.
- Direct_proof type Argument106648724.
- Direct_proof type Communication100033020.
- Direct_proof type Evidence106643408.
- Direct_proof type Indication106797169.
- Direct_proof type MathematicalProof106647864.
- Direct_proof type MathematicalProofs.
- Direct_proof type Proof106647614.
- Direct_proof comment "In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established facts, usually existing lemmas and theorems, without making any further assumptions. In order to directly prove a conditional statement of the form "If p, then q", it suffices to consider the situations in which the statement p is true. Logical deduction is employed to reason from assumptions to conclusion.".
- Direct_proof label "Direct proof".
- Direct_proof label "Dowód wprost".
- Direct_proof label "Prova direta".
- Direct_proof sameAs Přímý_důkaz.
- Direct_proof sameAs Dowód_wprost.
- Direct_proof sameAs Prova_direta.
- Direct_proof sameAs m.01jm50.
- Direct_proof sameAs Q3240280.
- Direct_proof sameAs Q3240280.
- Direct_proof sameAs Direct_proof.
- Direct_proof wasDerivedFrom Direct_proof?oldid=547264707.
- Direct_proof isPrimaryTopicOf Direct_proof.