A contradiction is an assertion or collection of assumptions from which logical falsity follows. Deriving both a statement P and its logical negation is a standard example. A contradiction under a temporary assumption can establish that assumption's negation; classical proof by contradiction additionally uses this to establish positive conclusions.
Ancestors (6)
Incoming links (43)
- Barber paradox
- Bounded completeness of an arithmetic theory
- Cantor's theorem
- Contrapositive
- Endpoint-false disjunctive normal form
- Exactly one infinite equivalence class is not first-order axiomatizable
- First-order consistency
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- Proof by minimal counterexample
- Propositional consistency
- Propositional logic
- Reductio ad absurdum
- Separation of number sets in an arithmetic theory
- Strong induction with four starting cases
- Unrestricted consistency self-strengthening is inconsistent
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