proof by contradiction
Assume, derive absurdity
Proof by contradiction is a method of logical argument that establishes a claim by showing its opposite leads to an absurdity.
You assume the negation of what you want to prove, then derive a logical impossibility—demonstrating the original claim must be true.
The classic proof that the square root of 2 is irrational proceeds by contradiction.
Also called reductio ad absurdum.
- reductio ad absurdumDisproof by absurd consequence
- refutationDisproving a statement
- contrapositiveEquivalent reversed conditional
- negationDenial or cancellation
- mathematicsScience of quantity and structure
assumption · theorem · deductive reasoning · counterexample · logical paradox · logic · deduction · falsifiability · logical consistency · axioms · Euclid · impossibility · tautology · soundness · argumentation · lemmas · validity · corollaries
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- Proof Theorytheorem, axiom, lemma, corollary, natural deduction
- proofscontrapositive, theorem, lemma, corollary, QED
- mathematicsalgebra, arithmetic, calculus, geometry, number
- logicpremise, premises, conclusion, conclusions, inference
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