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The 22 pages that link to Proof by contradiction, each with the reason it gives.

• Mathematical inductionCompared with: It can establish universal claims without explicitly building an inductive chain.

• Mathematical proofBroader topic: It establishes the claim by showing its negation cannot hold.

• Pigeonhole principleRelated: Assuming every container stays below a proposed occupancy bound often contradicts the total count.

• Irrational numberRelated: The classic proof for the square root of two assumes a rational fraction and reaches impossible parity.

• CounterexampleCompared with: Unlike direct disproof by example, this method establishes a claim through contradiction.

• ContradictionBroader topic: It uses contradiction as evidence that an assumption must be rejected.

• Constructive proofCompared with: A contradiction can rule out nonexistence without identifying an object.

• Law of Excluded MiddleRelated: Classical versions can rely on excluded-middle reasoning to establish claims indirectly.

• TheoremRelated: It proves a theorem by showing that denying its conclusion conflicts with established facts.

• Constructive mathematicsCompared with: Some classical uses establish existence without producing the object required constructively.

• Diagonal argumentNarrower topic: Diagonal proofs often begin by assuming a complete list, then refute that assumption by construction.

• Reductio ad absurdumBroader topic: This is the standard mathematical form of reductio ad absurdum.

• Uncountable setRelated: Uncountability proofs often assume a complete enumeration and contradict it.

• Conditional proofCompared with: It also uses temporary assumptions, but discharges them through contradiction rather than a consequent.

• Geometric proofCompared with: Some geometric claims are established more directly by ruling out their negations.

• Euclid's theoremNarrower topic: Euclid's argument rules out the assumption that a finite list contains every prime.

• Existence theoremRelated: It can establish existence indirectly by ruling out the possibility that no object qualifies.

• Wilson's theoremRelated: The converse can be proved by assuming n is composite and examining a proper divisor.

• ConstructivismCompared with: Classical versions can establish existence without producing a witness, unlike constructive contradiction arguments.

• Discrete mathematicsRelated: It establishes many discrete results by ruling out impossible configurations.

• Consequentia mirabilisRelated: The principle can be derived by assuming the proposition false and using its consequence to reach a contradiction.

• Proof that π is irrationalNarrower topic: The irrationality argument begins by assuming π is a ratio of integers.