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Proof by Contradiction


A proof by contradiction establishes the truth of a given proposition by the supposition that it is false and the subsequent drawing of a conclusion that is contradictory to something that is proven to be true. That is, the supposition that P is false followed necessarily by the conclusion Q from not-P, where Q is false, which implies that P is true.

For example, the second of Euclid's theorems starts with the assumption that there is a finite number of primes. Cusik gives some other nice examples.


See also

Euclid's Theorems, Proof, Reductio ad Absurdum

This entry contributed by Corwin Cole

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References

Cusick, L. W. "Proof by Contradiction." 2006. http://zimmer.csufresno.edu/~larryc/proofs/proofs.contradict.html.

Referenced on Wolfram|Alpha

Proof by Contradiction

Cite this as:

Cole, Corwin. "Proof by Contradiction." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ProofbyContradiction.html

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