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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Cusick, L. W. "Proof by Contradiction." 2006.

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Proof by Contradiction

Cite this as:

Cole, Corwin. "Proof by Contradiction." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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