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 is false followed necessarily by the conclusion from not-, where is false, which implies that 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.