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.
