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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 
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.
See also
Euclid's Theorems, Proof, Reductio ad AbsurdumThis entry contributed by Corwin Cole
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References
Cusick, L. W. "Proof by Contradiction." 2006. https://zimmer.fresnostate.edu/~larryc/proofs/proofs.contradict.html.Referenced on Wolfram|Alpha
Proof by ContradictionCite this as:
Cole, Corwin. "Proof by Contradiction." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ProofbyContradiction.html