proof by contradiction
Sign in to saveAlso known as apagogical argument, proof by assuming the opposite, reductio ad impossibilem
form of proof
~24 min read
Encyclopedic overview
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884
In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum, (Latin for "argument to absurdity") apagogical argument, or proof by contradiction, is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof.
Excerpted from Wikipedia’s “proof by contradiction” article, available under the CC BY-SA 4.0 licence.