What is "proof by contradiction"

n. (context mathematics logic English) Proof of a statement adduced by derive a contradiction from the statement's negation.

In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition. It starts by positing the opposite proposition is true, and then shows that such an assumption leads to a contradiction. Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem. It is a particular kind of the more general form of argument known as reductio ad absurdum.

G. H. Hardy described proof by contradiction as "one of a mathematician's finest weapons", saying "It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."