##### Wiktionary

**proof by contradiction**

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

##### Wikipedia

**Proof by contradiction**

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."