Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition being false would imply a contradiction. Since by the law of bivalence a proposition must be either true or false, and its falsity has been shown impossible, the proposition must be true. In other words, to prove by contradiction that P, show that lnot P Rightarrow perp or its equivalent lnot P Rightarrow (Qandlnot Q). Then, since lnot P implies a contradiction, conclude P. Proof by contradiction is also known as indirect proof, apagogical argument, reductio ad impossibile. It is a particular kind of the more general form of argument known as reductio ad absurdum. A classic proof by contradiction from mathematics is the proof that the square root of 2 is irrational.

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