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contradiction$16365$ - translation to ελληνικό
![This 6th century Athenian black-figure urn, in the [[British Museum]], depicts the olive harvest. Many farmers, enslaved for debt, would have worked on large estates for their creditors.](https://commons.wikimedia.org/wiki/Special:FilePath/Amphora olive-gathering BM B226.jpg?width=200 "This 6th century Athenian black-figure urn, in the [[British Museum]], depicts the olive harvest. Many farmers, enslaved for debt, would have worked on large estates for their creditors.")
![China's Land Reform Movement]]](https://commons.wikimedia.org/wiki/Special:FilePath/Choubapi.jpg?width=200 "China's Land Reform Movement]]")
![Gavin Hamilton]]](https://commons.wikimedia.org/wiki/Special:FilePath/Gavin Hamilton - Coriolanus Act V, Scene III edit2.jpg?width=200 "Gavin Hamilton]]")
![Rousseau by [[Maurice Quentin de La Tour]], 1753](https://commons.wikimedia.org/wiki/Special:FilePath/Jean-Jacques Rousseau (painted portrait).jpg?width=200 "Rousseau by [[Maurice Quentin de La Tour]], 1753")
![Jobless black workers in the heat of the [[Philadelphia]] summer, 1973](https://commons.wikimedia.org/wiki/Special:FilePath/NORTH PHILADELPHIA JOBLESS BLACKS. MAN STANDING AT RIGHT IS GERALD "HEAT WAVE" JONES, WHO WORKS FOR "THE NETWORK", A... - NARA - 552754.jpg?width=200 "Jobless black workers in the heat of the [[Philadelphia]] summer, 1973")
![[[Noam Chomsky]], 2004](https://commons.wikimedia.org/wiki/Special:FilePath/Noam Chomsky, 2004.jpg?width=200 "[[Noam Chomsky]], 2004")
![The [[Pyramid of Capitalist System]] visualizes and explains class conflict.](https://commons.wikimedia.org/wiki/Special:FilePath/Pyramid of Capitalist System.png?width=200 "The [[Pyramid of Capitalist System]] visualizes and explains class conflict.")
Ορισμός
Βικιπαίδεια
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, and reductio ad impossibile.
A mathematical proof employing proof by contradiction usually proceeds as follows:
- The proposition to be proved is P.
- We assume P to be false, i.e., we assume ¬P.
- It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the law of noncontradiction.
- Since assuming P to be false leads to a contradiction, it is concluded that P is in fact true.
An important special case is the existence proof by contradiction: in order to demonstrate that an object with a given property exists, we derive a contradiction from the assumption that all objects satisfy the negation of the property.
