Proof by contradiction | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-13

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Proof_by_contradiction


00:01:07 1 Principle
00:03:57 1.1 Law of the excluded middle
00:05:54 2 Relationship with other proof techniques
00:09:53 3 Examples
00:10:03 3.1 Irrationality of the square root of 2
00:10:36 3.2 The length of the hypotenuse
00:11:45 3.3 No least positive rational number
00:12:54 3.4 Other
00:13:36 4 Notation
00:14:54 5 Principle of explosion
00:15:17 6 See also
00:17:01 7 References
00:19:18 8 Further reading and external links



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SUMMARY
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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 assuming that 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."