235contradiction - Proof by Contradiction Math 235 Fall...

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Proof by Contradiction Math 235 Fall 2000 Proof by contradiction is perhaps the strangest method of proof, since you start by assuming that what you want to prove is false , and then show that something ridiculous happens - thus your original assumption must have been false! For example, suppose you wish to prove a statement S is true. You start a proof by contradiction by supposing that the statement S is false . Then you make logical arguments and conclusions that follow from this supposition that S is false, until you arrive at a contradiction (for example, two logically contradictory statements, or a statement that contradicts one of the assumptions of the problem). Since the assumption that S is false led to a contradiction, the statement “ S is false” must itself be false; in other words, S must be true! One final note: Proof by contradiction should not be used if you can think of a more “constructive” proof, i.e. a proof that starts only from the assumptions of the problem and
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This note was uploaded on 01/31/2011 for the course COMP 101 taught by Professor Rajivsir during the Winter '10 term at National.

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