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Unformatted text preview: Thus the work is completed after finding the contradiction. The proof usually terminates at this point with a comment equivalent to “This is a contradiction,” simply to emphasize to the reader that your goal has been achieved. It is natural to ask when a proof by contradiction is the best approach. This is not at all obvious. As you gain experience with proofs, you will sometimes get a feeling. At other times you may have to try various approaches in order to find one that shows your result. It never is wise to restrict yourself to a single method, trying to force all proofs into that one approach. The question becomes trickier when you are not sure whether a proposed theorem is true or not. This often happens when conducting research. In that case you may alternate between attempting to prove the theorem by any method you deem promising, including contradiction, and attempting to find a counterexample to it....
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This note was uploaded on 07/24/2011 for the course MAS 3106 taught by Professor Brigham during the Spring '11 term at University of Central Florida.
- Spring '11