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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 23

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Techniques of proof III: Contradiction

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Let me never fall into the vulgar mistake of dreaming that I am persecuted whenever I am contradicted.

Ralph Waldo Emerson, Journal entry, 8 November 1838

The law of the excluded middle asserts that a statement is true or it is false, it cannot be anything in between. We can use this as another method of proof. We assume that the statement is false and proceed logically to show that this gives a statement that we definitely know is false such as 1 = 0 or the Moon is made of cheese. Thus our assumption ...

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