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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 26

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Techniques of proof V: Contrapositive method

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If it isn’t hurting, it isn’t working.

Prime Minister John Major’s comment after being told that his government’s policies were hurting the country

The contrapositive method is very confusing to grasp initially – however, one student told me that she liked using it as it made her feel that she had done something clever. I think this feeling comes from the fact that the method is very indirect.

We saw in Chapter 8 that the statement ‘A B’ is equivalent to ‘not B not A’. The contrapositive ...

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