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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 9

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Converse and equivalence

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But the fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton [steamboat inventor], they laughed at the Wright brothers. But they also laughed at Bozo the Clown.

Carl Sagan, Broca’s Brain, 1979

Statements of the form A imageB are at the heart of mathematics. We have seen that for an implication A B we can take its inverse (not( ...

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