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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 14

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Definitions, theorems and proofs

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The highest form of pure thought is in mathematics.

Plato

We now come to the heart of how mathematicians organize and present their work. Look through any high-level mathematics book (or see Chapter 1) and you will find that mathematics is not presented as one continuous piece of prose like a novel. Instead the text is divided up into small nuggets of information such as a Theorem, Proposition, Lemma, Corollary, Proof, Definition and Conjecture. All of these have special meanings and we will see how to ...

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