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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 12

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Examples and counterexamples

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Some facts can be seen more clearly by example than by proof.

Leonard Euler

If I were wrong, one would be enough.

Einstein’s reply to hearing of the Nazi book 100 Authors Against Einstein

Now we come to one of the biggest secrets in thinking like a mathematician. So far in this book we have covered many of the important tools for logical thinking: statements, implications, quantifiers. Many other books cover these. But they cover in little detail what I consider to be one of the most important tools. It is ...

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