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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 1

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Sets and functions

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Everything starts somewhere, although many physicists disagree.

Terry Pratchett, Hogfather, 1996

To think like a mathematician requires some mathematics to think about. I wish to keep the number of prerequisites for this book low so that any gaps in your knowledge are not a drag on understanding. Just so that we have some mathematics to play with, this chapter introduces sets and functions. These are very basic mathematical objects but have sufficient abstraction for our purposes.

A set is a collection of objects, and ...

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