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Good Math by Mark C. Chu-Carroll

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Part 5Sets

Set theory, along with its cousin first-order predicate logic (FOPL), is pretty much the foundation of all modern math. You don’t absolutely need set theory, because you can construct math from a lot of different foundations. But the combination of FOPL and axiomatic set theory is currently the dominant approach. Set theory gives us the objects to reason about, and FOPL gives us the ability to do reasoning. The combination of the two gives us math.

There are many kinds of objects that we could use to build math. We could start with numbers or with functions or with a plane full of points. But in modern math we always start with set theory, and not with any of the alternatives! Set theory starts with some of the simplest ideas and ...

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