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Good Math by Mark C. Chu-Carroll

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Sets, Naively

What Cantor originally invented is now known as naive set theory. In this chapter, we’ll start by looking at the basics of set theory using naive set theory roughly the way that Cantor defined it. Naive set theory is easy to understand, but as we’ll see in Don’t Keep It Simple, Stupid, it’s got some problems. We’ll see how to solve those problems in the next chapter; but for now, we’ll stick with the simple stuff.

A set is a collection of things. It’s a very limited sort of collection where you can only do one thing: ask if an object is in it. You can’t talk about which object comes first. You can’t even necessarily list all of the objects in the set. The only thing you’re guaranteed to really be able to do is ask if specific ...

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