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Good Math by Mark C. Chu-Carroll

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18Models: Using Sets as the LEGOs of the Math World

Mathematicians like to say that they can re-create all of mathematics using set theory as a basis. What does that even mean?

Sets are amazingly flexible. With the basic structure given to us by sets in ZFC set theory, we can build anything. They’re basically a lot like the mathematical version of a kid’s LEGO set: they’re easy to put together in a lot of different ways, so you can use them to build whatever you want. You can pick pretty much any field of math and build the objects that you need using sets.

Suppose we wanted to build a new mathematical system, like topology. A simple way of describing topology is that it’s a way of studying the shape of a surface by looking at which points ...

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