What is the purpose of studying set theory?

[Brunno]

What is the great mathematical utility of set theory?


When you study set theory or when you studied do(did ) you know for what ecxacly you are(were) studying?And what do you know now?

 

[HallsofIvy]

Yes, when I studied "set theory" I knew exactly what I was studying. In fact set theory basics (fundamental definitions) are remarkably simple (although like anything, it has some complex ramifications).

 

[yossell]

When I studied set-theory, I tended to reject question `for what exactly am I studying this?' - but in those days I was very theory oriented and interested in foundational questions.

After studying it, I knew a lot more set-theory. I also understood a lot more about logic.
I also had some idea of how certain constructions in classical mathematics - the construction of the reals, the existence of bases for infinite dimensional vector spaces - depended on some subtle and contestable basic principles.

But mainly, I knew a lot more set-theory.