Does anyone know of nice results / pictures that use set theory? Have always felt 'averse' to learning set theory - it's used as basic formalism in many parts of math, but always wondered why this and not something else? Is there some inherent beauty to it?
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Right - I've used it in many basic problems in topology / probability - but I haven't taken the time to try to really *understand* why it looks the way it does, why each axiom is there, etc. Just curious if there's a specific nice motivation for it?
The math person's version of the Theory of Everything is to conceptualize all of math in terms of the primitive simplest thing possible, so as to understand and prove the maximum amount of stuff. ZFC (a flavor of set theory) is the current most-popular basis for that, to my
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understanding. So part of the way set theory looks like it does, and is taught as it is, is because it is used to explain the rest of math. (Category Theory is a newer contender for same position, kinda, I guess).
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