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Understanding Math Logic/Foundations

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Math is kind of a unique subject in that the easy topics are in the 'middle' (counting, addition, etc.) and then things get more complicated are you move to both more advanced (algebra/geometry/analysis) and more fundamental topics (logic/sets). So this is definitely an excellent topic to study, but be aware that without a strong understanding of arithmetic and high school algebra, studying the foundations can be difficult.

The foundations of most branches of mathematics are built in set theory. Specifically the ZFC axiomatization of set theory. Goldrei's *Classical Set Theory: For Guided Independent Study* is an excellent introductory text. Paul Halmos's Naive Set Theory is also very good.

For intro logic, I've heard Velleman's *How to Prove It* is very popular. I learned the basics from Rosen's *Discrete Mathematics and its Applications.* For the foundations of logic, Hunter's *Metalogic* is very thorough.

But again, all of these texts could be more difficult than what you're looking for. If you're passionate about foundational mathematics then give them a try! (It is in my very biased opinion the most interesting field.) If they click then that's great! And it will help a lot with relearning the basics too, but if you get stuck then it's ok to go back to high school math, relearn the basics, and come back when you're ready. I'd start with either the Velleman or Rosen texts and see if they're up your alley, then move on to the others.

Good luck! And if you have any questions r/learnmath has your back!

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