So, I'm going back to school. I already have a B.S. in biochemistry but I've found out that junior scientists aren't really in any demand whatsoever. So, I want to study bioengineering and try to make myself more competitive. If I'm going to become a better scientist I need to know how to play around with sets, classes, categories, systems, whatever the nomenclature/method. That's where math is, hopefully, gonna save the day for me. I guess I need explicit definitions to better understand mathematics. Hopefully, I'm studying the right stuff?
Set Theory (Stanford Encyclopedia of Philosophy)
Set theory alternatives
Alternative Axiomatic Set Theories (Stanford Encyclopedia of Philosophy)
Category Theory (Stanford Encyclopedia of Philosophy)
I'm working on conceptualizing set theory with my current understanding of mathematics (I've taken Calculus II). I think I'm starting to understand first-order logic and higher-order logic? I've seen the Russian nesting doll analogies, fractals, and other examples of how math/logic is made heirarchical. Even though I'm encountering very explicit definitions for objects it seems that they are still recursively defined? Is that where ZFC is supposed to save the day? I guess I just need to keep reading more and more and play around with the concepts. I can see how a cartesian system becomes entirely unintelligible without explicit rules to build from. It's starting to make some sense I guess?