5

Set theory has no important implications for 99% of normal mathematics, and the difference between, say, ZFC and NF has even less. Mathematics isn't generally written in the language of ZFC, it's written using more basic ideas and notation that are the same in other foundational systems. If I'm teaching freshman calculus and I talk about $\{x|x>0\}$, ...


3

This question is mixed with a lot of speculation and commentary, so I'm going to try to focus on the questions. Should the limits of one system of set theory be the limits of a student's mathematical world? No. The idea that a system of set theory should be a limit to mathematical ideas seems like poor pedagogy (as arbitrary restrictions usually are), ...


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