Thank you, but I would say it is too general answer. For example, suppose your problem is to figure out planet motion. You need calculus, that’s clear. So, according to this logic, you would first need to look at the building blocks. Introduce natural numbers using Peano axioms, then study their properties, then introduce rational, and only then construct real numbers. And this is fun, I really enjoyed it. But does it help to solve the initial problem? Not at all. You can just introduce real numbers immediately. Or, if you care only about solving mechanics problems, you can work with the “intuitive” calculus of infinitesimals, like Newton himself did. It is not mathematically strict, but you will solve everything you need. So, when you study other areas of math (like probability theory, for example), you need some knowledge of set theory, that’s right. But this set theory is not something profound, which has to be studied separately. It will be introduced in a couple of pages. I don’t know much about the decision theory, does it use more?
Thank you, but I would say it is too general answer. For example, suppose your problem is to figure out planet motion. You need calculus, that’s clear. So, according to this logic, you would first need to look at the building blocks. Introduce natural numbers using Peano axioms, then study their properties, then introduce rational, and only then construct real numbers. And this is fun, I really enjoyed it. But does it help to solve the initial problem? Not at all. You can just introduce real numbers immediately. Or, if you care only about solving mechanics problems, you can work with the “intuitive” calculus of infinitesimals, like Newton himself did. It is not mathematically strict, but you will solve everything you need.
So, when you study other areas of math (like probability theory, for example), you need some knowledge of set theory, that’s right. But this set theory is not something profound, which has to be studied separately. It will be introduced in a couple of pages. I don’t know much about the decision theory, does it use more?