One way to think about it is that functions in mathematics are “Platonic lookup tables” (I prefer “Platonic” to “static” because in mathematics the distinction between static and dynamic is a matter of perspective and it’s useful to switch between the two); given an input there’s some Platonic fact about what the output is, and that’s all a function is. In general most of pure mathematics is implicitly Platonist in some sense and you’ll have an easier time with it coming at it from that angle.
Bingo. As a computer scientist, I have an incredible urge to figure out how functions are built. Of course, I knew on some level that functions aren’t “built” the same way in math as in CS… When I reached the Axiom of Choice and it proclaimed, “Let there be arbitrary choice functions”—that was my Oops moment. Functions either exist, or they don’t. Similarly, you don’t “find” or “build” sets, they simply can and do exist, or they can’t and don’t (under the specified axioms, at least). You may need to show you can construct a set for a proof, but that’s a little different.
Obvious in retrospect, and a good data point for improving my ability to notice confusion.
Bingo. As a computer scientist, I have an incredible urge to figure out how functions are built. Of course, I knew on some level that functions aren’t “built” the same way in math as in CS… When I reached the Axiom of Choice and it proclaimed, “Let there be arbitrary choice functions”—that was my Oops moment. Functions either exist, or they don’t. Similarly, you don’t “find” or “build” sets, they simply can and do exist, or they can’t and don’t (under the specified axioms, at least). You may need to show you can construct a set for a proof, but that’s a little different.
Obvious in retrospect, and a good data point for improving my ability to notice confusion.