>>10876626Wildberger's main issue is in the way calculus is taught. Before calculus, the only definitions a student have of a real number, in general, is
>any length I could draw>any decimal I could write if I could write forever>any math expression I could make and solve numerically (incorrect)So you take calculus, learn about limits, learn about derivatives, arc length, finite area contained under an infinitely long curve, etc usually without any definitions or mathematical rigor, until the very end of calculus. And then In analysis they teach that real numbers are Cauchy sequences of rationals, but you still have to prove that a Cauchy sequence converges to a real number by saying
>for all epsilon>0 in R....So it's circular logic, but it's further than any engineer or physicist gets. This is pretty much as far as an applied math major gets. Then pure math majors will construct the reals in their final year of math, which is finally correct, but even then, you don't have to understand the proof that every ordered field with the least upper bound property is isomorphic to R.
