[DArcMattr]

I have a Master's in Applied Math.

The comments about how "few students take [Real Analysis]" doesn't square with my experience and survey of an undergraduate mathematics education. Such a course is often called "Advanced Calculus", and is a required course for a Bachelors-level education in Math. I also understand in the European-style approach to teaching Math, students start off with a foundational approach to Calculus through Real Analysis, and not the hand-wavy & computation-driven Calculus course.

The equivalence class approach attributed to Cantor is more generalizable in discussing sets. The theoretical foundation of Fourier Transforms lies in a similar completion of functions.

[pedrosorio]

"I also understand in the European-style approach to teaching Math, students start off with a foundational approach to Calculus through Real Analysis, and not the hand-wavy & computation-driven Calculus course."

Yes. Where I graduated, all engineering majors learn the axiomatic definition of the real numbers including the "supremum (least upper bound) axiom" at the beginning of the first calculus class.