We lie when when we teach calculus by relying on hand-wavy 'limit' proofs, without grounding students in the foundational aspects of point set topology. It's m

We lie when when we teach calculus by relying on hand-wavy 'limit' proofs, without grounding students in the foundational aspects of point set topology. It's much more productive pedagogically to get an intuition for slope and area than it is to get an intuition for compactness and the infinite intersection of open sets, but slope and area are A LIE.