> the removal of sequences and all the associated theorems from the introductory calculus. Instead, start with limits of functions and the notion of continuity.
replyStrongly disagree.
Sequences(discrete) and Convergence are vital to understanding Calculus. Only then the idea of converging to a limit from left or right makes intuitive sense. Pair it with a graphical view of secants converging to a tangent(continuous) and you get the idea of instantaneous change however infinitesimal it might be.
You need both discrete and continuous ideas to build intuition before you introduce limits of functions and continuity.
Some books that i have found useful - https://news.ycombinator.com/item?id=49308281
I don't disagree. Sequences are important, and the bridge between sequences and functions (Bolzano–Weierstrass theorem, mean value theorem, etc.) is crucial.
replyBut they are not immediately needed to understand the limits.
Try to see how far you can get just with the epsilon-delta formulation of limits of functions.