Hacker News Reader

I agree with that. You can hand limits as a tool to someone already comfortable with the concepts and present them as a way to quantify their intuitive understanding.

View on HN

But without limits, you cannot actually do much with the concepts. Whether you call limits a concept or a tool, they are essential to the practice of calculus, and, historically, to its emergence (and not trivially so, either.)

Yeah but you can do well on the AP calculus exam without understanding limits, if you can calculate derivatives and solve some word problems related to derivatives.

Hence, the gap between "5 year old calculus" and "high school calculus" is smaller than the gap between "high school calculus" and "actual calculus"

Reply on news.ycombinator.com