On Mon, 21 Jul 2014 09:38:50 -0600, Bishop, Wayne <email@example.com> wrote:
> I don't disagree mathematically but I do disagree pedagogically. Few > students really understand point-wise continuity, on their first > introduction, let alone uniform continuity.
Who said anything about uniform continuity? And if it were the issue, one could observe that students are likely to understand that we mean uniform continuity when we talk about pointwise continuity. Cauchy himself did that.
I said uniform *limit.* It's no harder to understand the notion that some curves must lie close to another than it is to understand that some points must lie close to another. And it makes subsequent dealings with derivatives much easier---unnecessary pathology being banished to higher level courses, where it belongs.
- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver