## Saturday, September 15, 2007

### Delta/Epsilon in HS

I was tutoring a AP calculus BC student today that goes to a different private high school. I saw in her notes there the definition of the limit as it regards the definition of the definite integral. It was complete with delta and epsilon, and of course mesh size and all the rigmarole. I am teaching Calc BC at my high school and we had gone over such stuff this week, and I didn't mention this topic at all.

I know why I did this. The short list is (and in no particular order):

* Not on the test so why burden the students
* Delta/Epsilon definitely not the test at all
* I have previously tried to explain Delta/Epsilon arguments to people and found that every method/analogy I have is ultimately more complicated than the actual argument. People clear agree that Delta/Epsilon is complicated, so why try to make what you can't make simpler simpler.

The only thing I have found that helps explain Delta/Epsilon proof is the following diagram:

This image is meant display that the function maps from the real numbers to the real numbers. What we are trying to do is show that a for a every little region around what anticipate will be the limit, it is possible to find a region of the domain that maps into the chosen section of the range.

This might be what Alfred S. Posamentier is talking about in this op-ed.

#### 1 comment:

Anonymous said...

I'm wondering how you describe continuity and differentiability without epsilons and deltas. You actually can do without them, and quite rigoroslty depelop differentiation and integration theory by using uniform estimates instead. See my web page at http://www.mathfoolery.org and there is a book by a Chinese mathematician Qun Lin coming out soon: http://www.fetchbook.info/fwd_description/search_9789812704597.html