Date: Nov 10, 2012 3:26 PM
Author: Joe Niederberger
Subject: Re: How teaching factors rather than multiplicand & multiplier<br> confuses kids!
Clyde Greeno says:

>But the essence is that: (1) students first must grasp that the line of rational numbers is dense ... but also having a density of "irrational" holes, and (2) also perceive how the "zoom in" squeeze on a function, at each point within or outside its domain, converges to a (sometimes empty, sometimes single-point, sometimes otherwise) "vertical" interval.

I would say the common sense view is that a continuous function is one whose graph can be drawn without lifting the pencil off the page. What you describe is a mental picture to go with the more advanced understanding. All well and good and I wouldn't be surprised if someone has created a nice interactive computer animation to illustrate.

Joe N