Uhhh.... Having done some research with adults and with 15 year-olds on concepts of infinity, I hope folks are recognizing that these are very non-trivial ideas. For example, about two different lengths of segments having the same number of points. Hey -- 98% or more of the educated, adult population could tell you -- a longer segment has more points! It's obvious! In fact, many important understandings of infinity are quite young historically.
What tends to happen in schools is that students are "told" all about infinity, leading to school-knowledge that has little impact on their underlying knowledge structures. Their intuitions in this area are very compelling and very resistant to change! I could write an article on this. In fact, I have. :) But just to say, PLEASE be careful in pushing students into premature "generalizations" about infinity that are not their own! It's better for them to be confused than to come to believe something for the wrong reasons, which leads to brittle, unusable knowledge.
Rev. Gary, on his soapbox again
============================================================ W. Gary Martin 1776 University Ave. University of Hawaii Honolulu, HI 96822 Curriculum R & D Group (808)956-9956; FAX (808)956-4984