> As more that 100-years experience of mathematical education shows, all
> students comprehend the "delta-epsilon" definition of the continuity
> of a (real) function f at a (real) point x without any problems.
If only that were true! I have just marked an exam, and I can tell you
there are a lot of students out there who don't comprehend it. There
are also a lot who now comprehend it but had severe problems along the
way, like me when I found that the "delta-epsilon" definition I learnt
from G H Hardy's "Pure Mathematics" is no longer operative, if I may
borrow a phrase from a certain US politician. [Let f(x) = 0 for all
rational x, with f defined only for rational x. Then Hardy Exs 37 no 20
says f is discontinuous for all real x, but modern books e.g. Rudin
"Principles of Mathematical Analysis" disagree for rational x.]
John Harper, School of Mathematical and Computing Sciences,
Victoria University, Wellington, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)471 5341 fax (+64)(4)495 5045