On Sun, 2003-02-02 at 04:31, Michael Barr wrote: > I'm glad you enjoyed it, but it really is a waste of time to study set > theory to do calculus, since the nature of the actual sets involved is > utterly irrelevant. I agree. The thing that sticks with me is not the memory of how rings and groups and so on work, but the fact that I was able to perceive beauty in the way it all fit together. (A mathematician friend once explained the non-standard real numbers to me, and after I understood it, I knew what people meant by getting "high on math".) Proving how the underlying mechanisms fit together is a superb way of demonstrating what you can do with logic and derivation from first principles, and I think walking children through that kind of demonstration as soon as they can understand it could be a good way to point out *why* it's useful to learn to apply logic like that, but it's of little practical use in most fields. It should be taught all or nothing, not the half-assed wait-until-you-get-to-college-and-take-an-advanced-math- course way it was in my schools. -- %% Max Rible % slothman at amurgsval.org % www.amurgsval.org/~slothman/ %% %% "Before enlightenment: sharpen claws, catch mice. %% %% After enlightenment: sharpen claws, catch mice." %%