Christoph Zwerschke <[EMAIL PROTECTED]> wrote: > mathematics, everything is a set and set theory is the "theory of > everything". When I grew up pedagogues here in Germany even believed it > would be best if kids learn set theory and draw venn diagrams before
An alternative theory, of course, is "God made the natural numbers; all else is the work of man" -- and that one is by a German, too (Kronecker, if I recall correctly). The hope to found all of mathematics on set theory was primarily a _British_ effort, as I see it (Russell and Whitehead), and failed a long time ago... I'm not sure what, if anything, a mathematician of today would propose as the foundational theory... perhaps modal logic, but I'm really just guessing, being, myself, an engineer rather than a mathematician (perhaps category theory? it's hard to say...). What, if anything, is the theoretically proper foundation, is of course a separate issue from where is it best to start _teaching_ maths... with geometry as the Greeks would have it, with arithmetic as in traditional schooling, or with sets as the modern pedagogues would have it. Me, I'm partial to arithmetic, but sets are just fine with me if they turn out to work better (I wonder if proper controlled studies have ever been done before revolutionizing the teaching of elementary maths, though...!). Again you see my engineer's bias: "whatever works"!-) But OO really requires a different mindset, particularly when operating under a regime of "mutable" objects. "A circle IS-AN ellipse" in Euclidean geometry... but inheriting Circle from Ellipse doesn't work in OO if the objects are changeable, since you can, e.g., change eccentricity in an Ellipse but not in a Circle... Alex -- http://mail.python.org/mailman/listinfo/python-list
