[Edu-sig] RE: PEP0238 lament
Moshe Zadka
moshez@zadka.site.co.il
Sun, 22 Jul 2001 22:05:17 +0300
I'm the last person to avoid going off on a tangent.
On Sun, 22 Jul 2001 14:22:21 -0400, "Tim Peters" <tim.one@home.com> wrote:
> I wish the definition of continuity were
> easier to teach too, but that doesn't mean I'll settle for an easier
> definition that doesn't actually work <wink>.
Here is one that is easier to teach, if you just reverse the order
of teaching calculus and first-order logic and basic set theory.
A function is continuous at c if, when embedding the world of Reals
into a saturated model (or, say, 2^{Beth_omega} saturated, if you
don't want to get into subtle assumptions), for every infinitesimal x,
f(c+x)-f(c) is an infintesimal.
Of course, you might think that teaching about saturation is hard --
well, it might be ;-)
i-always-blamed-cauchy-and-weirstrass-for-tormenting-the-world-
with-epsilons-and-deltas-ly y'rs, Z.
--
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