[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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