At 10:59 pm +0000 13/11/98, you wrote:
[snip]
> My discussion with Schechter, as I saw it, centered on teaching
> *elementary* calculus. For more advanced work, I would have other
> opinions about the value and usefulness of nonstandard analysis.
In the context of teaching elementary calculus, I agree with your
conclusion (ie that NSA is not suitable as the sole or main approach) but
not with most of your reasons.
[snip]
> Also, more quantifiers or not, I think the epsilon-delta styles are better
> fitted to approximation techniques and applications, such as appear in
> numerical analysis.
This is a good point. In this connection, it is interesting to recall
Leibniz' explanation:
Car au lieu de l'infini ou de linfiniment petit, on prend des
quantit\'es aussi grandes et aussi petites qu'il faut pour que
l'erreur soit moindre que l'erreur don\'ee, de sorte qu'on ne
diff\ere du style d'Archim\ede que dans les expressions, qui sont
plus directes dans notre m\'ethod et plus conformes \a l'art
d'inventer (1701).
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