Re: Infintesimals

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 07/01/04 

Date: Thu, 01 Jul 2004 18:31:09 -0300

Please don't top post.

In <p3c4e059kflf16bskajurp01ctfvkumaj2@4ax.com>, on 06/30/2004
   at 03:32 AM, Brian VanPelt <bvanpelt@neo.rr.com> said:

>Do you think that, fundamentally, mathematicians are simply happy
>with epsilon-delta?

Pretty much. It's a simple approach that doesn't require complicated
machinery like ultrafilters.

>Could it be that mathematicians don't feel sure about the validity
>of the hyperreal system?

Highly doubtful.

>I am not at all trying to be argumentative, but I would like a
>discussion. If anyone is like me, teaching epsilon-delta in calc I
>has been almost a total failure.

Perhaps, but IMHO that is due to lack of preparation. A few decades
ago, students were expected to be able to follow proofs in high
school; that no longer seems to be the case.

>In any event, is there some validity to teaching a calculus course
>that uses the hyperreals in place of the epsilon-delta idea?

It's been done. Why not look at the available[1] texts using that
approach and decide whether they're suitable for your students?

[1] Assuming that they're in print. 

-- 
     Shmuel (Seymour J.) Metz, SysProg and JOAT
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