Re: The Paradox of Zeno
From: robert j. kolker (nowhere_at_nowhere.net)
Date: 11/13/04
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Date: Sat, 13 Nov 2004 07:28:02 -0500
Virgil wrote:
>
> Gee, I wonder whether eelaticus has ever read any of those definitions,
> in which the independent variable does not, in fact, approach anything.
> That word and graphic are left over from days before there was any
> proper definition of limit. eeleaticus' objections are as outdated as
> those of Bishop Berkely's to "the ghosts of departed quantities" on the
> isue of limits.
The Bishop's criticism of infinitesimals was on the mark. Because
infinitesimals were not (until recently) properly grounded, the limit
concept was developed to plug the holes. It turns out, at long last,
that infinitesimal elements in a non-Archimedian field can be rigoursly
defined and used. But neither Newton nor Leibniz knew how.
Bob Kolker
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