[FOM] reply to s.s. kuteladze

Gabriel Stolzenberg gstolzen at math.bu.edu
Wed Nov 14 14:05:19 EST 2007

   This is a reply to portions of S. S. Kutateladze's "Re: constructive
cauchy (10 nov).

> Cauchy described the functions under study as follows: `An infinitely
>small increment given to the variable  produces an infinitely small
>increment of the function itself.''  This yields uniform continuity
>rather than continuity as envisaged by nonstandard analysis.

   Not on my reading, as I believe I explained in "constructive
cauchy."  It's just the definition of a function.  In practice,
this definition will contain a modulus of locally uniform continuity
but that's not a theorem.  (To say more, or even just this, is
delicate.  So I won't attempt to elaborate.)

 > Cauchy was a brilliant mind who looked at the entities of analysis
> in a fashion closer to Leibniz than Newton. He felt the difference
> between ``assignable'' and ``nonassignable'' numbers which was
> neglected  in the epsilon-delta technique but reconstructed by
> Robinson.

   But Robinson said that Leibniz treated talk of infinitesmals merely
as a convenient "facon de parler."

   Also, does your use of"nonassignable" have something to do with the
Name Worshippers??

   Gabriel Stolzenberg

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