[FOM] reply to s.s. kuteladze
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
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
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