Juan R.
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arivero said:I can tell you that I understand the objections you formulate about the use of the infinite and the infinitesimal in mathematical practice. The only thing I am disagreeing is about if such objections can be applied directly in the parragraphs of Connes's work we are discussing about.
My impression is that the generality of such objections carries you to think there should be present also in this work, and then you are reading into the text instead of from the text. Anyway I think we have both exposed our interpretations of the text and any third reader could decide by herself by reading them. From my part, any further prolongation of the thread whould be simple repetition or, at most, rewording.
In short, what is n in Connes approach?
It cannot be infinite because then he would use the notation n = infinite but uses the standard notation "--->" what means in words "infinitesimally close to". In fact if Connes had used n = infinite then (1/n) = 0 but the size of an infinitesimal may be different of zero.
but n cannot be any real number, because the size of an infinitesimal is not (1/n) for any n real.
If cannot be infinite and cannot be real what is then n?
a) hiperreal number or
b) epsilon number if my approach is correct.
And YES this thread is very large, i am exhaust, but discussion with you was very interesting.

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