```Date: Oct 4, 2017 3:16 PM
Author: bursejan@gmail.com
Subject: Re: An infinite sum is NOT a limit and 0.333... is not well defined<br> as 1/3.

You see bird brain John Gabriel doesn't understand howthe reals are constructed in the case of Cauchy Q-series.Some weeks ago I posted a PDF from cornell university,which showed the construction of reals from Q-series,MATH 304: CONSTRUCTING THE REAL NUMBERSyPeter Kahn Spring 2007http://www.math.cornell.edu/~kahn/reals07.pdfhere it is again. What Markus Klyver wrote is correct,check it by yourself, the construction involves theconcept of so called Z series.4.3 The Field of real numbers"Z is defined to consist of all sequences in C that converge to zero."Am Mittwoch, 4. Oktober 2017 21:08:51 UTC+2 schrieb John Gabriel:> Wrong. All limit definitions require prior knowledge of the limit. This is especially true in the case of the derivative.> > > We can perfectly define limits without knowing how to prove limits or evaluating limits.> > Wrong.> > > > > And no, we don't define real numbers as limits of Cauchy sequences. > > Yes, you do! All the sequences of an equivalent Cauchy sequence have one thing in common - the limit.
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