Date: Oct 4, 2017 3:16 PM
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 how
the 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 NUMBERSy
Peter Kahn Spring 2007
here it is again. What Markus Klyver wrote is correct,
check it by yourself, the construction involves the
concept 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.
> > 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.