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Topic: An infinite sum is NOT a limit and 0.333... is not well defined
as 1/3.

Replies: 5   Last Post: Oct 5, 2017 10:11 AM

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bursejan@gmail.com

Posts: 4,509
Registered: 9/25/16
Re: An infinite sum is NOT a limit and 0.333... is not well defined
as 1/3.

Posted: Oct 4, 2017 3:18 PM
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But you don't need the value zero, you indentify
those sequences that have property Z with zero.

Same with other limits, you don't have them as
value, you only have the sequences itself.

Am Mittwoch, 4. Oktober 2017 21:16:21 UTC+2 schrieb burs...@gmail.com:
> 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 NUMBERS
> Peter Kahn Spring 2007
> http://www.math.cornell.edu/~kahn/reals07.pdf
>
> 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.
> >
> > 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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