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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: 5,418
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 3:37 PM
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That no limits are available has Markus Klyver
already explained a 3 trillion times, Q-sequences

need not have a Q-limit. So bird brain John
Gabriel, maybe open a book once a while,

you know these beige things. You say its
brain wash? Ok so then, stay illiterate.

Am Mittwoch, 4. Oktober 2017 21:27:46 UTC+2 schrieb burs...@gmail.com:
> The problem here is a confusion of "Cauchy sequence" used
> in real analysis, where the "Cauchy property" implies limit.
> And the "Cauchy sequence" in foundational construction
> of the reals. Where you don't have any limits available,
>
> because you are just about to construct the reals.
> I admit, it needs a little bit elasticity of the brain,
> a big problem for bird brains like John Gabriel.
> It wouldn't be a problem if his brain had a switch,
> which reads as follows:
> - Switch State 1: We doing foundational math
> - Switch State 2: We are doing real analysis
>
> Of course the are not seemless State 1 and State 2.
> We wanted to explain this to you already in the
> case of the rational numbers. Foundational they
> are pairs <p,q> representing fractions p/q.
>
> But if you work with Q, these pairs disappear.
> Its like with "S=Lim S", the difference disappears,
> its a lot of magic for a bird brain, and very
> different from cheese rolling, pitty you didn't win:
>
> Cheese Rolling 2017 at Cooper's Hill
> https://www.youtube.com/watch?v=pK1j06Gjp94
>
> Am Mittwoch, 4. Oktober 2017 21:18:25 UTC+2 schrieb burs...@gmail.com:

> > 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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