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Topic: Finally the discussion is over: S = Lim S is a bad definition.
Replies: 3   Last Post: Oct 6, 2017 10:26 AM

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bursejan@gmail.com

Posts: 5,412
Registered: 9/25/16
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 6, 2017 8:57 AM
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Measurement in base 10 is not a criteria for a limit,
some Q-series indeed have a limit in Q, for example:

0.333... = 1/3

Am Freitag, 6. Oktober 2017 14:57:16 UTC+2 schrieb burs...@gmail.com:
> Thats the same what Markus Klyver already told you
> 3 trillion times, namely Q-series need not have
> a limit in Q. Here see for yourself:
>
> 1 + 1/2 - 1/8 + 1/16 - 5/128 + 7/256 ... = sqrt(2)
>
> Each partial sum is from Q, i.e. is a rational number,
> their values are, all from Q, aka rational numbers:
>
> 1
> 1 1/2
> 1 3/8
> 1 7/16
> 1 51/128
> 1 109/256
> Etc...
>
> Nevertheless the limit is not from Q, since sqrt(2)
> is an irrational number, or in Euclid terms an
> incommensurable magnitude ratio.
>
> Got it?
>
> Question: Why do you sign your posts with "Baboon",
> is this the reason you don't understand real analysis?
>
> Am Freitag, 6. Oktober 2017 13:36:11 UTC+2 schrieb John Gabriel:

> > It applies to rational numbers that can't be measured in a given base.
> > Incommensurable magnitudes cannot be measured.
> >
> > Baboon.





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