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Topic: Finally the discussion is over: S = Lim S is a bad definition.
Replies: 5   Last Post: Oct 3, 2017 9:01 PM

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bursejan@gmail.com

Posts: 4,540
Registered: 9/25/16
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 3, 2017 9:01 PM
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But if you plot the two series, 0.999... and 0.999...9995
you will see that neither of them is below the other,
there is always one summand that makes it bigger:

0.999... 0.999...9995
0.9
0.95
0.99
0.995
0.999
0.9995
Etc..

So we can only conclude Eulers series are brilliant,
interpreting a1+a2+a3+... as lim n->oo sum an, is
the only viable way,

any non-standard numbers with 0.999... != 1 dont
make any sense, they dont obey the standard laws
of algebra and blow up the

number space with a lot of cripples.

Am Mittwoch, 4. Oktober 2017 02:32:47 UTC+2 schrieb burs...@gmail.com:
> Well its the mean value between 0.999... and 1.0.
> Look if we have a and b, the mean value is (a+b)/2:
>
> a b (a+b)/2
> 0.9 1.0 0.95
> 0.99 1.00 0.995
> 0.999 1.000 0.9995
> 0.9999 1.0000 0.99995
> Etc..
>
> If 0.999... <> 1, then also 0.999... <> 0.999...9995
> and then also 0.999...9995 <> 1.
>
> And so on, as soon 0.999... <> 1, there are miriad
> other numbers inbetween.
>
> My suggestion: Don't do this nonsense, just interpret
> 0.999... as limit. Then you can also interpret
>
> 0.999..9995 as limit, namely this charming limit,
> the following summands summed up to finity:
>
> 0.5
> 0.45
> 0.045
> 0.0045
> ...
>
> Guess what is the result?
>
> 1/2+sum_i=1^n (45/10^(i+1)) = 1/2 + (1 - 10^(-n))/2
>
> lim n->oo 1/2 + (1 - 10^(-n))/2 = 1
>
> Am Mittwoch, 4. Oktober 2017 02:24:32 UTC+2 schrieb burs...@gmail.com:

> > So whats this Gabriel number:
> >
> > lim n->oo 0.999...9995 = ?
> > \---n---/
> >
> > Am Mittwoch, 4. Oktober 2017 02:08:09 UTC+2 schrieb burs...@gmail.com:

> > > So if 0.999... <> 1, do we have:
> > >
> > > 0.999... < 1
> > >
> > > Or rather?
> > >
> > > 0.999... > 1
> > >
> > > Am Mittwoch, 4. Oktober 2017 01:40:31 UTC+2 schrieb John Gabriel:

> > > > > nonsense. Right. But this was clear from the beginning.
> > > >
> > > > Yes. Of course S = Lim S is nonsense. So why do you still believe in it?





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