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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: 4,592
Registered: 9/25/16
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 3, 2017 8:32 PM
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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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