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Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 5   Last Post: Oct 4, 2017 3:15 PM

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bursejan@gmail.com

Posts: 5,410
Registered: 9/25/16
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 3, 2017 5:33 PM
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Why are they the same? Simply because oo is not
an element from the natural numbers. So

\sum_{k=1}^oo 9/(10^k)

cannot mean something where the last summand is
9/(10^oo) because a value 9/(10^oo) doesn't exist

in Q, since there is no k=oo. So all you have is
the partial sums that go on and on,

\sum_{k=1}^n 9/(10^k)
0.9
0.99
0.999
...

And you cannot identify a final value. To extract
a value from the series you need the limes.

Am Dienstag, 3. Oktober 2017 23:21:40 UTC+2 schrieb burs...@gmail.com:
> Since \sum_{k=1}^n 9/(10^k) = 1 - 10^(-n),
> and \sum_{k=1}^oo a(k) = lim n->oo \sum_{k=1}^n a(k)
>
> The two are synonymous:
>
> lim n->oo (1-10^(-n)) = \sum_{k=1}^{\infty} 9/(10^k)
>
> https://en.wikipedia.org/wiki/Synonym
>
> BTW: The following authors here on sci.math already
> explained this two you like a dozen times:
> - Dan
> - Me
> - Markus Klyver
> - Zelos Malum
> - Etc..
>
> You, bird brain John Gabriel, probably qualify
> for the most stupid human being on the planet.
>
> Should we call the Guiness book of records?
>
> Am Dienstag, 3. Oktober 2017 22:04:52 UTC+2 schrieb John Gabriel:

> > > lim n->oo (1-10^(-n))
> >
> > No. 0.999... = \sum_{k=1}^{\infty} 9/(10^k)





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