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

Replies: 14   Last Post: Oct 2, 2017 6:05 AM

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

Posted: Oct 2, 2017 1:29 AM
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sunnuntai 1. lokakuuta 2017 23.21.58 UTC+3 Me kirjoitti:
> On Sunday, October 1, 2017 at 9:48:24 PM UTC+2, John Gabriel wrote:
>

> > SUM_{k=1...oo} (3/10^n)
> >
> > It is most definitely not the same as 1/3

>
> Well, actually it is. There's a simple prove for the theorem
>
> lim SUM_{k=1..n} (3/10^k) = 1/3 .
> n->oo
>
> Hence
>
> oo
> SUM (3/10^n) = 1/3 .
> n=1


are you trying to insist that 0.(3) is equal to
lim{n \to infinity} s(n) = lim{n --> infinity} 0.3 + 0.03 + 0.003 + ... + 3*10^(-n) = 1/3 ?

Using the real numbers 0.(3) is not equal to 1/3.

But it seems you have chosen to prefer eating the cake and having it too,
meaning you have rejected the infinitesimals but using them too.
That's why you end up with a falsehood 0.(3) = 1/3 in real numbers.

You should be able to check a simple arithmetic
0.(3)3 + 0.(3)3 + 0.(3)4 = 0.(3)(3)+0.(3)(3)+0.(3)(3) = 1
and therefore 0.(3)(3) = 1/3








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