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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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Posts: 285
Registered: 11/4/16
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 4, 2017 1:30 AM
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keskiviikko 4. lokakuuta 2017 0.21.40 UTC+3 kirjoitti:
> 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)

are you trying to insist that 0.(9) is equal to
lim{n \to infinity} s(n) = lim{n --> infinity} 0.9 + 0.09 + 0.009 + ... + 9*10^(-n) = 1 ?

Using the real numbers 0.(9) is not equal to 1

and you have not demonstrated how do you get S(?) = 1. You have only shown
S(?) = 0.(9)

and because you are not willing to tell what you are doing, I have to
explain everything myself:

S(?) = 1 is possible only if you have included infinitesimals into the real numbers, but since you all have rejected them you are not supposed to use them too, right? Would you agree that it is reasonable to demand
that one cannot eat a cake and have it too? Or perhaps doing so brings
some benefits to all of you so you are not going be so strict when
you give some liberties to yourself. Yet, you deny these liberties from the so called "cranks".

> BTW: The following authors here on sci.math already
> explained this two you like a dozen times:
> - Dan
> - Me
> - Markus Klyver
> - Zelos Malum
> - Etc..

yes I know who they are, they deny the liberties of eating a cake from the so called "cranks".

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

check it and multiply it by 3 and arrive at
0.(9)9 + 0.(9)9 + 3*0.(3)4 = 0.(9)(9)+0.(9)(9)+0.(9)(9) = 1
and therefore 0.(9)(9) = 1

if you have difficulties performing the multiplication 3*0.(3)4 that's
only because you did not take my advice seriously early enough.

> You, bird brain John Gabriel, probably qualify

you forgot, again, that it may not the best possible choice to end up with
0.(9) = 0.(9)(9) and immediately deny the infinitesimals in real numbers.
Since clearly 0.(9)(9) contains the infinitesimal part 0.(0)(9)

> for the most stupid human being on the planet.

oops you did it again......

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