/sci/ - Science & Math » Thread #14206593

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Anonymous Wed 09 Feb 18:12:35 2022 No.14206593 View Reply Original Report

Quoted By: >>14206655 >>14207778 >>14208367 >>14210120

Anonymous

Anonymous Wed 09 Feb 2022 18:28:37 No.14206655 Report

Quoted By: >>14206688

>>14206593
Maybe it has something to do with 1/99.

Anonymous

Anonymous Wed 09 Feb 2022 18:37:07 No.14206688 Report

Quoted By: >>14207828 >>14212469

>>14206655
By definition $0.\bar{ab}$ is defined through a geometric series via the following.
$0.\bar{ab} = \sum_{n=1}^\infty \frac{ab}{10^{2n}}$ .
Of course, since $10^{-2} <1$ , the series converges using the usual formula
$\sum_{n=1}^\infty \frac{ab}{10^{2n}} =\frac{ab\cdot 10^{-2}}{1-10^{-2}} = \frac{ab}{10^2 -1} =\frac{ab}{99}$ .

That being said, we can simply bypass the three distinct calculations in OP's image.

$0.\bar{99} = 0.\bar{9} = \sum_{n=1}^\infty 9* 10^{-n} = \frac{9 *10^{-1} } { 1- 10^{-1} } = \frac{ 9 }{ 10-1} = \frac{9}{9}=1$ .

Anonymous

Anonymous Wed 09 Feb 2022 22:25:29 No.14207778 Report

Quoted By:

>>14206593
Rounding error

Anonymous

Anonymous Wed 09 Feb 2022 22:34:52 No.14207823 Report

Quoted By: >>14207828 >>14207848

what OP has shown is that repeated decimals represent the infinitesimal trending/trending toward the true value of the fraction.
But the repeated decimal is not the fraction.
iow : 99/99 - 0.999... = epsilon.

Anonymous

Anonymous Wed 09 Feb 2022 22:35:54 No.14207828 Report

Quoted By:

>>14206688
so, the mathematical representation of >>14207823
good job

Anonymous

Anonymous Wed 09 Feb 2022 22:38:44 No.14207848 Report

Quoted By:

>>14207823
epsilon = 0

Anonymous

Anonymous Wed 09 Feb 2022 23:13:06 No.14207985 Report

Quoted By: >>14209696 >>14209706

>0.9999... = 9/10 + 9/100 + 9/1000 + ...
>9/10 is smaller than 1
>9/100 is smaller than 0.1
>and so on
>so the sum of them is always just not 1 + just not 0.1 + just not 0.01 forever
>this sum of items that are always smaller than the next higher number is supposed to be the next higher number according to maffs

Anonymous

Anonymous Thu 10 Feb 2022 01:11:35 No.14208367 Report

Quoted By:

>>14206593
10 stock goes down 9.999...% then goes up 9.999...%
where did my dollar go?

Anonymous

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Anonymous Thu 10 Feb 2022 02:01:30 No.14208502 Report

Quoted By:

Anonymous

Anonymous Thu 10 Feb 2022 05:15:21 No.14209247 Report

Quoted By:

explain this one sciece

Anonymous

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Anonymous Thu 10 Feb 2022 05:16:39 No.14209252 Report

Quoted By: >>14209321 >>14210276

forgot pic

Anonymous

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Anonymous Thu 10 Feb 2022 05:27:31 No.14209321 Report

Quoted By:

>>14209252
use a real programming language

Anonymous

Anonymous Thu 10 Feb 2022 07:10:46 No.14209696 Report

Quoted By: >>14209699

>>14207985
there's literally nothing in real life that requires enough precision for that to matter, hell even (1-10^50) is good enough

Anonymous

Anonymous Thu 10 Feb 2022 07:11:48 No.14209699 Report

Quoted By:

>>14209696
10^-50
don't even THINK of nitpicking that typo you hypothetical turboautist

Anonymous

Anonymous Thu 10 Feb 2022 07:14:49 No.14209706 Report

Quoted By: >>14210199

>>14207985
0.999... is static, the length is aleph_0 from the get go.
Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.

Anonymous

Anonymous Thu 10 Feb 2022 11:29:59 No.14210120 Report

Quoted By: >>14210479 >>14212469

>>14206593
I don't find it trivial that 0.999...= 99/99
While 99/99 is a rational number, 0.999... might just be irrational

Anonymous

Anonymous Thu 10 Feb 2022 12:11:43 No.14210199 Report

Quoted By: >>14210386

>>14209706
>i’m right because the rule i made up says i’m right
this is why aliens don’t visit us

Anonymous

Anonymous Thu 10 Feb 2022 12:40:55 No.14210276 Report

Quoted By: >>14210993

>>14209252
>Cnile discovers UB
Behind every security flaw... der cnile.

Anonymous

Anonymous Thu 10 Feb 2022 13:26:26 No.14210386 Report

Quoted By: >>14210828

>>14210199
read a book

Anonymous

Anonymous Thu 10 Feb 2022 13:47:23 No.14210479 Report

Quoted By: >>14212447

>>14210120
It is not clear. Like, $\frac{113}{355} \pi$ happens to equal 0.9999999...
Yet, who is to say that $\frac{113}{355} \pi$ is not rational?

Anonymous

Anonymous Thu 10 Feb 2022 15:17:41 No.14210828 Report

Quoted By: >>14210954

>>14210386
>see here the rule book i wrote says so! q.e.d.!

Anonymous

Anonymous Thu 10 Feb 2022 15:47:16 No.14210954 Report

Quoted By:

>>14210828
book > random schizo

Anonymous

Anonymous Thu 10 Feb 2022 15:58:22 No.14210993 Report

Quoted By:

>>14210276
floating point representation is UB?

Anonymous

Anonymous Thu 10 Feb 2022 20:34:35 No.14212447 Report

Quoted By:

>>14210479
Suppose
$\frac{113}{355}\pi$ is rational. Then
$\frac{113}{355}\pi = \frac{p}{q}$ for integers $p,q\not=0$ . Then $\pi = \frac{355p}{133q}$ . This implies that $\pi$ is rational. This is a contradiction since $\pi$ is irrational.

Anonymous

Anonymous Thu 10 Feb 2022 20:37:40 No.14212469 Report

Quoted By:

>>14210120
$0.\bar{9} =\sum_{n=1}^\infty 9\cdot 10^{-n}$ by definition. Now see
>>14206688

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