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0.9999... = 1 - Proof for the Retarded

Anonymous Tue 05 Oct 19:33:46 2021 No.13719450 View Reply Original Report

Quoted By: >>13723046 >>13725673 >>13726086 >>13726733 >>13728228

There's 0.9999... of them in every thread: retards who don't understand how infinite series work. If they passed Algebra 2, they can follow this proof (pic related). Anyone who still doesn't understand it is a troll and shouldn't be fed.

Anonymous

Anonymous Wed 06 Oct 2021 12:11:37 No.13721827 Report

Quoted By:

>>13721763
numbers aren't "real", they're just a model

Anonymous

Anonymous Wed 06 Oct 2021 12:18:51 No.13721835 Report

Quoted By:

>>13721607
>>13721407

Anonymous

Anonymous Wed 06 Oct 2021 13:09:17 No.13721935 Report

Quoted By: >>13722870

>>13719509
Imagine actually thinking knowledge/practice is equal to intelligence. Anyone who isn't a retard could learn that proof you posted. The fact of the matter is that many people haven't put the time into it because they haven't needed to.

Anonymous

Anonymous Wed 06 Oct 2021 15:15:45 No.13722229 Report

Quoted By: >>13726657

>>13719459
$0.9 = 1 - 0.1$
$0.99 = 1 - 0.01$
...
$0.999...9 = 1 - (0.1)^n$ where there are $n$ 9's to the right of the decimal place.
As $n\to \infty$ , $(0.1)^n \to 0$ , hence $0.\bar{9} = 1$ .

Anonymous

Anonymous Wed 06 Oct 2021 15:18:56 No.13722236 Report

Quoted By: >>13722672

>>13720023
It's a matter of the definition of convergence of a series. You can find everything you need in your basic analysis textbook.

Anonymous

Anonymous Wed 06 Oct 2021 17:51:41 No.13722672 Report

Quoted By: >>13722770 >>13722887

>>13722236
no, I meant him specifically. the dude is pretty strictly against infinite and infinitely precise things.

Anonymous

Anonymous Wed 06 Oct 2021 18:33:48 No.13722770 Report

Quoted By: >>13723735 >>13724624 >>13725588

>>13722672
Believe it or not, $0.\bar9$ is not infinitely precise

Anonymous

Anonymous Wed 06 Oct 2021 18:35:47 No.13722775 Report

Quoted By:

>>13719459
Meds. Now.

Anonymous

Anonymous Wed 06 Oct 2021 19:28:34 No.13722870 Report

Quoted By:

>>13721935
>I can do it but I've just never tried but i for sure know that i can do it cause reasons

Yeah you belong here

Anonymous

Anonymous Wed 06 Oct 2021 19:30:52 No.13722876 Report

Quoted By:

>>13719465
Why choose $N=\log_{10}\frac{1}{\epsilon}+1$ instead of $N=\log_{10}\frac{1}{\epsilon}$ ? Is it to express the largeness of N?

Anonymous

Anonymous Wed 06 Oct 2021 19:36:59 No.13722887 Report

Quoted By: >>13724624 >>13725637

>>13722672
$0.\bar{9}$ is just formal notation for the limit of the series $a_n = 1 - (0.1)^n$ , $n=1,2,3,...$ . The limit just happens to be 1. Likewise $a_n \to x$ as $n\to \infty$ is just formalism as well. Everything having to do with infinite decimals is just formalism for convergent series. The series or the limits themselves do not require infinity or "infinite preciseness." It's a matter of the definition of convergence.

Anonymous

Anonymous Wed 06 Oct 2021 21:12:53 No.13723046 Report

Quoted By: >>13723133

>>13719450
your proof assumes the thing you're trying to prove...

Anonymous

Anonymous Wed 06 Oct 2021 21:48:32 No.13723133 Report

Quoted By:

>>13723046
It doesn't.

Anonymous

Anonymous Thu 07 Oct 2021 02:35:06 No.13723735 Report

Quoted By: >>13723884

>>13722770
>let's pretend finite is infinite
wrong
it's infinitely precise

Anonymous

Anonymous Thu 07 Oct 2021 03:54:34 No.13723884 Report

Quoted By: >>13723890

>>13723735
And yet Wildberger doesn't seem to think so

Anonymous

Anonymous Thu 07 Oct 2021 03:57:11 No.13723890 Report

Quoted By: >>13724861

>>13723884
>Wildberger
lol

Anonymous

Anonymous Thu 07 Oct 2021 05:00:14 No.13723967 Report

Quoted By: >>13724046 >>13724868

Its interesting that over and over people independently come up with the idea that .999...?1. I think its because, even if people aren't aware of it, there's a rigorous way one can construct a system where the two numbers are different. It ultimately comes down to crafting a non-zero number such that $\varepsilon < \frac{1}{n} \forall n \in \mathbb{N}$ . Within the usual real numbers, such a small number can't exist, so we are forced to assign .999.. and 1 to the same value, since there difference cannot be anything other than 0. It turns out that if you take any statement which holds for every finite natural number (in this case, the family of statements are 1 ?.9, 1?.99, 1?.999, etc.), its possible to construct a system where the statement holds for all natural numbers (in this case, a system where it holds that 1?.9999...). The idea is called compactification (iirc, I don't quite remember the name of the theorem).

Anonymous

Anonymous Thu 07 Oct 2021 05:40:22 No.13724046 Report

Quoted By: >>13724770

>>13723967
3 < ?
3.1 < ?
3.14 < ?
3.141 < ?
3.1415 < ?
3.14159 < ?
3.141592 < ?
3.1415926 < ?
3.14159265 < ?
this continues endlessly
? < ?

your fields medal is in the mail

Anonymous

Anonymous Thu 07 Oct 2021 11:46:50 No.13724624 Report

Quoted By: >>13725648

>>13722770
elaborate? do you mean that it's just 1, or that you think it corresponds to some finite number below that? or that it's just an object that's somewhere there but has no precise value?
>>13722887
sure, I was just wondering how wildberger copes about it. his takes are sometimes interesting.

Anonymous

Anonymous Thu 07 Oct 2021 12:44:31 No.13724770 Report

Quoted By: >>13725009

>>13724046
you're assuming that 3.14159265.. = pi. you have to do it like this:

0.9 < 0.999...
0.99 < 0.999...
0.999 < 0.999...
this continues endlessly and there is no reason to assume that it stops being true
0.999... < 0.999...

Anonymous

Anonymous Thu 07 Oct 2021 13:23:28 No.13724861 Report

Quoted By:

>>13723890
Remember that God created the concept of numbers.
Satan created the concept of collecting several numbers together, thus allowing
them to become indecent with one another.
Wildberger is fighting the good fight. Do not take his name in vain.

Anonymous

Anonymous Thu 07 Oct 2021 13:25:59 No.13724868 Report

Quoted By:

>>13723967
If you are thinking of Robinson arithmetic and hyperreals, then .999... and 1 are still the same:
https://en.wikipedia.org/wiki/Hyperreal

Anonymous

Anonymous Thu 07 Oct 2021 14:06:36 No.13725009 Report

Quoted By:

>>13724770
someone give this genius two medals

Anonymous

Anonymous Thu 07 Oct 2021 17:03:28 No.13725588 Report

Quoted By: >>13725598

>>13722770
Aren't you aware of significant figures? Of laboratory measurements?

Anonymous

Anonymous Thu 07 Oct 2021 17:05:20 No.13725598 Report

Quoted By: >>13725608

>>13725588
what do significant figures have to do with 0.999... being 1?

Anonymous

Anonymous Thu 07 Oct 2021 17:07:14 No.13725608 Report

Quoted By:

>>13725598
Fixing a finite number of significant figures there's not infinite decimals at all and for example $1$ is quite different from $1.00$ .

Anonymous

Anonymous Thu 07 Oct 2021 17:12:59 No.13725637 Report

Quoted By:

>>13722887
Wilberger have no problem with reapeating decimals per se. He just wonders why arithmetic with reapeating decimals is so difficult and different from arithmetic with the corresponding $\frac{a}{b}$ fractions.
See pic attached in the post: >>13719803

Anonymous

Anonymous Thu 07 Oct 2021 17:15:05 No.13725648 Report

Quoted By: >>13726569

>>13724624
Wilberger has no problem with reapeating decimals per se. He just wonders why arithmetic with reapeating decimals is so difficult and different from arithmetic with the corresponding $\frac{a}{b}$ fractions.
See pic attached in the post: >>13719803

Anonymous

Anonymous Thu 07 Oct 2021 17:15:26 No.13725651 Report

Quoted By: >>13725673

the 0.999... = 1 believe they are houdini, slipping a 0.0...1 up their sleeve and hiding it in the ... portion of the notation.

They arn't fooling anyone

Anonymous

Anonymous Thu 07 Oct 2021 17:18:31 No.13725673 Report

Quoted By: >>13726234

>>13719450
>>13725651
Is the notation $0.\bar{9}$ any less ambiguous than the $0.999\ldots$ for you?

Anonymous

Anonymous Thu 07 Oct 2021 19:02:26 No.13726080 Report

Quoted By: >>13726161 >>13726637

>>13719632
WTF Bro? This is like a circular proof. you are using 1/3 = 0.333...

Anonymous

Anonymous Thu 07 Oct 2021 19:03:33 No.13726086 Report

Quoted By:

>>13719450
stop rounding, absolute midwit

Anonymous

Anonymous Thu 07 Oct 2021 19:21:23 No.13726161 Report

Quoted By:

>>13726080
>>13721407

Anonymous

Anonymous Thu 07 Oct 2021 19:40:03 No.13726234 Report

Quoted By:

>>13725673
But the difference betwixt the lefte and right sleeve

Anonymous

Anonymous Thu 07 Oct 2021 21:08:47 No.13726569 Report

Quoted By:

>>13725648
ah right, thanks. I guess this should be evident from the pic.

Anonymous

Anonymous Thu 07 Oct 2021 21:27:04 No.13726637 Report

Quoted By:

>>13726080
circular reasoning kills the schizo

Anonymous

Anonymous Thu 07 Oct 2021 21:32:05 No.13726657 Report

Quoted By:

>>13722229
>converges
>equals
retard

Anonymous

Anonymous Thu 07 Oct 2021 21:59:52 No.13726733 Report

Quoted By: >>13726755 >>13726869

>>13719450
>mathematicians seriously think that 0.9999999...=1 but won't accept that 1/0=infinity, something so patently obvious that any sixth grader with an undertanding of 0, infinity, and division would tell you it's true.
why are mathematicians so retarded?

Anonymous

Anonymous Thu 07 Oct 2021 22:08:53 No.13726755 Report

Quoted By: >>13726810

>>13726733
Your sixth grader, who knows more than any mathematician ever knew, also knows that 1/-0 = -infinity, right?

Anonymous

Anonymous Thu 07 Oct 2021 22:30:26 No.13726810 Report

Quoted By: >>13726890

>>13726755
It's not that the sixth-grader is smarter, it's that he hasn't yet been indoctrinated to believe that division by 0 is impossible.
There are definitely peculiarities to division by 0, but they are not insurmountable. You might use a signless infinity, or a signed 0.
Either way, x/0=infinity is supported by the fact that
x*0=0 , therefore 0=0/x and x=0/0
As dividing by 0 yields infinity, 0/0 is the same as 0*infinity, meaning:
x=0*infinity , therefore x/0=infinity and x/infinity=0
If that doesn't convince you, consider a finite segment of the number line. The length of this segment could be any non-zero real number X. The segment is made up of an infinite amount of dimensionless (length=0) points, which when added together (0*infinity) add up to the length of the line segment (X).

Anonymous

View Same Google iqdb SauceNAO divideby0.png, 76KiB, 1498x1153

Anonymous Thu 07 Oct 2021 22:49:52 No.13726869 Report

Quoted By: >>13726974 >>13727147

>>13726733
infinity or -infinity?

Anonymous

Anonymous Thu 07 Oct 2021 22:54:47 No.13726890 Report

Quoted By:

>>13726810
Good luck with passing sixth grade anyway.
Maybe hire a fourth grader as a tutor who will explain stuff to you.

Anonymous

Anonymous Thu 07 Oct 2021 23:24:18 No.13726974 Report

Quoted By: >>13728165

>>13726869
Both, just as the square root of 4 is both +2and -2

Anonymous

Anonymous Thu 07 Oct 2021 23:47:48 No.13727041 Report

Quoted By:

>>13721430
can confirm.

t. numerical anal major

Anonymous

Anonymous Fri 08 Oct 2021 00:35:53 No.13727147 Report

Quoted By:

>>13726869
Unsigned infinity

Anonymous

Anonymous Fri 08 Oct 2021 05:55:18 No.13728019 Report

Quoted By:

>>13719520
that’s literally what that means though

Anonymous

Anonymous Fri 08 Oct 2021 07:05:45 No.13728165 Report

Quoted By: >>13728194 >>13729134

>>13726974
>square root of 4 is both +2and -2
nope
$<br />\sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right |<br />$

Anonymous

Anonymous Fri 08 Oct 2021 07:18:01 No.13728194 Report

Quoted By:

>>13728165
you have literally agreed with him

Anonymous

Anonymous Fri 08 Oct 2021 07:33:23 No.13728228 Report

Quoted By:

>>13719450
How to get from line 6 to 7? Am retarted

Anonymous

Anonymous Fri 08 Oct 2021 15:33:11 No.13729134 Report

Quoted By:

>>13728165
While the radical sign, by convention, does only result in a single, "principal" square root, that doesn't change the fact that there numbers also have an equivalent but negative square root.
Regardless, if it's valid to take an operation that has two results with an equal absolute value and just take that absolute value as the "correct" result, then it should also be valid to take the absolute of both positive and negative infinity as the answer to x/0.

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