>>16786015
midwits want to disprove mathematics by attacking the syntax, that's why.
it's easily proven with low-level axiomes.
Suppose we have a real number a that's equal to 0.99999.... By definition, the 9s go on forever. each time you have found the last one, there'll be another one waiting for you. This is our definition of this number a.
Now let's multiply a by 10. Obviously, 10a = 9.9999999.. For any last 9 in 10a, you'll find another one behind it. Now, if we subtract a from 10a, we calculate: 9.9999.... - 0.9999..... which is equal to 10a-a=9a.
Following from the axiomes of addition(subtraction), we know: 9.999... -0.999... = 9. Since 9=9a, we can also say: a= 1. q.e.d

>>16786015
Intuitively you can imagine an infinitely small number between the two:
...0001
But this isn't defined in mathematics so the two are equivalent

>>16786112
What if we define r=0.999999999... as the number where there is actually no real number that's greater than 0 and smaller than or equal to 1-r?

>>16786102
>these two numbers are equal because my system would break otherwise
Not a really convincing proof desu

>>16786102
>Non unique syntaxes for an equality written
Anon...

I just thought of it. Doesn't 0.999... = 1 basically disprove Plato's theory of forms? I guess that's why people can't accept it. It goes against how we intuitively think of abstract ideas.

>>16786102
>For any last 9 in 10a, you'll find another one behind it. Now, if we subtract a from 10a, we calculate: 9.9999.... - 0.9999..... which is equal to 10a-a=9a.
Okay ramanujan

>>16786015
Because on a fundamental level it looks wrong. 1 from our perspective should be 1.0 and that's it. No series of infinite digits repeating or otherwise, after that should get you to 1. Whether it terminates or goes on forever we already have said it is 0.999... and somehow they want that to equate to 1.0? Makes no sense to me. By rounding up then yeah we can say that 1.0 and 0.999 are basically the same shit. But as an identical value upfront? I'm just not seeing it. Maybe there is some math way over my head making it make sense but I haven't seen it yet.

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>>16786015
there never was any ‘contraversy’. more like claims of 'heresay' from the usual suspects.

>>16786102
Just a magic trick

- you can't generate infinite 9s
- you can't mulipy infinite 9s by 10 (it's undefined but you pretend it is well defined)
- you then can't generate infinite 9s again and then subtract them from another infinite 9s in a finite time.

>B-but I just did it.
No you didn't - you actually worked just with 0.9999 to perform the trick. And you will never be able to show the trick with actual infinite 9s. You just PRETENDED, using a finite notation, that 0.999... contains actual infinite 9s.

Q. E. D.

>>16786160
>You just PRETENDED, using a finite notation, that 0.999... contains actual infinite 9s.
demonstrate that it doesn't

>>16786015
>Why is 0.999... = 1 considered a controversial topic?
If something is not incontrovertible, someone is going to controvert it at some point, resulting in a controversy, which makes the topic controversial. It's not incontrovertible that identifying an infinite sum with a number using limits is a philosophically sound idea. The most you can prove is that it's internally coherent. But internal coherence is not enough. Mathematics matters because relationships between numbers seem to correspond to actual real relationships in reality. If you "overextend" your notion of numbers to include things that have nothing to do with reality, you can end up breaking that correspondence without doing something wrong "mathematically". I'm not saying 0.999... actually does this, but some people clearly are and you can't prove them wrong using definitions, let alone algebraic tautologies.

>>16786131
Please look up ancient mathematics. You can be glad that I used symbols at all.

>>16786102
>Now let's multiply a by 10
You have not defined what it means to do this. Try again.

>>16786126
Just wait until you find out why exactly 1a = a and a + 0 = a. It'll blow your mind to pieces

>>16786183
>1 of a is a
Yes.
>a + nothing leaves you with a
Correct.
>so that means if "idk bro its cuz i said so stfu" and if i have already defined 1.0 as 0.999... then it is cuz... well cuz i sed so
The other two make sense. I can comprehend those. The last one comes off like a bit of an asspull.

>>16786182
>Sir please, I dident have an elementry school in kolkata, i never had the chance to familiarize with multiplication of real numbers and their five (5) rules, please sir just explain to me sir

>>16786015
What everyone seems to forget is that Mathematics is a language and there are more than just one mathematical language. Some are very similar. Some exist purely as a form for a niche application, Some are very different.
The equation of 0.999...= 1 is absolutely correct within the form of standard mathematics, which is the most commonly used mathematical language. Because its core tenets allow such a construction to exist and therefore it follows quite logically.
However there exist some forms of mathematics where a construction such as 0.999... does not exist. Others where such a construct could not even be derived.
Arguing about the differences between these languages is similar to arguing that German is more "correct" than Chinese. Or that Italian is more "correct" than Russian. Some languages such as English are very common and spoken internationally. Others like Ainu are only spoken by a small and specific group. There are some things in some languages that have no equivalent translation in another language while others may be very similar, such as Spanish and Portuguese. Some languages allow more precision within some contexts but are less precise in other contexts. This is the same with mathematical languages.
Of course midwits and contrarians will seethe but to anyone with a decent education and reasonable intelligence this is self evident and a complete non-issue.

>>16786185
>1 of a is a
oh is it? why? For me, it looks a lot like 1a is 1a and not a.

>>16786186
Ok, what's the elementary school definition of multiplying a sum with an infinite number of terms by 10?

>>16786183
I guess all of mathematics is just like that. Maybe this is the limitations of mathematics as a self contained system. It can describe a lot of things in real life accurately but this one doesn't seem to be one of them.

>>16786187
>umm, sweaty? numbers are subjective, ok?
>it's a social construct
Fuck off, tranny.

>>16786190
multiply every term by 10 and add them, duh(distributivity). if 0.999 is an infinite sum of 9*10^(-n) with n increasing by 1 with every step, then any term 9*10^(-n) will become 9*10^(-n+1) after multiplication by 10. Since we all know and agree on how the decimal system works, it's obvious that every single 9 "goes one decimal place to the left" and thus if a = 0.999...999...999, 10a = 9.999...999...999

Possibly tangential questions but what about in real life? Would you say that a mass that weighs 0.999... lb weight as much a mass that weighs 1 lbs? Irrational measure definitely exist in real life because it's the circumference of a circle with 1 unit length diameter. Does a 0.999... inch line exist?

>>16786197
>multiply every term by 10
Ok.

>and add them
What does this mean? How do you add an infinite number of terms.

>>16786198
>Possibly tangential questions but what about in real life? Would you say that a mass that weighs 0.999... lb weight as much a mass that weighs 1 lbs?
The way it's defined 0.999... and 1 are literally the same number so your question is moot.

>Irrational measure definitely exist in real life because it's the circumference of a circle with 1 unit length diameter. Does a 0.999... inch line exist?
How do you know circles exist in real life?

>>16786199
>>multiply every term by 10
>Ok.
multiplication of any number k by a natural number p is defined as adding k together p times. addition of numbers is defined via the real life concept of putting two different amounts (a, b) together and receiving a new amount (c) that's also an amount and also the only amount that's exactly as big as the amounts of a and b together.
That's all there is, I'm not schizo enough to go down even further

>>16786202
>addition of numbers is defined via the real life concept of putting two different amounts (a, b) together and receiving a new amount (c)
Jesus, you really are retarded. So again, how do you put an infinite number of amounts together? This is a doubly good question now that you went for the American public school product's vague concept of addition instead of actually knowing what it means.

>>16786201
Does numbers exist in real life?

>>16786206
Reality faithfully instantiates numerical relationships. Does it instantiate circles?

>>16786204
>actually knowing what it means
you tell me then how you'd define addition of numbers
>how do you put an infinite number of amounts together
By doing the addition over and over and over again. Then you ask yourself: is the sum ever increasing? Or does it seem to grow only to a certain value, because every new term gets smaller, fulfilling the definition of a converging series. If the latter is true, you can say that the infinite sum is equal to that certain value. For the infinite sum of 9*10^(-n), the value it converges to is 1.

>>16786015
It's the breakfast problem but for midwits

>>16786215
>By doing the addition over and over and over again.
And how many times do you do this before you get your sum? Be sure to name an actual number.

>>16786218
>how would you feel if infinity wasn't infinite?

>>16786212
Then is a 0.999... inch line the same length as 1 inch line?

>>16786222
>is a x inch line the same as a 1 inch line if i define x=1?
Yeah. What does this have to do with my post or with anything?

>>16786225
What a shit answer

>>16786163
I see exactly three 9s in 0.999...

Or: it takes time T to generate a 9, how much time T will be needed to generate them all? Cleary, by your logic, T = inf. Will anyone ever be able to generate all 9s? Obiously not because infinity is a process and not a number. Since the process won't ever finish it will never reach 1.

Now that I proved that, show me that it contains infinite 9s.

>>16786219
You don't have to, it's kinda obvious from the definition of the infinite series/sum which one it is.
You've got me though, I don't know as much about series and sums as I want to, so I'll now learn

>>16786228
It's the only correct answer to your "is 1 = 1 in real life?" dumbfuck question. How many of you retards are under the wrong impression that 0.999...=1 actually implies adding an infinite number of terms?

>>16786187
Fuck off retard. There is only one mathematical language and that says 0.999...=1.
Anything else is fucking retarded, just like you.

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>>16786235
Not so fast

https://en.m.wikipedia.org/wiki/Hyperreal_number

>>16786234
Are you now arguing that 0.999.. is not made up of the sum of 9/10^n where n ranges from 1 to infinity?

>>16786233
>You don't have to
You literally just said I do, but I accept your retraction.

> I don't know as much about series and sums as I want to, so I'll now learn
Will you, though? If I inform you that most sane mathematicians accept that finishing an infinite process is a contradiction, will you actually learn from this? You have to jump through some artificial hoops and definitions to get 0.999...=1. The logic roughly amounts to "IF we WANT to identify this infinite expression with some number in R, we can use convergence and limits to DEFINE it to be equal to this one specific number unambiguously". There's nothing "obvious" about it.

>>16786243
I'm not arguing anything. I'm just informing you about the difference between "sum" as American highschool retards understand it and "sum" as in the fuckery of associating a single numerical value with an infinite sequence that represents the "sum".

>>16786234
Can you have thave 0.999... without a process?

Can you see a number without writing it down?

Do numbers exit without a brain thinking them?

Can your brain imagine something infinite?

I have a question:

0.999... + 0.999... = 1.999...8?

Is addition with infinitsimals even defined witout the snake oil method of converting them into whole numbers first?

>>16786015
>Why is 0.999... = 1 considered a controversial topic?
decimalism is just a language game.

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So I understand that multiplying a negative number by another negative number makes the number positive.
See pic related.
I personally think that 0.999_ is not equal to 1 but this could also be from the same lack of understanding of mathematics that trips people up on negatives, not that it is the same misunderstanding but an incomplete picture of the concept of why 0.999_ is equal to 1.

>>16786263
>I have a question:
>0.999... + 0.999... = 1.999...8?
Well, you seemingly did find a way to manipulate the endless sequence of 9s to come up with that 8 in the end, so maybe you can formalize the thought process and make it work. :^)

>>16786263
In hyperreals, the real number 0.999... = 0.999...999... = 1. The intercalary ... doesn't have a place value. So 0.999...9 + 0.999...9 could be written as 1.999...8 or 1.999...98 or 1.999...99999999998. It's not a very useful notation for arithmetic.

>>16786015
Because the world is full of idiots who think that anything beyond their instinctual "common sense" understanding of reality is a gay commie conspiracy to steal their vital fluids.

>>16786326
>think that anything beyond their instinctual "common sense" understanding of reality is a gay commie conspiracy
It's called "learning". You're getting replaced by """AI""" because you've been crippled into a state where it can learn from examples to model reality better than public school retards.

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>>16786015
so you're telling me the area of this is 0?

>>16786126
numbers are part of the system though

0.99.. - 1 = 0
So it's 1

>>16786102
Firstly, show that .999... exists. You can't, without taking it as an axiom. This is a very strange thing to do, when the only benefit is to have some strange, alternative form of a number that never arises from any calculations that you do, and can't be worked with in the usual way. Furthermore, even if you do this, you can't show that 10*.999... = 9.999..., nor that 9.999...-.999... = 9, without describing in detail, the algorithms used to perform these calculations, and verifying that these algorithms are correct.

>>16786356
>You can't, without taking it as an axiom
man, you'll get a whole mental crisis when you find out that mathematics is literally built on a few "it just is, okay..!", especially concerning numbers and some calculation rules

>>16786336
Your base doesn't even satisfy 10 > 1 lol

>>16786356
NTA but 0.999... exists to the same extent that 1.000... exists and that's all you need.

>>16786015
Firstly, ask yourself, "what is the meaning of numbers like .1..., and how are they similar and different from numbers like .5?" The answer is that these are both representations of numbers that resulted from calculating a long division problem, 1/9 the former, 1/2 the latter. However, we cannot reintroduce the former directly into a calculation like we can the later. If I want to calculate something like .(123)...*3.(987)..., I cannot directly apply the long multiplication algorithm taught to all of us in elementary school. With numbers that have terminating decimals, this is a trivial matter. Of course, it is useful to speak of numbers like 13/99 as .(13)..., to teach children about the non-terminating cases of the division algorithm. On the other hand, .(9)... does not result from any proper calculation, nor do any repeating decimals arise in any application where decimals are more appropriate than fractions. Why then, should we even claim that .9... Exists? To be fair to all the numbers and let you put a bar over any decimal? There's no reason for this.

>>16786367
I have a math degree. Obviously math is built on axioms. The point is that there's usually a good reason for each axiom. There's no good reason to take the existence of .9...
>>16786373
>To the same extent
Very non rigorous

>>16786382
0.999... exists to the same [level of rigor] that 1.000... exists.

>>16786397
1.000... exists for convenience of calculating. .999... Exists for no reason. As mathematicians, we try to limit the foundations of our theories to their minimums. For that reason, .999... Doesn't exist.

>>16786382
I doubt your math degree, maybe it's a degree of retardation concerning mathematical questions.
0.999... can be defined as an infinite sum as seen many times above. It exists. No need for a good reason. Maybe, if you're actually mathematical, let's ask the simple question: which value does the sum 9*10^(-n) approach, when n gets bigger and infinitely big?

>>16786402
0.999... exists because 1.000... exists. To the extent to limit the one, you limit the other.

>>16786015
I think for some people (me including) 0.999...9 is different from 0.(9) .

Second one is a periodic number written with finite number of symbols.
It is defined as 9/9 = 1.

But first one is thought of as if you've really written zero period infinitively many nines.
So I'd consider it to be sequence of 0.9, 0.99, 0.999, ... (and not necessary limit of this sequence).

Now intuitively 1 - 0.999...9 won't be *exactly* equal to zero no matter how many digits you write down. There will be a finite difference (if we use finite number of digits) and infinitesimal difference otherwise.

That's actually one way to construct hyperreal numbers in nonstandard analysis, and IMO it is more intuitive then considering infinisimals to be zero *without proper explanation*.

To get expected 1 - 0.999...9 = 0 we need to ignore an infinitesimal difference, which is not intuitive and sometimes wrong.

For example, if we have x = 0.999...9 (as a hyperreal/sequence of numbers/intuitive way of thinking), then (1 - x)/(1 - x) is defined (for each item in the sequence) and equals to 1.

(1 - x)^2 / (1 - x) = 1 - x = 0.000...1, an infinisimal hyperreal.
So the standard part of that number (the limit of the sequence) is 0.

>>16786406
>which value does the sum 9*10^(-n) approach, when n gets bigger and infinitely big
You forgot to tell me where n starts. The specific sum that you are trying to define as .999... converges to 1. So why define it as .999...? What use is .999... to anyone? Give me one good reason to use 1.999... in a calculation instead of 2.000....
>>16786408
That's very a very Indian observation.

>>16786406
NTA but 0.999... as an infinite sum only exists if you agree that infinite sums exist. 1 - 0.999... = 0 is always true whether or not you agree that infinite sums exist.

>>16786412
>very a very
How's the weather in Bombay lol

>>16786188
Because it's well known that 1x of a thing can just be said to be X. It's a shorthand. Nothing, anywhere, has a value less than 1 magically becoming equivalent to 1 no matter what you do with the only exception to that being rounding. But every time I bring rounding up I get told no, it's nit rounding but that somehow, as if by sheer magic, I have a value less than 0. And somehow get a 1.

>>16786418
>has a value less than 1 magically becoming equivalent to 1
True, and 1 - 0.999... never magically becomes greater than 0.

>>16786406
0.999... is not a rational number.

0.999... is not even a correct notation for a decimal number.
(Because '...' is not a digit.)

0.999... can be defined as either "what you get when you write 0.99(infinitively many nines)9" or as a limit of sequence 0.9, 0.99, 0.999, ... or as a hyperreal represented as a sequence 0.9, 0.99, 0.999.

These two things are different.
Again, (1 - 0.999...) / (1 - 0.999...) may have different values depending on a definion.

And some people here expect laymen to know calculus and to take limit of a sequence in a *right* place.

>>16786422
I agree. If I subtract it I should never get greater than 0. I should have a 0.0000 to however many digits back and then get a 1 somewhere. At least as I see it.

>>16786431
>and then get a 1 somewhere. At least as I see it.
I don't see it. It's like saying all the nines in 0.9 + 0.09 + 0.009 ... will magically all switch off to zeros if you just keep doing long enough.

.99(repeating) plus .00(repeating)1 =1

>>16786474
.99(repeating) plus .00(repeating)1 = .99(repeating)9 ≠ 1

I am sorry. The math is beyond you. The one adds into the last nine. The answer becomes 1. Does .9 plus .1 not equal 1?

>>16786478
You can't have a last 9 on 0 + 0.999... without having a last 0 on 1 - 0.999...

As long as the number of 9’s equals the number of 0’s plus 1. You get 1. Does that make sense now?

.999+.001=1
.999+.01=1.009

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>>16786482

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>>16786484
True

>>16786102
>by definition it goes on forever
and yet it stops the moment it reaches the physical limit of whatever you’re using to calculate it with

retards

>>16786499
>and yet it stops the moment it reaches the physical limit of whatever you’re using to calculate it with
So do the zeros of 1 - 0.999...
There's no configuration of reality where 1 - 0.999... ever ends in a 1

The original question was why does .9999=1 cause controversy? Because .9999 doesn’t equal 1.

>>16786516
No one thinks that, go back to reddıt.

By definition .999…. does not equal one unless something is added to it.

>>16786522
By what definition?

By the definition of the number .999…. Defined not as 1

>>16786527
I speak more than one language. Can you say what you mean in your own language?

I have explained the concepts and ideas. I have proven it with math. If you reach this point in the thread and you still do not understand why .999… does not equal one then I suggest more education for you.

>>16786534
Just say what you mean. Don't be coy about it

[math] \displaystyle
0. \bar{0}1
= \lim_{n \to \infty} 0. \underbrace{0 \dots 0}_{n ~ \text{times}}1
= \lim_{n \to \infty}
\left [
\left (
\sum_{k=1}^n \dfrac{0}{10^k}
\right )
+ \dfrac{1}{10^{n+1}}
\right ]
=0
[/math]

Yeah you found a fancy way to subtract the 1. Good job!

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>>16786553

>>16786187
Based take but way above the pay grade of most of these imbeciles. They are more interested in slinging bullshit than learning.

>>16786522
>>16786527
>>16786534
>>16786555
Praying for you

>>16786570
Ainu was a biological girl who was sexually abused by people like you and ended up killing people like you. Get her name out of your mouth.

Math is not a language it’s an idea. Based!

>>16786580
>>16786580

>>16786015
The controversy is that you can't make 0 plus a bunch of nines equal to 1 plus a bunch of zeros.

Nobody ITT has answered OP's question. Why is it a controversial topic? Like why is everybody ITT so rude and mad?

>>16786683
Ever had to explain someone why your left arm is your left arm and not your right arm?

>>16786747
That's your excuse? So you're a mentally volatile kid that gets mad when people don't immediately give you what you want lol.

Fun fact: if your math cannot be defined without reliance on natural language or embodied cognition then it is a strict subset of natural language and embodied cognition.
As in, not only is math a language, it's explicitly a constructed language.

>list all numbers
does cantors diagonalization argument assume existence of an injective map from the written script to real numbers?

>>16786776
Yes, yes I am and yes I do. Helps me stay sharp, relevant and in control.

>>16786784
And what follows from that?

>>16786242
per the transfer principle, 0.999...=1 in the hyperreals, retard

>>16786784
>if your math cannot be defined without reliance on natural language or embodied cognition then it is a strict subset of natural language and embodied cognition
It's another episode of midwits confusing different metalevels.

>>16786244
>There's nothing "obvious" about it.
but there is, since 0.999... is in the rationals

>>16786553
>Infinity
Try again.

>>16786181
1 = 7
And by this I mean 1 according to the arabs and 7 according to the Romans. I'm mixing syntaxes. Problem? Lrn math, fgt

FYI this is how the media works.
>>16786683
>Nobody ITT has answered OP's question.
Not true. Starting your post with a lie predisposes people to be rude and mad.
>Why is it a controversial topic?
Now you're trying to create a controversy that doesn't exist so you can report on it. This is a deranged grift.
>Like why is everybody ITT so rude and mad?
Now you're blaming everyone else for your own intentional lies and intentionally manufactured controversy.

>>16786411
wrong >>16786935

>>16786499
>the physical limit
what a failure you are

>>16786831
nah, numbers to numbers

>>16786942
On a scale from 0(very dissatisfied) to 100 (fully satisfied), how good do you feel about your response?

>>16786978
89

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>>16786015
jeets show some arithmetic, geometric, ... proof which shows completeness of the system not the philosophy behind picking 0.999... = 1 as an axiom, which is what the argument is about...

>>16787105
The only axiom you need is that an integer has enough zeros after the decimal point to compare it to any other decimal.

>1 - 0.9 isn't 1
>1 - 0.99 isn't 1
>1 - 0.999 isn't 1
>1 - 0.99999999999999999999999999999999 isn't 1
>1 - 0.999 is one cuz i said so bro trust me man if i do it a bajillion shaontillion times it's never 1 but if i do it "infinitely" it is :^)
This is such fucking bait garbage. If I was a mathematician I'd be coping finding a gaping flaw like this in mathematics. But I assume it's easier to just assert it's 1 by fiat rather than find the ERROR that leads to this nonsense.

>>16787587
>1 - 0.9 has a 0 in the ones place
>1 - 0.99 has a 0 in the tenths place
>1 - 0.999 has a 0 in the hundredth place
>1 - 0.99999999999999999999999999999999 has a 0 in the niggerth place
It's literally all zeros, anon. 0.000...

>>16786479
you can't have a last 0 on 1 - 0.999... without having a last 4 on 20 - 19

>>16787620
>1 - 0.9
what does it have in the tenths place?

>1 - 0.99
what does it have in the hundreths place?
etc

It’s comical at this point that some continue to say .999=1. Please keep it going. I need to laugh more.

>>16787646
Nothing, nothing. In every place that you can write something, it will always be a zero 0.

>>16787643
I don't understand how you got a 4 somewhere?

>>16787653
People like you need to be violently abused and face fucked by the other inmates until you throw up on yourselves. I welcome the new order.

>>16786126
Yes and 1 is not equal to 0 because the system of logic would not be logical anymore and you would have a broken system of logic if you tried assume as much.

>>16786160
So in your system, division by 3 can't be undefined since you can't actually generate infinite 3s?

it is 0.999...=1.0000 because if you 1.0000-0.999...., it leaves u with 0.00000..

>>16787674
Is this a bot? What is 1 - 0.9? What is 1 - 0.99?

>>16788100
What’s 1 - 0.8? What’s 23 - 7?

>>16787949
yes, and division by 2 isl also impossible because
[math]
0.5_{10}=0.333..._7
[/math]

0.999... = [math]\lim_{n \to \infty} \Sigma_{i=1}^n 9/10^i[/math]

>>16788216
Yeah, 0.999... = 1 because it's literally defined that way. The only problem is that this is also meant to imply an expression with infinite terms evaluates to something and using the word 'sum' to refer to this as if you actually sum up all the terms to arrive at 1. This part of it isn't made explicit in your equality but it's the part people object to.

>>16786112
So there is a 1 at the end of a number of with endless 0s, do I get that right you dumb motherfucker?

>>16788257
>This part of it isn't made explicit in your equality but it's the part people object to.
then they object to every single number with infinite digits, and their insistence with focusing on 0.9... is completely niggerful at absolute best and repugnantly facetious in actuality

>>16788271
>then they object to every single number with infinite digits
Sorta, I guess, but if you're thinking about something like pi or e, you could say it's not the decimal expansion that defines the number but the other way around, whereas the 1=0.999... rules out that reasoning by definition (not by refutation).

>>16788283
i mean, technically the 0.9... is due to the same mechanism that makes 456782/999999=0.(456782)..., and the same goes for swapping the 9's for the base-1 in other bases, oh and it is the same reason as to why 1/3=0.3..., since 1/3 is the simplified form of 3/9

>>16787620
>1 - 0.9 has a 0 in the ones place
>1 - 0.98 has a 0 in the tenths place
>1 - 0.998 has a 0 in the hundredth place
>1-0.99999999999999999999999999999998 has a 0 in the niggerth place
Yet indians like you will claim .999....8 doesn't exist, but .999...9 does.

>>16788436
Both exist and both are less than 1. And your H1B is denied.

>>16788451
>Both exist
Only in your fairy tale retard land. Neither exist.

We can all agree that 1/9*9=1

Now why is 1/9=0,1 periodic?

If you do division by hand you will observe a recusive formula on how the rest is generated. Therefore 9*0,1 (periodic) = 0.9 (periodic) = 1/9*9=1

This is the most down to earth explenation I could come up with.

>>16788459
0.999...8 could mean 0.99998 or 0.999999998 or 0.99999999999999999998. All of those exist. What it can't mean is that the nines go on "forever" then "end."

>>16788463
>It could mean one thing or another thing or some other thing
I see, completely meaningless.

>>16788467
Yes. You thought otherwise?

Hi, nominalist here. 0.999... and 1 don't exist. They're just made up abstractions. They are equal because we arbitrarily say that they are. Deal with it.
>b-but I don't personally say that they are
You don't matter as you do not have the power. Write that they're unequal in a math test and the math teacher will lower your grade.

>>16788469
Most people mean something else by .999... and .999...8

>>16788490
0.999... means the nines keep going. That's not compatible with ending in 8, therefore 0.999...8 has to mean something else. What else could it mean? What do "most people" mean by 0.999...8?

>>16788434
>i mean, technically the 0.9... is due to the same mechanism that makes 456782/999999=0.(456782)...,
I literally just explained to you why this is a moot argument: a number can imply a process that generates as many decimal digits as you care to know, but in and of itself, this does not imply you can add up an infinite number of terms and get back a number. If that were the case, you wouldn't have to jump through the hoop of convergence and limits.

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>>16788484
>Hi, nominalist here. 0.999... and 1 don't exist. They're just made up abstractions.

Nah, those numbers exists and are different.

1/(0.999... -1) = -inf
1/(1-1) = undefined
1/(1.000...1 -1) = +inf

>>16788564
>1.000...1
This number ends so 1/(1.000...1 - 1) has to be finite. Like 1000...0.

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>>16788490
>>16788503

0.999...8 or 0.999...x are all equals to 1-

0.999...8 = 0.8 + 0.1999...8
0.999...8 = 0.8 + 0.18 + 0.018 + 0.0018 + 0.00018 + ...
0.999...8 = 0.8 + 2*(0.09 + 0.009 + 0.0009 + 0.00009 + ...)
0.999...8 = 0.8 + 2*(0.0999...)
0.999...8 = 0.8 + 2*(0.1)
0.999...8 = 1


It works with whatever the 0.999...x ends :

0.999...3 = 0.3 + 0.6999...3
0.999...3 = 0.3 + (0.63 + 0.063 + 0.0063 + 0.00063 + ...)
0.999...3 = 0.3 + 7*(0.09 + 0.009 + 0.0009 + 0.00009 + ...)
0.999...3 = 0.3 + 7*(0.0999...)
0.999...3 = 0.3 + 7*(0.1)
0.999...3 = 1

>>16788579
>A number
>has to be finite.

Nah, and there is plenty of examples.
Here is one my fav.

1/2 in base 10 is finite :
1/2[base 10] = 0.5[base 10]

But 1/2[base 10] is not finite in base 3 for example :
1/2[base 10] = 0.5[base 10] = 0.111...[base 3]


Some numbers are finite in base 3, but not in base 10 :
1/3[base 10] = 0.333...[base 10] = 0.1[base 3]

>>16788604
1/2 and 1/3 are both finite no matter how you write them.
>>16788595
0.999...x ends so it's less than 1.

>>16788621
>1/2 and 1/3 are both finite no matter how you write them.
Ok, so what's a non-finite number for you ?

>>16788637
That's not a thing. Infinity isn't a number.

>>16788155
I accept your concession.

>>16788649
I accept your concussion.

>>16788650
I accept your contrition.

>>16788651
You should go to bed. Brain injury is serious.

>>16788649
>>16788650
>>16788651
I concept your circumcision.

>>16788649 >>16788650 >>16788651 >>16788655
i accept all of your cunts

>>16788687
Your cunt accepts all of me.

>>16786102
a deeper dive into your problem or solution or whatever it is you've decided to shitpost here is that your inference of "a" and "10a" are actually two different "a" values. your original "a" contains (a certain) amount of 9's, and your 10a contains an adjusted (certain) amount of 9's by elevating over the decimal point, but in all reasonable utility, is in-fact one less 9 at the trailing end of your 10a compared to your a.

[math]A: \sum_{n=1}^{\infty} \frac{9}{10^n} = 0.999... \\ B: 10 \times \sum_{n=1}^{\infty} \frac{9}{10^n} = 9.999...[/math]
this construct for "0.999" is only as meaningful as visualizing some bit of partial sums for it, that is to say the "n= (a number)" part of it is necessary. for n=n in both A and B, for any n, B contains one fewer decimal places than A as B has translated one of those above the decimal to construct the whole "9"; therefore, equivalently, 0.9999 and 9.9990 are not meaningfully corroborated, and 9.999 - 0.9999 = 8.9991 =/= (B-A = 9)

little known fact: every single occurrence of the number 1 that exists actually has its own unique identifier at the end of an infinitely long string of 9s

>>16786015
obvious proof with math
https://github.com/Packmanager9/Ditzler_Park_Wei_Invariant/blob/main/Ditzler_Park_Wei_Invariant.pdf

>>16786015
It's not, people just enjoy being wrong the same way psychopaths enjoy lying.

>>16788787
Works too with 0.999...x with "x" whatever the number, a real, Pi, e, etc.

Proof here :
>>16788595

>>16786102
To play devil's advocate here, that looks more like a procedure for converting a repeating decimal to a rational number once one has ALREADY accepted the foundational premises in dispute. Whatever merits the procedure may have, it never has and never will convince the unironic Wild-spergers and ultrafinitists.

>>16786126
Dangerously based and rigor-pilled.

>>16786427
>0.999... is not a rational number.
3/3 = 3*(0.33333....) = 0.999999... = 1.
Your claim is demonstrably false.

>0.999... is not even a correct notation for a decimal number.
You can't write out an infinite amount of the same number or any infinite pattern. The idea is that it represents 9 in each of the decimal digits going on forever, so in essence a geometric sum with a starting value of 0.9 and an additive ratio of 9/10^n.

>0.999... can be defined as either "what you get when you write 0.99(infinitively many nines)9" or as a limit of sequence 0.9, 0.99, 0.999, ... or as a hyperreal represented as a sequence 0.9, 0.99, 0.999.
Those are all the same thing. No mathematician even argues this unless they come up with their own mathematical system where they aren't the same and then derive the consequences of this or see which of the standard number theoretic axioms have been thrown out to achieve this.

>Again, (1 - 0.999...) / (1 - 0.999...) may have different values depending on a definion.
That's dividing by zero in every single case, which tells me you're full of shit since it's common sense that dividing by zero (whether the numerator is finite and no zero, zero or infinite) results in undefinable nonsense.


Can you faggots actually learn mathematics or just get a new fucking hobby that doesn't require critical thinking? This clearly isn't your wheelhouse and saying shit that people conclusively proved 200+ years isn't true just makes you look like a fucking arse at best but more than likely just like a walking retarded mess.

>>16789088
Your grandfather has been fucking your ass again we see.

>>16786015
It's the sort of argument first-year maths students argue about in the library. Next year they'll be arguing about set theory. The year after combinatorics. Finally, they'll compare abstract math to wizardry, insisting it requires faith and is therefore no different than a religion. They're right about the last part.

>>16786015
Lmfao at that first thread. Brainlet wordcels are the best.