/lit/ - Literature

>>17574139
Hume
Shakespeare
No.

shut up retard

>>17574139
Guenon(pbuh) didn't believe in calculus so neither do I

>>17574139
If they were the same thing, they would use the same symbolic representation.

>>17574139
Well 1 is 1.000... which is not 0.999...
N
Poe

>>17574201
So does 1 not equal 2/2? They are exactly the same /lit/ is embarrassingly bad at math.

>>17574139
>>17573618

>>17574201
It is just to make it fit, but that is pretty fucking stupid, if you ask me.

>>17574201
Fucking retard

>>17574139
This is a trick question.
If you subtract 0.999... from 1.0, the answer is not zero, which means it's not equal. However, there are mathematical proofs that 0.999... does equal 1. I'm not educated in math so I can't say any more.

1/infinity > 0

>>17574263
It is 0, but the notation is still retarded.

>>17574139
Guenon
Sanai
no

Ayn Rand
I don't read such stuff.
I don't believe, I know.

>>17574313
>I know
Then prove. Must be easy, right, pretentious faggot?
They are literally - literally - different numbers. It’s so absurdly obvious that I wonder if this is some kind of bait I’m not aware of

>>17574270
>Some proofs that 0.999... = 1 rely on the Archimedean property of the real numbers: that there are no nonzero infinitesimals. Specifically, the difference 1 − 0.999... must be smaller than any positive rational number, so it must be an infinitesimal; but since the reals do not contain nonzero infinitesimals, the difference is therefore zero, and therefore the two values are the same.

I guess the difference is an infinitesimal, but they pilpul the answer to zero by technicality.

>>17574327
I'll bite.
>(0.333...)*3 = 1
>(0.333...)*3 = 0.999...
>1 = 0.999...
WWWWW

>>17574341
Yeah, asking whether 1 - 0.999... = 0 is basically asking whether 1/infinity = 0 (which it does not)

>>17574373
To clarify further
>(1/3) = 0.333...
>(1/3)*3 =1

>>17574373
>1 = 0.999...
How can you not perceive that you’re equaling different numbers? The problem here is that there’s a notation problem that implies in such error. Fucking retards can’t see past this notation error and believe that different numbers are equals somehow.

>>17574398
Do you accept that (1/3) = 0.333...?

>>17574201
share your author of choice please

>>17574139
bill nye
whoever the fuck wrote the spider climbed up a pipe nigger
no

>>17574373
>Take 1 and divide it by 3
>We have 1/3
>Multiply that quantity by 3
>We have 3/3 = 1
>>17574384
>(1/3) = 0.333...
>(1/3)*3 = 1
>Therefore, (0.333...)*3 = 1

>>17574139
If 0.999... = 1

Then 1.00000... = 1.000...1

Then 1.000...1 = 1.000...2

Following this logic, we get to 1.00999... = 1.01, and that 1 = 1.01, and if you keep pushing it, we get to infinitely more absurd equalities, that 1 = 2, 1 = 2.000...1 and so on.

>>17574139
Bolaño, yes

>>17574139
Hume, Edgar Allan Poe, yes

>>17574146
>>17574469
One of these two don’t get Hume. Who is it?

>>17574464
No, because 1.000000... would never round up to 1.0000...1

>>17574139
Montaigne
Shakespeare
No

>>17574421
Kafka.

>>17574139
Holy shit, the amount of mathlets here is staggering. It objectively does. >>17574373 a perfectly adequate proof

>>17574201
>>17574327
>>17574398
Embarrassing posts desu

>>17574139
>Philosophy
Plotinus
>Poetry
Andreas Gryphius
>0.9999...
I don't believe that 0.999... actually exists.
0.9... really is a notational shorthand for lim n->inf sum from 1 to n of 9 * 10^(-n).
Again, a limit, I don't believe, is a metaphysically real entity. But within the calculus of modern mathematics, it is well defined, and 0.9... = 1 is a true proposition.

>>17574464
>1.000...1
How would you even define this? Complete nonsense

The amount of ass-pulling retardation on this board never ceases to amaze me.

t. actual mathematician

>>17574581
>t. actual mathematician
Not an argument

>>17574593
Makes me an authority on the subject. And I've never claimed anything to begin with.

>>17574474
one of this one doesn't get poe or shakespeare. who is it?

>>17574581
>t. actual mathematician
So, what's your perspective on OP's question?

>>17574598
>And I've never claimed anything to begin with.
>>The amount of ass-pulling retardation on this board never ceases to amaze me.
>this statement does not carry within it the claim that there is ass-pulling retardation on this board
And this is why you aren't an authority, because you formula monkeys don't even understand the basics of philosophy, let alone philosophy of mathematics.

0.9999...=x
9.9999...=10x
9.9999...-x=10x-x
9.9999...-0.99999...=9x
9=9x
1=x
I dont read fiction because it's for children

>>17574623
>I dont read fiction because it's for children
Neither philosophy nor poetry are (necessarily) fiction, my boy.

>>17574616
>>this statement does not carry within it the claim that there is ass-pulling retardation on this board
When did I point to any single argument in particular?

Anyway, philosophy is just a temporary cope for the lack of better understanding.

>>17574616
>Mathematician
>Not an authority in mathematics

Let me guess, you're an authority on shit-posting?

>>17574210
>So does 1 not equal 2/2?
Correct. It's simply two twos with a symbol in between until you perform the operation.

You don't think a hospital considers a patient a success until the operation has been performed does it? In the same way, I don't know HOW many twos will fit into one two until I determine so by dividing.

>>17574637
I was just joshing my favorite author is dav pilky

>>17574623
This, which is the same as:

1/3 = 0.333...
0.333... + 0.333... + 0.333... = 0.999...
1/3 + 1/3 + 1/3 = 3/3 = 1
Therefore 1 = 0.999...

>>17574638
You made a claim, namely that there is ass-pulling retardation here, did not provide any argument for it, when called out on it claimed that you in fact never made any claim, and when it was pointed out to you, you still did not understand.
Moreover you still evade substantiating your claim, even in the form of answering the question yourself as >>17574614 demanded.
All while continuing to embarrass yourself.
>Anyway, philosophy is just a temporary cope for the lack of better understanding.
Typical fedora.

>>17574646
What the correct answer within ZFC set theory is, is perfectly clear and uncontroversial. Any discussion that goes beyond that, however, lies out of the scope of the modern mathematician.

>>17574657
>confusing sense and reference

>>17574623
>0.999... = x
>9.999... = 10x
>9.999... = 9.999
>9.999... - 0.999... = 9.999... - 0.999...
>9 = 9

>>17574139
What we cannot speak about we must pass over in silence

faggot

>>17574696
>Typical fedora.
Not an argument.

>>17574638
>holy shit I don't know what to reply
>welp I'll just say some stupid shit about philosophy

>>17574707
Why turn the RHS into the LHS

Einstein is unironically the biggest philosopher the world has ever known.

>>17574733
>>17574739
>>17574139
Fun fact I just changed my major from Business Administration to Philosophy today, did I do good Anons?

>>17574748
Why didnt you change it to math

>>17574739
>can't refute his argument
>>"welp I'll just say some stupid shit about philosophy"

cope.

>>17574696
Please explain to us what the ZFC set theory is.

>>17574733
>Not an argument.
An argument would have been wasted on you, and this I conclude from the basic lack of understanding of philosophy that you have demonstrated since entering this thread.

>>17574768
A set of 9 axioms from which (nearly) all of modern mathematics claims to be deducible.
I am sure you will find an exact statement of the axioms, as well as explanatory material, without too much trouble.

>>17574791
>An argument would have been wasted on you, and this I conclude from the basic lack of understanding of philosophy that you have demonstrated since entering this thread.
I accept your surrender.

>>17574740
>9.999... = 10x
>x = 0.999...
>9.999... = 10(0.999...)
>9.999... = 9.999...

>>17574800
>>An argument would have been wasted on you, and this I conclude from the basic lack of understanding of philosophy that you have demonstrated since entering this thread.
Note how this is (though its strength may be debated) an argument.
>I accept your surrender.
This is still not an argument.

>>17574657
>>17574203
>>17574146
>>17574201
retard

>>17574807
Why eliminate the x from the RHS

>>17574743
/lit/cels can't cope with this.

>>17574139
This is only a problem in languages that have an expression of zero.

>>17574139
It has been quite a long time since I dabbled in mathematics and limits but, as I understand, whether or not the two are equivalent is perspective contingent. For example, 1 is functionally .9999 but, when graphed, the two don't intersect.

All I know, though, is that our mathematic must come up with new notation because .99999 can be conceptually different from 1

Plotinus

>>17574139
>do you believe 0.999... is equal to 1?
Do you believe in facts?

>>17574820
Respond to the first post you linked please.

>>17574696
Let us be clear, there is absolutely NO WAY that 10/12 is the same thing as 5/6, otherwise Copernicus would have simplified it. 10/12ths is a completely different number than 5/6ths, simply by sheer understanding and comprehension.

>>17574593
>Doesn't know the difference between fact, opinion and argument.

>>17574820
1 - 0.9 = 0.1 = 1 x 10^-1
1 - 0.99 = 0.01 = 1 x 10^-2
1 - 0.999 = 0.001 = 1 x 10^-3
...
1 - 0.999... = 1 x 10^-infinity
I do not take 1 x 10^-infinity to be 0. For 1 to equal 0.999..., their difference must be 0.

>>17574201
Based

>>17575064
>I do not take 1 x 10^-infinity to be 0

I recall seeing a set, or was it matrix? that explained how .999 equals 1 and it made sense at the time.

>that tfw when math is infinitely more rigorous, logical, and useful when it comes to understanding reality and human beings than anything in the humanities

You study philosophy and the social "sciences" in order to understand human beings, but subsequently get lost in tangles of unfalsifiable garbage. Meanwhile, STEMchads are harvesting raw data and are using it to shape humans into their ideal form. Decade by decade, STEMchads make progress and man is fashioned into their liking. At the sidelines, the humanities cuck writes impotent criticisms of the damage done and eventually offs themselves. Your time is over. This is the era of the mathematician and our new man is the Bugman.

>>17575064
>What are limits and calculus

ngmi

>>17575099
As someone who reads historical scientific books, I have ample discussions both here and /sci/.

Is nice.

>>17575095
>>17575103
Limits are fake

1/3*3=1
this is fair enough, but if we write 1/3 in decimal form, then we get 0.3333...*3=0.9999....
why should i believe the former equation and discard the latter?

>>17575140
If you don't believe in limits how can you assign any value to 0.999...?

>>17575154
He's one of the few individuals with 1 digit IQ, it's impressive

>>17575140
>Modern engineering is fake

The things you learn on /lit/

>>17574411
No. 1/3 is best represented in our current system by .333... It is not equal to it. Just like how the square root of -1 is not literally equal to the letter i - that's just the best representation of it we can put forth.

>>17575145
There is no decimal form for 1/3. It's an irrational number.

>>17575240
Irrational means can't be written as a fraction or ratio. You just wrote the fraction 1/3.

>>17575240
extremely embarrassing

>>17575240
>>17575250

>>17574139
No I don't. It approaches 1 but isn't 1

Žižek, Ashbery, yes.

>>17575266
In between any two real numbers there is another real number. What is the number between 1 and 0.999...? Try (a+b)/2

>>17575281
What is the number between 1.999... and 2?

>>17575145
You simply need to accept that 0.333... and 0.999... are artifacts of the decimal system. They can only be truly represented using fractions.
Those numbers are finite, but their decimal representation is not.

>>17575314
There is no number between 1.999... and 2 because 1.999...=2 in the same way 0.999...=1.

>>17575315
What's stopping someone from claiming only the decimal system is a true representation instead of the fraction one? Also, how can a finite representation (1/3) be equal to infinite representation (0.333...)?

>>17575154
ok so "limits are fake" may have been a bit hyperbolic. but 1/infinity is not equal to 0 in the surreal numbers. it's defined as epsilon. but since the surreal numbers contain the reals 0.999... is still 1. I just want 0.999... and 1 to be different bros

>>17575328
Is 1.899... equal to 1.9?

>>17575337
If 0.999...=1 wasn't true calculus would be fucked. The Riemann integral is defined as an infinite series just like 0.999.... And yes 0.999...=1 in the hyperreals and surreals

>>17574139
If .99999 = 1 then there would be no multiverse.

>>17575341
You're catching on now. Any finite decimal expansion can be written in a second way with repeating 9s

>>17575334
You're confusing the "decimal system" with "decimal representation" of a number.

It's impossible to write an infinity on a paper/machine. 1/3 is something that you can work with. Writing 0.3333 is simply a rough approximation. Writting 0.333 or 0.999 doesn't mean anything because there's always another 3 or 9 missing afterwards.

Think of the number that represents PI. you can deduct with with an incredible amount of precision, but you cannot write it in a decimal representation accurately to the same degree of precision.

>>17575337
hmm, actually I think surreal numbers solve my problem. In my head, I was defining 0.999... as 1 - epsilon, and I had the intuition that 1 - epsilon is not equal to 1, but that's not what 0.999... is. 0.999... is a real number, not a surreal one. So I've changed my answer.
>>17574203
N
Poe
Yes

I assume they are the same because most mathematicians say they are equal and they have spent 30+ thinking about just math and I havent. Any attempt I make to disprove this would be silly and contrarian and fruitless since every possible thing that I could have come up with sitting at my computer before I am distracted by another thread has already been thought up and debated by more qualified people. Anyone on this board who seriously, or unseriously, thinks that they have the key to why 0.999... isnt equal to 1 is an idiot that should not be listened to. Nobody can just undo an entire field of study in 30 minutes of thought.

>>17575441
Oh no no no no, Anti-vax climate denier trumpets, We GOT TOO COCKY

>>17575441
that's pretty gay

>>17574139
Evola
Yes they are practically and mathematically speaking indistinguishable
>>17574201
based folk wisdom

0.333...+.0.333...+.0333... IS NOT 0.999999999, IT'S 1. Get this into your fucking heads.

0.999999999 is only what your calculator displays because it cannot deal with infinite representations of finite numbers.

>>17575482
but anon, .999... = 1

Philosopher: Augustine
Poet: Shakespeare
Answer: Yes. 0.999 (repeating) = 1 by convention of repeating decimal.

I clearly said:
>0.999999999
and not:
.999...

>>17574139
Hume
hehe nope
Yes, I didnt when i was a child until i saw a proof. 1/3=0,3333 then 1=3/3=0,99999

>>17574210
If we're speaking logically, no.
They have mathematical equivalence, but the idea of 2/2 vs the idea of 1 is completely different.
Saying 2 out of 2 people agree with something and decide to do something carries different implications to a single person agreeing to do something.

>>17574139
Uhh why not just add +.1 to it?
>tfw I was a mathematical genius this entire time.

>>17575554
That's 1.1

>>17574139
Bertrand Russell, Pushkin.
I am a mathematics major -- and unequivocally, yes. Numbers do not have unique decimal notations.

>”.9999999 will never be 1 for the same reason that the hare in Zeno’s paradox of the tortoise and the hare will never beat the tortoise in the race, the indefinite will never be equal to the infinite”

>>17574139
Aquinas
Vergil
Yes

its literally not the same. LITERALLY.

lol I love these threads

>>17574569
1 is just as close to 1.000...1 as it is to 0.999...

>>17574313
>>17574373
>i freakin LOVE science!

>>17574373
>1/3 = 0.333...
Prove that the infinite series is all 3's.

>>17575554
incorrect

>Poet
Sylvia Plath

>Philosopher
Camus

>0.99=1
Close but nah

>>17574373
This is why we need a duodecimal system combined with a decimal one. Just convert whenever this garbage pops up and it suddenly turns into real quantifiable values. Proceed to do your calculation and then convert back any moment you can get a real decimal number.

>>17574545
>>17574696
smart
>>17574313
>>17574373
>>17574438
>>17574499
>>17574525
>>17574581
>>17574623
>>17574638
>>17574733
110iq söy redditors subscribed to numberphile on youtube

>>17574139
Aquinas
Dosto
No

>>17577453
Proof is on wikipedo retard. We learn that in Calc II

>>17577570
>reddit basedcuck referencing jewpedia
Sasuga.

>>17577578
>>17577453
Cringe

>>17574139
For all intents and purposes .999 is one

omg /lit/ can't do math. It's basic knowledge that 1 = 0.999....

STEM FAGS UNITE

>x = 0.99999999....
>10*x = 9.9999999999...
>10*x - x = 9*x = 9
>x = 9/9 = 1

Favourite author: Herman Melville
Favourite philosopher: Friedrich Nietzsche
Favourite poet: Friedrich Hölderlin

>>17577878
Holy fucking based

>>17577878
>9*x = 9
Brainlet

>>17577878
What an absolute brainlet.

>>17574201
>1/2 is not the same as 2/4
>if it were it'd have the same symbolic representation

>>17574657
>until you perform the operation
math is not temporal. the reason you can perform the operation at all is /because/ they are equal. If they weren't equal, you couldn't perform the operation.

3/3 = 1
1/3 * 3 = 3/3 = 1
0.333... * 3 = 1
0.999... =1
Its just a limit of our decimal system. If we were to use say base 3 this problem wouldn't even arise.

I really don't get it. If "0.999..." is supposed to represent that the sequence of 9s never ends how could that ever add up to 1?

>>17578079
:interesting:

>>17574623
>>17574681
The only two intelligent people on this thread.

>>17577973
>>17578041
>>17578101
You're so fucking retarded, oh my god

It is
>Author
Gogol
>Philosopher
Cicero
>Poet
Faruddin "the friends we made along the way" Attar

>>17578157
No, you are.
>9*x = 9
LMAO
Embarrassing

>>17578157
Your demonstration is fallacious. Which makes your conclusion worthless by default.

>>17578178
>>17578198
https://www.youtube.com/watch?v=G_gUE74YVos

you know nothing about mathematics. Enjoy your humanities studies, stupid pieces of shit

>>17578218
>still doesn’t understand what he did wrong
ngmi

>>17578218
9*x = 9 is wrong. I'm not arguing 1 doesn't equal 0.999..., just that your "proof" is rubbish.

>>17578218
Embarrassing

>>17578229
>>17578230
kys

>>17577973
>>17578041
>>17578178
>>17578198
>>17578229
>>17578230
9.9999...
-0.9999...
--------------
9.0000...

It's not that hard retarded faggots

>>17578218
>you know nothing about mathematics.
Neither do you, it seems.

>>17578258
I accept your defeat.

>>17578267
What is wrong about saying that 10*x - x = 9*x = 9 ?
What is wrong about concluding that x = 9/9?

You're just calling me a pseud for no reason

>>17578267
>>17578277
>t. mathlet

Schopenhauer
Heine
I don't know :)

Carl F. v. Weizsäcker
i dont read poetry
i dont believe it, i am aware that it is true

holy shit this board is full of genuine retards, but ill have to assume most of you are just baiting

The fact that we've had this thread mulitple times and people still refuse to acknowledge the answer proves this board is full of either schizos or arrogant retards

>>17578371
This is what I argued in my original post >>17577878
but these brainlets told me that I knew nothing about mathematics

>>17578399
>he still doesn’t see it

>>17578371
If you’re multiplying .999... by 10, wouldn’t it become .999....0? There’s no way in our system to properly write that, but isn’t that more a failing of our system and our understanding of infinity? There are different infinities after all.

>>17578399
Your argument is wrong and different from >>17578371. Let’s see if that air-scattered brain of yours can figure out why.

>>17578415
Why is it wrong, again?

>>17578371
This has already been posted by >>17574623

>>17578429
No because .999... represents an infinite summation series, there's no magical "end" with a 0

>>17578449
Exactly. 0.333... is simply an artefact of the decimal system. It’s representation in that form is worthless and fallacious. 1/3 is the correct form.

>>17577410
It's pretty easy just do it with induction.

>>17578449
But compare that to the universe. The universe is said to be infinitely expanding but slowing and will stop expanding after an infinite amount of time. Doesn’t that mean infinities still have an end? For example, in .9999... we know that the final digit will be 9, so it has a theoretical, definite, infinite end point. We can define it because it will be 9 even if it doesn’t exist.

>>17578430
it's the same.

saying that 10*x = 9 + x =9.999999...
or saying that 10*x - x = 9x = 9

is the same. You clearly don't understand it. I hope you apologize after this

>>17574147
the thread should have ended here

>>17578506
>The universe is said to be infinitely expanding but slowing and will stop expanding after an infinite amount of time.
I don't know what this means but I assume you just have a bad understanding of cosmology
>For example, in .9999... we know that the final digit will be 9, so it has a theoretical, definite, infinite end point.
No we don't because there is no end point. There cannot be a real or "theoretical" last addition in an infinite summation or it's not infinite

>>17578537
>I don't know what this means but I assume you just have a bad understanding of cosmology
Okay let’s just ignore that and say I’m wrong so we don’t start a new discussion.

Just because something doesn’t exist doesn’t mean we can’t define it. The imaginary number i for instance. There is no square root of -1. That is simply not possible with our number system. But we still know what it is and we can use it. In the same way, even though there is no end point to .333..., we know what it is. It would have to be 3 or the series would be written incorrectly.

That’s the thing that’s not really clicking for me. Yes, I know it doesn’t make sense to say “there is no end but we still know what it is if there was,” but I don’t see anything logically wrong to all that. The fact that they do not have an end point is still an endpoint of a sort, isn’t it?

>>17578429
>There are different infinities
There are 'layers' to infinity in such that some cannot be matched with others but It really doesn't relate here.

>>17578616
Let us define .3333333... As a full representation of 1/3.
A full representation should retain this: 1/3 * 3 = 1.
Assume there is an 'end point' to .333... , In other words, that there is a finite number of digits.
Multiply by 3.
You get .9999 with finite amount of digits, which is not 1.
___
>There is no end but we would still know what that end 'would' be.
No. There is no end. We do not know what the end would be, because there is no end. What we do know that any digit we take no matter how 'far' will still be a 3.

>>17578679
0.333... is an imperfect representation, it's supposed to imply an infinite number of digits, just because you round it to 0.333 is your problem. Also, when written in a decimal form there is no problem, 1/3*3=1

/sci/ here. I used to believe that 0.999...=1 and argue with people about it. But now I realize it's (mostly) bullshit.
The confusion arises from the following divergence of thought. Regular people view 0.99... view as a process, of adding more and more 9s, while contemporary mathematicians view it as a completed whole, a completed infinite. It's not a shifting object, it's a constant, with a single value.
Now assuming it's a constant, it's not hard to see
0.999.. = 9 * (0.999...)/9 = (10*0.999... - 0.999...)/9 = (9.999... - 0.999....)/9 =9/9=1.
Seems reasonable enough. What's wrong with it?
The problem with it is that you cannot actually complete an infinite process, you can only pretend you do. So if you have digits d_1, d_2, d_3, the expression 0.d_1d_2d_3... doesn't make sense as a constant, since it's an ever evolving thing. The best you can get is better and better approximations.
But you might say: surely mathematicians have actually defined what they mean by such infinite expressions.
As a mathematician, I can assure you, they haven't! Their definitions don't involve constructing an actual object to which the infinite process converges, all they do is to ASSERT that it converges to something and ASSUME it all makes sense. This is an absolutely ridiculous position from a logical point of view.
The constructions of the reals, whether by Cauchy sequences or Dedekind cuts, are an absolute joke and any critically thinking person who choses to investigate the definitions will quickly see this for himself.
stead or explicitly specify that this is what he's doing, since it's not a common practice in mathematics.

>>17578774
The assumption that mathematicians make that you can complete infinite process and thus justify expressions like 0.999... denoting a completed number is ILLOGICAL and NONMATHEMATICAL.
The only logically coherent way to understand 0.999... in a way that is consistent with understanding similar decimal expansions like 0.1234567891011121314.... which are not rational number is to view them as an ever evolving sequence of approximations and not a single completed number. With this view, it's clear that at every point 0.999..9<1 no matter how many nines you have there, thus 0.99...<1.
You may still ask: what's wrong with just assuming you can complete such an infinite process and get back something reasonable? After all, we haven't found a contradiction yet while doing it.
This is about the issue of consistency. Is it enough for a mathematical theory to be consistent for it to be reasonable? Of course not. For example, if the basic axioms of arithmetic (called PA) are consistent, then so is PA plus another axiom which asserts that PA is inconsistent. This is Godel's second incompleteness theorem. Everyone intuitively sees that believing that PA is consistent and also believing the arithmetic statement not Con(PA) is bullshit, even though the result is consistent. Thus consistency is not enough, there needs to be justification for it (and also a much stronger form of consistency, called omega-consistency, which is closely related to the Godel's result just mentioned, but I won't go into that). What sort of justification have mathematicians provided for viewing expressions like 0.999... as completed infinite processes? Absolutely none! In fact, we don't even know our system is consistent. It could be that it's inconsistent but proving the inconsistency is a very hard theorem, similar to proving Fermat's last theorem.
....

>>17578787
There has been no convincing argument that the current axiomatic system of mathematics is consistent. To the contrary, the results of Godel suggest that it's not. Because if we know it was consistent, then we could prove it, but we can't. We expect mathematical facts that are true to be provable. Consistency is not. In fact, one of the best mathematicians of the last few decades, recently passed away, Vladimir Voyevodsky strongly believed that our current mathematics is inconsistent for the reasons outlined above, and he was looking for other, actually logically coherent systems to justify mathematics.

In conclusion, 0.999... is always smaller than 1 and never gets to one. Anyone asserting otherwise is either:
- Using completely unjustified assumption that you can complete infinite processes, thus is wrong.
- Only allows periodic infinite decimals, where he defines 0.(d_1...d_n) to be d_1...d_n / 99...9 (with n 9s). Then he should write the rational number 1/1 in

Here's a fun thought experiment: if we think all completed infinite processes make sense, then suppose
x= 1+ 2+ 4+ ....
2x = 2 + 4 + 8 + ...
x- 2x = 1 + (2-2) + (4-4) + ... = 1
-x= 1
x=-1
Take that, math!

>>17578774
>The problem with it is that you cannot actually complete an infinite process, you can only pretend you do
well duh, mathematics is a system constructed that is useful for approximating real things. its all pretending, but its useful. and within this construction it is perfectly consistent to say that 0.99999...=1. it doesnt matter if "ohh you cant ACTUALLY continue this process infinitely" but it doesnt matter.

>>17574139
>do you believe 0.999... is equal to 1
I believe in "theory" it does.

However I don't believe in reality it does, because I don't believe in infinity exists in reality too.

>>17578520
>He still doesn’t get it, even after being spoon fed.

At this point I might as well sit back and enjoy the show. Multiple people already pointed out to what you did wrong. You’re still missing the point entirely. Even your posts show a delicious level of uncertainty and denial. How many times did you go through the previous posts of people dismissing your argument? I can already sense your heartbeat’s speed increasing by the time you realise how idiotic you’ve been.

The funny thing is that you will be thinking about this thread long after it’s gone.
You’re quite literally the epitome of the “not gonna make it” meme. An apology is in order, to your parents.

>>17578916
>mathematics is a system constructed that is useful for approximating real things
There's nothing wrong with approximations. Approximations can be done rigorously. The problem is when you pretend to somehow complete the approximation process to get a single value, without actually specifying how you do it. That's antithetical to what mathematics is. Mathematics is supposed to be about careful analytical reasoning to arrive at results, not wishful thinking.
>its all pretending, but its useful
Something could be useful while its justification is bullshit. Look up umbral calculus or italian algebraic geometry.
I could "prove" an useful result by pretending I can divide by 0, that doesn't make it valid mathematically just because I arrived at a good result.
>perfectly consistent to say that 0.99999...=1
No, because writing 0.99999... implies you can complete an infinite process and you can't actually do it, just like you can't divide by 0. It's undefined.
What you're saying is as retarded as saying
>it doesn't matter if "ohh you can't ACTUALLY divide by 0", still the result is correct so it's perfectly consistent
Division by 0 is undefined, nor is the completion of the kind of infinite processes involved in 0.999.... So the claim 0.999...=1 is bullshit. Deal with it.

>>17578796
It's interesting to think that all scientists love anime waifus just as much as this guy.
Would Newton or Einstein have made their great discoveries if they had access to dakimakuras?

>>17579003
Not that guy, but what are the implications of 0.999 not equaling 1? The opposite is the consensus in math circles. Do any of the branches change if you accept the claim that 0.999...=/=1?

>>17579034
I already talked about that above. Not accepting the convergence of an infinite series fucks calculus. Calculus and differential equations are the basis of engineering.

>>17579034
There are implications of finitism, but of this particular claim not so much. It boils down to 0.999.. and 1 not being of the same type, so declaring them equal doesn't make sense, just like saying 2=animal is nonsense.

>>17579059
So this is more about something being practical rather than being true? Since engineering certainly has its uses.
Also, can you elaborate on
>x- 2x = 1 + (2-2) + (4-4) + ... = 1
if x is 1+2... and 2x is 2+4... shouldn't x-2x be (1-2) + (2-4)...?

>>17574139
Kierkegaard
Baudelaire
Yes

>>17578616
>Just because something doesn’t exist doesn’t mean we can’t define it. The imaginary number i for instance. There is no square root of -1. That is simply not possible with our number system. But we still know what it is and we can use it. In the same way, even though there is no end point to .333..., we know what it is. It would have to be 3 or the series would be written incorrectly.
i exists in the set of complex numbers...

>>17579003
division by 0 is undefined, but 0.999... is defined as 1.
by your logic any and all converging infinite series are "undefined" because muh its all just pretending (like all of the rest of math)

>>17574201
Would they though? You could say that they refer to the same practical term -- which is one -- but are denoted different for a specific reason. For example, to keep complexity in theory or to create a sort of infinity.

>>17579086
No it's very true and logically rigorous. The sequence x doesn't converge to anything so those operations aren't defined on it.

>>17574210
Philosophers should be hanged.

>>17579118
It actually does converge to -1 in 2-adic topology.

>>17577419
Well then what is true? It's nothing and all subjective. And 'truths' are mere guesswork and estimations for our feeble species

>>17578999
>he still has no life and tries to make fun of people, although they are right

>>17574139
Homer, Pindar, pre-Socratics.
You are simply another Athenian here to impose your institution.
Persia will rise again.

>>17578429
>>17578506
>>17578616
>>17578774
>>17578787
>>17578796
>>17579071
>I don't unterstand the meaning of infinitely repeating so you're wrong

>>17574646
>Mathematician
>Not an authority in mathematics
Yes? You are a mathematician if you are paid for it by someone, but I'm not that someone, so I don't have to listen to you.

>>17579990
>I don't have to listen to you.
I’m sorry to inform you, but the voices you’re hearing aren’t me. Take your meds.

>>17574681
>>17574623
2*a^n+2*b^n=2*c^n does not have any solutions for natural a,b,n and n>2
Therefore a^n+b^n=c^n does not have any solutions for natural a,b,n and n>2
Fermat's theorem is proven in two lines!

>>17580003
Ah, so you were just shitposting?

>>17574139
Guenon(pbuh)
Ezra Pound(pbuh)
no, you think im some kind of race traitor or something??

0.999...≈1.000...

>>17580057
Ok, so what’s the number between those two?

>>17578230
This desu.

>>17580076
What is the natural number between 1 and 2?

>>17580287
There is no natural number between 1 and 2 but there is a real number for example 1.5 Between any two different real numbers there is another different real number

>>17580287
based non sequitur retard

>>17579003
Just because you don't understand limits doesn't mean they don't make sense

>>17580445
Just because you think you understand limits, it doesn't mean you actually do.

>>17580491
Sure but I actually do :)

>>17580348
So when we are limited to naturals, 1 and 2 are the same.

>>17580506
Prove it.

>>17580513
You don't even need limits to prove it, it follows from the archimedean property

>>17580351
It's a good answer to >>17580076

>>17580512
No because in the naturals two numbers can be different and not have a natural number between them. That's not the case in the reals

>>17580520
I accept your defeat.

>>17580520
>archimedean property
Doesn't work for infinitesimals.

>>17580523
>That's not the case in the reals
That seems to be the case for 0.(9) and 1.(0) (unless, of course, there is a number between them, in which case it is the answer).

>I'm gonna disprove everyone using natural numbers as an argument.

>>17580528
I just proved you wrong but okay

>>17580530
What

>>17580544
0.(9)=1 so they're not different numbers. In the reals for numbers a and b (a+b)/2 will always be between a and b

>>17580553
>I just proved you wrong but okay
Incorrect, based on the fundamentals of the Archimedean properties. Sorry, but your fallacious arguments have been deconstructed.

>>17580569
You don't even know what the archimedean property is, do you?

Engineer: these machine parts are the same
Skeptic: but they are 9.99999 mm and 10 mm
Engineer: they may be, but assuming that they are the same simplifies my work
Skeptic: OK

Mathematician: these numbers are the same
Skeptic: but they are 9.999... and 10.000...
Mathematician: they may be, but assuming that they are the same simplifies my work
Skeptic: OK

Engineer: these machine parts are the same
Skeptic: but they are 9.99999 mm and 10 mm
Engineer: HOW DARE YOU THEY ARE METAPHYSICALLY PLATONICALLY THE SAME YOU ENGINEERING HATER
Skeptic: Are you OK?

Mathematician: these numbers are the same
Skeptic: but they are 9.999... and 10.000...
Mathematician: HOW DARE YOU THEY ARE METAPHYSICALLY PLATONICALLY THE SAME YOU MATH HATER
Skeptic: Are you OK?

>>17580521
no it isn't you fucking idiot

>>17580559
0.(9) ≠ 1 so they're different numbers.
>In the reals for numbers a and b (a+b)/2 will always be between a and b
So either there is a number between them, or that claim is false.

>>17578076
>If they weren't equal, you couldn't perform the operation.
I could give multiple examples of equations not being equal before the operation is performed.

>>17580605
Metaphysics is made up.

>>17580613
Yes it is you hack.

>>17580605
You're the one with the simplification by using the ellipse to denote an irrational

>>17580625
go ahead

>>17580617
Or the fact that there is no number between 0.(9) and 1 means they are equal

>>17580646
No, just like no number between 1 and 2 does not mean that they are equal.

>>17580642
Two divided by a throk.

You don't know what a throk is, so you can't say it's equal to any known extant number.

Quod.

Erat.

Demonstratum.

>>17580651
I already explained that >>17580523

>>17580605
An engineer would never say that 9.9999900mm and 10.00mm are the same.

You argument is invalid.

>>17574139
Aristotle. Practically speaking, they're equal. Mathematically speaking, they're not.

>>17580637
Do you know what irrational means? 0.(9) is not an irrational.

>>17580665
It's >>17580005-tier argumentation.

>>17580653
umm

>>17580673
Shows you how worthless Aristotle is for logical thinking. They're exactly equal

>>17580689
Approximately.

>>17580676
Fuk I'm retarded

>>17580687
You fucking dumbass. Learn what a throk is, or you can't do my math.

>>17580665
Either there is a number between 0.(9) and 1.(0), or they are the example where such a rule fails.

>>17580709

Or >>17580646. You can't even list all the possibilities

>>17580701
Grok your throk.

>>17580701
you can throk on my cock

>0.999...≈1.000...
>What is the natural number between 1 and 2?
>So when we are limited to naturals, 1 and 2 are the same.
>0.(9) ≠ 1 so they're different numbers.

>>17580718
Everything is possible! Then 0.(9) is equal and not equal to 1 and 1 is equal and not equal to 2.

>>17580721
Very good :) You've learned what a throk is and what a grok is.

Now then, could you POSSIBLY KNOW what a throk divided by a grok is until you perform the operation?

And how (to use the patient/doctor metaphor earlier) do you know the operation will BE SUCCESSFUL?

>>17580743
And im a girl!

>>17574139
>>17580737
>0.1111 is 1/9
>0.2222 is 2/9
>0.3333 is 3/9
>0.4444 is 4/9
>0.5555 is 5/9
>0.6666 is 6/9
>0.7777 is 7/9
>0.8888 is 8/9
>0.9999 is ?

>>17577386
No it isn't. You don't seem to understand notation. You can't have an infinite set of numbers and then something after it. 1.000...1 isn't even a coherent statement

>>17580767
All of those are correct except 5/9

>>17577386
Where exactly is that 1 on the 1.0000...1?

>>17580783
why

>>17580696
No, literally

>>17580785
You just placed it in the right spot.

>>17578101

>>17580794
Because it would round to exactly 1/2. Mathematicians round 5/9 to .5 all the time.

>>17580804
Infinity is not a spot. Your argument is therefore invalid.

>>17580816

>>17574139
This thread has really demonstrated /lit/'s absolute brainlet status. Holy shit, I did not think you guys could be this stupid, and what's more, to revel in your ignorance and lash out at the light. Subhumans, the lot of you

>>17580829
Not an argument.

>>17580825
>Infinity is not a spot
See >>17580826

>>17580829
Really invalidates any philosophy threads on here when /lit/ can't even handle basic math. They've got the logic of elementary students

>>17580767
Again, you don't know that 9/9 equals 1 until you perform the operation.

>>17580842
I accept your surrender.

>>17580767
>0.1111 is 1/9
Spoken like a true engineer.

>>17580825
Then ... is meaningless.

>>17580876
No shit Scherlock.

>>17580876
It's a short hand, not a rigorously defined algebraic symbol

>>17580829
>muh mathematical religion

How to study philosophy along with pure math and physics?

>>17580860
x/x is will always be 1 (except for x=0 maybe). You know the result before doing the operation.

>>17580923

Behold the greatest philosopher of all time.

>>17580928
>x/x is will always be 1
>(except for x=0 maybe).
Immediate self-refutation.

>>17580928
>x/x is will always be 1
https://www.youtube.com/watch?v=U1UtRnGn5hc
Oh no no no no no no

>>17578692
That's what the three dots are for.
.33... It means to repeat the pattern. You also see it with a line above the pattern digits.

>>17580767
Based, you BTFO the pseuds

>>17580869
the digits repeat, you knew what I meant
>>17580860
there is no operation. you don't understand mathematics

>>17580941
Those aren't seperate statements. It's 1 unless x=0 because division by zero is undefined.
How exactly does that refute the x != 0 part?

>>17579003
Please define what is "1" and how it is logically different than a limit condensing on 1.

>>17580966
>to repeat the pattern
For how long?

>>17581019
>Please define what is "1"
That requires like a whole book.

>>17574139
>ITT: insecure /lit/tards hold on to their delusions instead of being open to learning
Guys, it's okay. Just accept that you don't really understand math instead of trying to insert your sophistry where it doesn't belong. It takes a bigger man to expand his understanding than to dig your heels into the ground of your ignorance

>>17580669
Yes he would, if they're the same within his error margins.

>>17581039
>math dogmas said something
>therefore it must be a golden eternal truth
You should enter some religion then.

>>17581045
At least we now know that you never went to a numerical analysis class. Your opinion is worthless, since you're not an engineer.

>>17581036
Rec a book then

>>17581020
Till you get the room next to Cantor

>>17581064
Yeah yeah blah blah it holds a bit more information...

>>17581072
Bourbaki:
https://mathoverflow.net/questions/357498/bourbakis-definition-of-the-number-1

>>17580997
>mathematics
a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.

>>17581064
Do engineers really?

>>17581133
Not an argument.

>>17581111
That's arithmetic

Seneca
Blake
There is no 0.999. It’s one or nothing. Something can be reduced into thirds, but that doesn’t mean it has to be represented as one.
I get the point in technicality, I feel sorry for people that feel compelled to uphold it, though.

>>17581215
There is no spoon

>>17581144
That's from the definition of 'operation'.

>>17581215
0.999... exists, it's just 1. It's a notational quirk. The two are the equivalent of synonyms

>>17581311
but there is always a little bit missing no matter how many 9s you add

>>17581311
Yeah you're not a cuck my dick is just in your gf's psuy

>>17581311
See
>>17581338

>>17581327
Not if you can get arbitrarily close to 1

>>17581355
>arbitrarily close
what do these sneaky meme words even mean? You are always just adding another 9, it's always a bit off. I refuse your black magic

>>17581362
That's what "..." implies and it's explained with rigor through limits

>>17581379
if it means something other than adding more 9s it should be written differently

>>17581384
It is, but this is just a shorthand

>>17581379
>explained with rigor through limits
Do they use "for any" stuff? It is as rigorous as ..., ∞ and so on.

>>17581311
>0.999... exists, it's just 1.
Almost 1.

>>17581445
No, that would be 0.99990

>>17579003
Most people are willing to accept that 0.333... is not just an approximation of 1/3 though. And they're willing to accept that you don't have to approximate to know that 1/10 = 0.1000... because an infinite sequence of zeros seems fine to them.

0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990 is not 1.

>>17581445
If it exists, why can't you write it down?

>>17581479
based.

>>17581512
Can you write down a "4chan" you nigger

>>17578774
>t. Wildberger

NUMBERS WERE NEVER MEANT TO BE NAMED. INVOKE DIONYSUS AND REVOLT AGAINST THE TYRANNY OF APOLLONIAN ABSTRACTION. DANCE FOREVER.

>>17578796
>x= 1+ 2+ 4+ ....
Define what this means. The summation doesn't converge.

>>17581621
I accept your surrender.

>>17581903
Not all concepts are writtable nigerrrrrrrrr

>>17574139
if 0.9999...=1 then 99=100

>>17582444
wrong, but 99.999...=100