/sci/ - Science & Math

1/3 = 0.3333333333...
2/3 = 0.6666666666...
3/3 = 0.9999999999...
3/3 = 1

0.9999999999...=1

>>11866224
>pretend it's an accepted fact
It is, retard. You can't find 1 published mathematician who disagrees.

>>11866236
All of those numbers are imaginary. Imaginary numbers cannot equal real numbers.

>>11866237
Appeal to auhority, but I agree.

[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0. \bar{3} = 0. \bar{9}
[/math]

>>11866240
>source: my ass

>>11866237
Published mathematicians are retards.

>>11866245
source: basic logic

>>11866237
>Imaginary numbers cannot equal real numbers.
Theb explain to me the result of, let's say, 3/2. I'll wait.

>>11866247
4chan shitposters are retard's diarrhea

>>11866240
>Imaginary numbers cannot equal real numbers.
Then explain to me the result of, let's say, 3/2. I'll wait.

>>11866249
...and I'm sitting on it

>>11866254
1.5 dumbass

>>11866259
Shit, I meant to say 2/3.

>>11866259
Then explain to me the result of, let's say, 2.9.../1.9.... I'll wait.

>>11866264
Tu quoque.

>>11866236
You can't do math with infinite numbers

>>11866264
Undefined, because long division can only be done with finite numbers

>>11866363
nah it's 1.5
read a book

>>11866360
0.3... isn't any more infinite than 1.000... is

>>11866379
holy shit you're dumb

>>11866382
idiot

>>11866379
>>11866382
Have you never been to school? If you want to divide or multiply decimal numbers you have to start with their last digit. Can't do that when there are infinitely many digits. Like give me a general formula for the nth digit of pi*e? You can't.

>>11866379
No, it's not. You can't do math with infinite numbers.

>>11866383
>>11866389
cool math arguments, boi

>>11866398
You can't do math with infinite numbers, boi

>>11866391
so you can't divide or multiply with 1.000...
ok,
lol

>>11866403
>>11866382
slow learner, eh?

>>11866396
Those are very finite numbers.

>>11866407
>1.000...
this is the dumbest shit I've ever read. that's not a thing.

>>11866224
da juice

>>11866407
0.000... makes just as much sense as 0000....

You have to resort to nonsense to argue your point

>>11866391
>general formula for the nth digit of pi
https://mathworld.wolfram.com/PiDigits.html

>>11866407
>1.000...
really anon?

>>11866412
topkek

>>11866421
I asked for pi*e. Please learn to read.

>>11866421
>0.999...fag reading comprehension

>>11866417
neither are infinite

>>11866407
That's just 1 because 0 isn't a number. In fact 0 is the absence of any number.

>>11866432
the ... literally implies it's infinite dumbass

>>11866424
Impressive, did you quote that from your PhD?

>>11866438
Yep, I got my PhD in 2017. Cope.

>>11866429
>multiplying with a constant is impossible

>>11866444
You literally proved his point.

>>11866437
both are zero
>confusing zero with inf
lol

>>11866450
Zero is not a number. It's the absence of a number.

>>11866442
lol some wipeass "school" you came from

>>11866455
Not an argument.

>>11866453
found the virgin

>>11866444
Numbers like pi aren't constant. They are dynamic numbers since whenever you think you reached their end, new digits are discovered. Our knowledge of pi is growing every year. In 2020 we know more about pi than ever before. Pi in 1900 was not the same pi as today.

>>11866449
your "proofs" are laughable as ever

>>11866460
not a PhD

>>11866472
Where's your PhD?

>>11866462
>Numbers like pi aren't constant.
my sides

>>11866477
Okay, tell me the last digit of pi.

>>11866475
Hidden inside yours

>>11866484
Really? I just looked at mine and I didn't see any sign of yours. Sorry anon.

>>11866482
no such thing.
tell us the difference between cardinals and ordinals

>>11866486
>looked at mine
sure you did

>>11866498
Yeah, I did.

>>11866490
I obviously know the difference. What's the point of these off-topic questions? This has nothing to do with 0.999... not equaling 1.

>>11866506
>off-topic
found the retard

>>11866519
Read what I said again.

What's the distance between [math]\frac{1}{3}[/math] and [math]\frac{0.\overline{9}}{3}[/math]?
If they're separate numbers then the distance between them must be non-zero

>>11866552
You can't do math with infinite numbers.

>>11866559
Both of them are bounded by 0 below and by 1 above. They're in no way infinite.

>>11866242
appeals to authority are not always fallacious

>>11866593
{{}} = {} is by far the most common rhetorical fallacy on /sci/

>>11866631
Why are you using the vagina emoji?

>>11866631

i seriously hope that 0,999...=/=1 fags are just trolling, you cant be that retarded right?

refute this, but make sure to take your meds first

>>11866790
Has already been refuted in this ITT. Please read the proofs first, before you repost disproved claims.

>>11866237
https://arxiv.org/pdf/1007.3018.pdf

>>11866795
people have tried sure. if theres something of value i missed please remind me

>>11866795
>Has already been refuted
nope, not even close

>>11866814
>arxiv.org
>"Materials on this site are not peer-reviewed by arXiv"
kek

>>11866224
>Why is the current tactic for 0.999...=1 fags to spread their garbage to call everyone who disagrees a retard and just pretend it's an accepted fact?
>an accepted fact
>fact
numbers are not real, you can't have facts about things that are not real lmao, it's meaningless

>>11867082
are dollars real?

It's pretty easy.
0.999...=1 by definition, if you're simping the 𝛿,ε-thots.
If you don't want to be a simp, you can always start your own conversation.
None of that changes the fact that 0.999... is defined as 1.

>>11867076
I gave you the free pdf link so you didn't have to sci-hub it, faggot.

>>11866814
The authors say the proofs for 0.999... = 1 are correct on the first page. You'll have to try harder than that.

>>11867096
they are numbers on a screen, so no, but paper dollars and coins are real

Refute these proofs

Via Cauchy sequences:

0.999... = (0.9, 0.99, 0.999,...) = lim as n-> inf of 1-1/10^n = 1

Via Dedekind cuts:

Assume to contradiction that x is a rational number such that

0.999... < x < 1

0.999... is greater than any finite string of 9s so for any natural number n

1-1/10^n < 0.999... < x < 1

1-x < 1/10^n

10^n < 1/(1-x)

n < log(1/(1-x))

Let n = ceiling(log(1/(1-x)))+1

ceiling(log(1/(1-x)))+1 < log(1/(1-x))

This is a contradiction, so x does not exist and 0.999... = 1.

>>11867110
Did I say they weren't? I replied to a post with a disproof of the post. Now dance some more for me, retard.

>>11867115
Begs the Archimedean property. It's true because of the axioms you chose.

>>11867115
>Cauchy sequences
not real
>Dedekind cuts
not real

[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>>11867130
but if the subtraction is infinite, would you ever finish subtracting? would there always be more terms as much as you subtract?

>>11866224
>0.999...=1 fags
oh boy this site can turn anything into tribalist garbage

>>11867143
you can just supertask it.

>>11866391
>>11866429
Multiplying from left to right is very easy.

>>11867152
>In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time.[1] Supertasks are called "hypertasks" when the number of operations becomes uncountably infinite. A hypertask that includes one task for each ordinal number is called an "ultratask".[2] The term supertask was coined by the philosopher James F. Thomson, who devised Thomson's lamp. The term hypertask derives from Clark and Read in their paper of that name.[3]
wtf is this nerd shit?

>>11867143
>infinite, would you ever finish
It's static, the length is aleph_0 from the get go.
Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.

>>11867180
it's never going to end either way

>>11867128
I didn't choose the Archimedean property, it's a property of real numbers.

>>11867184
yeah, infinite isn't finite
>mindblown.gif

>>11867129
Not an argument.

>>11866224
0.999... isn't a number, it's a decimal expansion. Its limit is 1 (as the number of digits approaches infinity)
Claiming they're not equal amounts to claiming they COULD be equal but aren't. But that's not true, because 1 is a number and 0.999... isn't.

>>11867190
No shit, and real numbers chose it as a property. Are you historically illiterate?

>>11867154
Not really, it's actually quite beautiful and complex.

>via cauchy sequence
>via dedekind cuts

>>11866224
Prove requires math for 10 year old.
Adults are expected to know limits to understand.

>>11867115
0.999... is not a Cauchy sequence

>>11867216
What's it like being obsessed with a website?

>>11867225
it literally is tho

>>11867216
>i have no argument

>>11866224
classic bait. if not bait, you are mentally ill please seek help

>>11866236
You write 1/3 as an infinite decimal because you never truly reached the real value, you have an approximate value with tiny 1/3 of a digit rounded off.

So 0.33333....1/3
+0.33333....1/3
+0.33333...1/3
=1

But you rounded off those thirds in that base 10 approximation, so you're left with 0.99999....

Or did you really think 3+3+3=10?

>>11866224
1) It IS an accepted fact, because we can actually do math.
2) We call you retards because rigorous mathematical proofs like pic related are too much for retards like you to handle.
You are the one spreading garbage because you don't understand how Real numbers work.

>>11866240
Real numbers ARE Imaginary. Imaginary numbers are all numbers, Z, such that Z=a+bi where a,b are Real numbers and i is sqrt(-1). The Reals are just the case where b=0.

>>11866264
2.9.../1.9...=3/2=1.5
Stuff like this is trivial to someone who knows math.

>>11866482
Knowing or not knowing the last digit of Pi has NOTHING to do with whether it's a constant, and you are a retard for not knowing this.

>>11866559
lol wut?

>>11867225
Yes it is, retard.

>>11867342
can't be constant if it's changing all the time

>>11866790
0.333... isn't the equivalent value, it's an approximation in base 10. You wouldn't have to go to the infinith decimal place if you had an exact equivalent value

>>11867354
They aren't changing the number you fucking retard. They are revealing more digits of the number. Stop using terms you don't understand.

>>11867336
Why not 1.5000....1? Are you saying 0.000....1 isn't a number?

>>11867357
revealing, changing, it's the same, the numbers didn't exist until they were revealed

summary of thread
>it's not equal because I'm a fucking autist who thinks definitions aren't social
>it's equal because I'm a fucking fascist who thinks axioms are divine

>>11866224
I had someone try to argue with me that perfection is just "as good as something can get" and that you and I are already perfect because we are the sum of every decision we've made that we thought was best for us, and then he used 0.999...=1 as proof that perfection doesn't require precise perfection.

I assume this is either jew or chinese propaganda to make a populous accept themselves just the way they are and not try to improve.
The saying used to go "step 1 is identify the problem, step 2 is fix it". Now it's "step 1 identify the problem, step 2 accept yourself for who you are". Kind of a comfy way to let people accept mediocrity and fear if you ask me.

>>11867359
Case 1: I'm right and you're wrong.
Then I already showed why 2.9.../1.9...=1.5

Case 2: I'm wrong and you're right.
Then 2.9.../1.9...<3/2=1.5<1.50...1 which implies that 2.9.../1.9...<1.50...1

Stop being a contrarian retard.

>>11867370
fuck off you autistic fascist

>>11867383
This was schizo nonsense.

>>11867367
You are staring into a half open closet, and see a suit. Then you open the same closet so that it's fully open, and now you see a suit and rain jacket. Did the contents of the closet CHANGE, or were the contents REVEALED?

>>11867389
Pretty sure smaller denominators mean larger answers, and considering the denominator changed more than the numerator (%-wise) we can reasonably expect more than 1.5

Pic related

Either way you're super smart and should've just corrected me to 1.4999.... if you were so certain. It honestly doesn't change the main question: what happened to the 0.000...1?

>>11867370
Fascists are the ones who typically change and muddy definitions to sow doubt where none existed or was needed.

>>11867413
Pic unrelated because you didn't use ...

>>11867394
>countries and organizations don't exercise espionage for monetary gain
Get off the CNN and Fox train

>>11867421
kek, don't be a faggot anon

>>11867412
there's no Pi closet anywhere lmao

>>11867392
I'm right tho

>>11867415
>fascists do x
true and irrelevant
they also drink water

What do anons think of this silly proof:

S = 0.9999...,
10S = 9.9999...,
9S = 9,
S = 1,
0.9999... = 1

>>11867993
It’s axiomatic if you’re a hitler youth, or muh can’t into infinity if you’re an autist.

>>11867359
>Are you saying 0.000....1 isn't a number?
correct

>Is someone orchestrating this?
No, the powers that be are letting everything around them unfold as it will in a giant clusterfuck free from their manipulations.

>>11868339
Lol okay then describe the phrase “as close as you can get to 0 without getting there” in terms of R. I’ll wait.

>>11867359
0.1=10^-1
0.01=10^-2
0.001=10^-3
:
0.0...1=10^-inf=0

>>11868402
that isnt a thing in R you retard
we work in the reals not the hyperreals

>>11868986
lmao i just fucking owned you
R is the reals not the hyerreals

>>11866236
Incorrect

>DUDE ITS NOT 2020 ITS ACTUALLY 2019.999999...
this is what you sound like

>>11869244
incorrect what?

1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

>>11869244
you divided by 0

>>11869253
is there supposed to be something wrong with it?

>>11866240
>>11866245
>>11866360
>>11866363
>>11866391
>>11866396
>>11866403
>>11866434
>>11866437
>>11866453
>>11866462
>>11866482
>>11866559
>>11867082
>>11867129
>>11867206
>>11867310
>>11867354
>>11869244
THE ABSOLUTE STATE OF /SCI/
THIS BOARD IS AN EMBARASSMENT

refute this, 1.000...=1tards

>>11869514
nobody was able to refute this because it is true

>>11869514
>Algebraic manipulation does not work for infinities. To claim otherwise would be absurd.
based

>>11870048
>this piece of shit in the street is chocolate since nobody tasted it

>>11869514
Via Cauchy sequences:

1.000... = (1.0, 1.00, 1.000,...) = lim as n-> inf of 1 = 1

Via Dedekind cuts:

Assume to contradiction that x is a rational number such that

1 < x < 1.000...

1.000... is less than 1 followed by any finite string of 0s followed by a 1 so for any natural number n

1 < x < 1.000... < 1+1/10^n

x < 1+1/10^n

10^n < 1/(x-1)

n < log(1/(x-1))

Let n = ceiling(log(1/(x-1)))+1

ceiling(log(1/(x-1)))+1 < log(1/(x-1))

This is a contradiction, so x does not exist and 1.000... = 1.

>(1+1.000...)/2 is between 1 and 1.000...
Prove it.

>There is no number between 1 and 2
Wrong. 1 < 1.5 < 2

>0 does not equal 0.000... either
Wrong. The above proofs can easily be modified to prove that as well.

>>11870082
1.5 is not a number lmao

>>11870097
based, non-natural numbers are an abomination

>>11870097
Wrong, try again.

>>11870248
he's right though

>>11867330
Those are complex numbers, real and imaginary part

>>11870249
See >>11870248

>>11870532
what's even a 1.5 number, there's no such a thing

>>11866224
1/3 = 0.3 + (0.1/3)
1/3 = 0.33 + (0.01/3)
1/3 = 0.3... + (0.0...1/3)

>>11870055
it does, only for convergent infinities.

0.333... is the limit of the sum of 3*(0.1^n)

that sum is clearly convergent. If you disagree on this, you are a nigger and you should be shot

>>11871035
>it does, only for convergent infinities.
well, that's convenient...

>>11869244
>a= b^2
>ab=b^2
Immediately incorrect, ab=b^3.

>>11868979
That last one sounds like more of an approximation cause you got lazy. Obviously something is greater than nothing, no matter how infinitesimally small

>>11869512
seethe harder cause you accepted laziness as doctrine without thinking about it

>>11867593
Kek I know, but I couldn't let you get away with it that easy

>>11867144
welcome to life

>>11867102
We get for all real world intents and purposes 0.999... might as well =1, but in the pure vacuum of mathematics (where things like infinite exist) many of us argue it does not. I'm saying you're being lazy and confusing an approximation with a hard value. You have to go to infinity decimal places with 1/3=0.333... because you never reach the exact value in base 10 mathematics.
And by playing with infinite decimal places, you're playing by the rules of pure vacuum mathematics.

>>11871213
No, I'm saying it's literally defined as 1.

>>11871037
That's not convenient, it's just semantics. Convergent infinities are actually not infinities but finite quantities. In a nutshell, they're just an extremely inefficient notation of a finite number.

0.5 + 0.25 + 0.125 ... to infinity converges to 1. Does that mean that you can't add up 1 to any other number because "you can't add infinities ?"

That's retarded.

>>11871213


In the "pure vacuum" of mathematics, should there be an infinity of nines in 0.999, you'd be writing the sum of 0.9*10^n going from 0 to n (n going to infinity). But we all know what that means do we now ?

If the mods don’t delete this thread I’m going to DOS this site.

>>11866224
Completion is not possible within this material universe. A universe that includes the potential for fear and suffering is incomplete. If there is something to overcomes within this material universe, then completion is not a possibility. Something cannot be complete which sprung from incompletion. The creator is flawed and so are its creations.

>>11871430
I'm gonna DOS your mom right in the pussy, geek squad

>>11871503
Does geek squad even exist anymore? Don't most of the technologically retarded just have their millennial crotch-fruit resolve their issue?

>>11866453
>guys im trolling

>>11871509
apple paid $4B cash for the franchise and rebranded it as genius bar

>>11868979
and that limit is 0 not 0.0...1

>>11870066
kek

>>11866240
Numbers arent real in the first place

>>11866236
>infinite numbers
wrong

>>11871997
>2/3 is infinite

0.999... + 0.111... =
0.9 + 0.1 + 0.09 + 0.01 + 0.009 + 0.001 ... =
1 + 0.1 + 0.01 ... =
1.111...
0.999... + 0.111... - 0.111... = 1
0.999... = 1

0.999... = 1 - x
multiply both sides by 10
9.999... = 10 - 10x
subtract 9 from both sides
0.999... = 1 - 10x
1 - x = 0.999... = 1 - 10x
(1 - x) - (1 - 10x) = 0
9x = 0
x = 0

0.999... = 1 - x
multiply both sides by 10
9.999... = 10 - 10x
subtract (1 - x) from both sides
9 = 9 - 9x
divide both sides by 9
1 = 1 - x
x = 0

>>11866224
>FFS NOT AGAIN
SAGE AND HIDE

>>11871399
>Convergent infinities are actually not infinities but finite quantities.
you can never know unless you add all the numbers, which is impossible

>>11871408
i think if it's more than 100 nines it's already pretty much 1

>>11871523
his right doe

>>11872130
2/3 is a ratio, not a number

>>11872185
you are just defining the problem away, that's not allowed in maths

>>11872615
make a wikipedia page about it then genius

>>11872610
What is the result of [math] \sum_{n=1}^436255638 1 [\math] ?

>>11872610
What is the result of [math] \sum_{n=1}^436255638 1 [/math] ?

>>11872795
95159491061521341, why?

>>11872798
a number, why?

>>11866252
1.5

>>11866790

>>11872854
that's not meds, it's a dumb book

>>11872610
last try. what is the result of [math]\sum_{n=1}^{436255638} 1[/math] ?

>>11871167
>Obviously
nice maths you got there bro

>>11871075
the original starts with a=b leading to a division by zero

>>11871213
why does this post reek of dunning-krueger?

>>11871320
This. Decimal representations aren't what numbers actually are. For actually defining numbers, you will need things like set theory or lambda calculus and then you can start converting between the definition and the representation. And if you do that, you will come to the conclusion that 0.999... = 1.

>>11871430
based

>>11871484
god I hate this board

>>11871503
DoS is rape, DDoS is gangbang

>>11872612
based engineer

>>11872615
my sides are in orbit, this bait is pretty good

>>11872618
how is he doing that?

>>11872800
>>11872803
He was trying to get you to realize that you don't need to add up all the numbers. Maths is about finding patterns to be able to deduce results more easily. That's why we invented formulae.
See >>11872926

>>11872854
First of all, he should really prove that the representation is unique now, but I guess he's correct. Anyways if we accept this notion, 0.999... doesn't exist anymore so there's no problem at all.

>>11872615
no, it is a number.

>>11873689
Define the number 2/3 without using ratios.

The problem is that
1/3 doesn't equal .3333333333333
2/3 != .6666666666666666666

Slice something perfect 3 times and it has a very well defined edge and size. It's like that arrow problem that never reaches the target because it keeps closing "half the distance." It's bullshit. Using infinitely repeating decimals is the same as a 3 year old saying unicorns are real to justify why the living room looks like it was ran through by a horse.

>>11873851
this

>>11873851
Psst. Get this shit.
>0.1 = 1/3
>0.2 = 2/3
>1 = 3/3

Your whole argument begs the base.

>>11873874
>.1 = 1/3
Nobody said that though

Something divided by 0 has no good answer so it is undefined. Dividing numbers into infinite decimals should also be undefined because it is not a real thing.

>>11873874
>>0.1 = 1/3
>>0.2 = 2/3
What the fuck are you talking about?

>>11873840
the equivalence class of (2,3) in Z×N/~ where (a,b) ~ (c,d) if and only if ad = bc

>>11873888
You used like 4 ratios in that sentence alone lmao.

>>11873892
can you name all 4 ?

>>11873879
>>11873885
Just choose a better base to describe 1/3 and 2/3
Choosing base ten just makes you look stupid.

>>11873895
>Z:N/~
>N:~
>(2,3):(a,b)~(c,d)
>ad:bc

>>11873906
and not a single ratio was named that day

>>11873922
Holy fuck you're stupid