/lit/ - Literature

He'd endorse you getting banned, that's for sure.

>>16388137
It depends in which theoretical context you are asking this question, which is very important. In an abstract mathematical sense the bottom would be right, but in a symbolic sense the top one would suffice.

>>16388137
Hegel unironically discusses Calculus in the Science of Logic. Only real Niggas know this.

>>16388160

>>16388137
Honest apologies for anything said against you and all the creepy Hitlerist stuff but holy fuck, you are one major loser dude. Why would someone like me want to hear about Big Bang Theory? Hey fatty, does that sound like something I would like? No. "Childish wonder" means you're a fucking loser. 60 yr olds don't watch kid's cartoons like it's normal. I guarantee Josephine or whoever the fuck isn't watching the juvenile crap you and your norwood 7 geek face brothers do.

>>16388157
I'm a mathlet, can you explain why the bottom one is correct? Popsci midwits on YT insisted the upper one is correct

>>16388204
And dude, I HAVE to say this or else you would all continue on with the bizarre idea that we're friends. NO, we aren't.

I don't know how that geek could show someone like me his worthless family with a straight face and not expect me to laugh at them behind their back.

>>16388157
>an abstract mathematical sense the bottom would be right
Moron.

>>16388137
>0.9999...
becoming
>1
being
>0
nothing, which is the same as being

>>16388212
Oh boy! Some fat dude who shovels donuts down his gullet and watches sitcoms and charlie brown kid's cartoons? Holy fwark yeah, that would be fun to have a conversation with!!! oh fwark yeah!!!!

>>16388222
Seek mental help

>>16388222
Deranged.

Sophie understands where I am coming from. Make Sophie spend a day with these geeks. I promise you she will be even angrier and more annoyed than I am.

>>16388227
The worst part is I wouldn't even think of all the people I rant against for even a second if they left me alone. I don't want to think of any of them at all. I don't know what world you come from where Charlie Brown and kid's shows sound like things that would interest me in any way.

>>16388227
Oh and I have to admit I have done some bad shit to them but they are still complete losers though. Like threatening them and all is lame but you're still children's cartoon watching geeks.

>>16388227
If they were young, they would be the exact people that are mocked here and called onions.

>>16388212
Are you telling me 0.9999 is not a different paradoxical number from 1? What a retard, I base my understanding of mathematics on the Greeks.

>>16388227
Like this guy is a bald loser and he thinks we're friends. He was telling me about how he lectured his class in school about fire station history or some bullshit and I was just thinking to myself "dude, if you were my age I would have mocked the Hell out of you."

>>16388257
0.9999 is indeed different from 1.
0.9999...., however, denotes exactly the same thing as 1.
>I base my understanding of mathematics on the Greeks.
Real analysis was not developed until at least 19th century, moron.

x = 0.9999....
10 x = 9.9999....
9 x = 10 x - x = 9
x = 9 x / 9 = 9 / 9 = 1
quod erat demonstrandum, bitcheeeess

>>16388257
if they're different numbers then there's a difference between them yes? so what is 1 - 0.9999... = ?

>>16388276
>9 x = 10 x - x = 9
Fail. That's not how algebra works

>>16388269
>0.9999...., however, denotes exactly the same thing as 1.
It must be denoting something different if it is itself different in someway.

>>16388278
>so what is 1 - 0.9999... = ?
Pointless question which is answered by intuition, but to give a technical one which is necessarily tautological(otherwise everything's a complex, see Zeno): 0.00001

>>16388137
Anyone who argues the bottom one is a brainlet.

>>16388285
>It must be denoting something different if it is itself different in someway.
Idiotic assertion.
2+2 and 4 looks different therefore they must be different numbers according to you?

>>16388269

>ye-ye-you guys...said start...and the Greeks? Because I started with the uh-uh-uh the Greeks

>>16388288
substitute 9.999... for 10x and 0.999... for x. he's not saying 10x-x = 9 for all x

>>16388291
the dots represent infinite nines. 1 - 0.999... must be smaller than 0.00001

>>16388311
>>16388288
Clearly you're too stupid to deal with letters. Let me prove it avoiding letters.
10*0.999... = 9.999....
thus
9*0.999.... = (10-1)*0.999.... = 10*0.999... - 0.9999... = 9.999... - 0.999... = 9.000.... = 9
Thus 0.999... = 9/9=1.

>>16388323
i mean, the guy still didn't make any errors until the last line but sure.

Anyone who says 0.999...=/=1 is basically saying A=/=B tautologically because A and B look different. It's a failure of the most rudimentary aspects of logic.

1=0.999... because both serve as the algebraic identity on the real numbers, and it's possible to directly prove that any two symbols which function this way must be the same. You don't even need numbers, just being a ring is enough.

>>16388317
I forgot to put dots on it, what's your point? However I did explain that with my reference to intuition and tautologies.

R E F U T E D.

>>16388288
>Fail. That's not how algebra works
>>16388311
>substitute 9.999... for 10x and 0.999... for x. he's not saying 10x-x = 9 for all x
when I was posting that lil proof, I typed out the extra step on that line where I substituted the numbers for x and 10 x, but then I thought, 'naah, anons are smart, I don't need to dumb it down that hard'
O how I was mistaken.

>>16388204
its pretty simple.. 0.999(repeating) is not 1 its 0.999(repeating). the more 9’s you add, the closer you get to 1 but the slower rate you approach 1. i believe this is called a limit in math. you will never reach 1. i have no training in math but im confident this is right. visualize a loading bar that keeps getting slower so you keep having to zoom in to see progress infinitely

>>16388204
What the fuck is there to explain that 0,9999...=/1 ?
The first one only (0,999=1) happens to be "true" in pratical real life stuff, but even that depends on the context of the situation you are trying to apply it and the relative degree of difference they have.
Sometimes in control theory, it is better to use 1,001... to represent 1 instead of 0,999.. depending on the nature of the things you are working with and the results that you want.

In real life you kinda only apply stuff in a statistical aggregate kind of way based on approximations

In order for .999... to equal 1, you would first have to disprove infinity. It doesn't really matter how nicely any other interpretation would fit into Hegel's philosophy unless Hegel disproves infinity first.

>>16388389
>In order for .999... to equal 1, you would first have to disprove infinity
Why?
What do you even mean by "disprove infinity"?

>>16388382
Based.

>>16388398
If there is any distinction between two infinitesimals, there must categorically exist a unit of separation. The formulation of the problem .99 = 1 implies that separation exists in and of itself, otherwise you could have written 1 = 1 and everyone goes home happy. It assaults the concept of infinity because it implies some arbitrary precision where two different quantities equal each other if only you can make the quantities small enough. In order words, it claims that infinitesimals can't exist, which itself claims that infinity can't exist, the definition of an infinitesimal naturally presupposing infinity.

If we accept that there exists a point where two different numbers are equal, our entire mathematical system breaks down, because if .99 =1, .98 = .99, and so forth. The simple old transitive property forbids this.

>>16388137
probably the second, he was retarded.

>>16388204
0.999... cannot be equal to 1 in practical terms.

Using another anons analogy, imagine a loading bar that starts with 0.9 and adds a 9 after, forever. If the loading bar ever hits 1.0 the world is destroyed. But because 0.999... to infinity is never a round 1, we continue shitposting on /lit/ and masturbating to amateur porn.

If you're solving a physics problem, however, you can round the number up, unless you need extremely accurate results but even then most of the times a round 1 will suffice.

>>16388291
>It must be denoting something different if it is itself different in someway.
"Close" and "shut" are 'different in some way' but denote the same thing. The only difference between 0.999... and 1 is that they are different notations. The quantity they denote is one.

>>16388476
there good explanation of the problem on youtube i suggest you cheek them out. It is 1

>>16388476
Holly fuck /lit/ is full of brainlets. Can you guys please take a basic real analysis class, this is just embarassing.

>>16388491
again, not practical

if you ever study math (in academia and not youtube) youll see that there are practical and non practical solutions to different problems depending on the context and what theory youre practicing

>>16388503
dived 1 by 3 and them multiply it by 3 and tell me what you get, to see practicality in action

>>16388481
Close and shut ostensibly mean different things.

>>16388476
1/3 = 0.333...
1/3 * 3 = 1
0.3333... * 3 = ?

>>16388257
>the Greeks
You mean the guys who killed themselves when they discovered they were irrational numbers?

If .99 = 1, how is 1 =/= 2?

>>16388448
This is gibberish. Infinitesimal don't exist in the real numbers due to the least upper bound property that is necessary to define the real numbers in the first place.

>>16388344
The number 0.000...0001 with an infinity of zeroes doesn't exist. Try to define it as a limit of a sequel of decimal numbers of you'll see.

>>16388516
>>16388526
multiply 0.9.... by 1 and divide by 1, tell me what you get

perhaps you gentlemen should stick to reading fiction

>>16388137
>0.9999... =/= 1
It's really about time this meme died, along all those who propagate it.

>>16388541
have a relevant point pls

>>16388503
Find one instance of a calculus or real analysis textbook saying 0.999...!=1. I'll help you out some the section you're looking for is the sum of an infinite series.

>>16388527
What are you trying to say?

>>16388538
I never said infinity of zeroes, that is just the essential limit imposed upon it. Same with your "0.9999" wherein I could bring the same critique as you propose me.

>>16388520
This is true, but it's hard to find perfectly-equivalent words for real things because reality is overdetermined and most synonyms bring out at least slightly different shades of the thing they're referring to. On the other hand, 0.999... and 1 have exact mathematical meanings, as does the true equivalence relation 0.999... = 1. The only point I was trying to make is that notations can be different but that doesn't in itself imply the denoted-thing is different.

>>16388555
You don't even know what limit means do you?

>>16388208
?

>>16388552
there >>16388503
>>16388553
not sure id trolling at this point, 0.99..!=1 because its not practical, are you seriously talking about infinite series right now?

>>16388586
0.999... is 0.9+0.09+0.009 and so on into infinity. It is the sum of an infinite series that is how it is defined in actual math and not your made up shit.

>>16388137
both

>>16388586
its the opposite, 1/3 is a perfect example even for brailets like you, your dumbass bar example has 0 mathematics in it.

>>16388607
yeah its equal to 0.99... sure, but not to 1. i cant understand your argument right now. do you even know what youre trying to prove?
>>16388624
1/3 does not explain why 0.999...=1. have you ever written a proof?

>>16388672
The sum of that infinite series is 1 you jackass.

>>16388672
it does, it a simple pre calculus argument.

>>16388672
Serious question.
Have you ever actually studied mathematics, or did you just read books that you failed to understand?

>>16388137
Decay fulfills the remaining distance

>>16388560
But it depends in which context you look at it. Generally I agree with you.

>>16388561
What do you mean?

>>16388769
Limit has a specific meaning in math. This
>I never said infinity of zeroes, that is just the essential limit imposed upon it.
is definitely not what is meant by a limit in mathematics. A limit is always a real number not a sequence.

>>16388137
> A “1 does not equal .999...” thread on /lit/

Please, no. I thought this would be the least of my worries when I emigrated from /sci/

>>16388137
He's distinguish a sense in which it does, another one in which it doesn't. He'd place each at its rightful place in the total "map" or "journey" of the Spirit, giving them a context.
Or something like that I guess.

>>16388448
>There exists a point where two different numbers are equal
That point is as close as you want.

Any of the actual math anons tell me what 0.88... equals to? Not sure how to get the limit.

>>16389028
If 0.999...=1=9/9 it's pretty obvious that 0.888...=8/9

>>16389028
10*0.88... = 8.88...
9*0.88... = 8.88... - 0.88... = 8
0.88... = 8/9

>>16388137
0.9999...=1 is a change of quantity in quality, so I'd say Hegel would agree with that, whereas 0.9999.... =/= 1 is a metaphysical viewpoint.

>>16388476
0.999... can't be likened to a loading bar. Values change in a loading bar, moving towards some limit. 0.999... is a single number. Its value doesn't change. Additions are not being constantly applied to it.

>>16388834
Can't wait for the -1/12 to up....

>>16388323
>(10-1)*0.999.... = 10*0.999... - 0.9999...
what did he mean by this

>>16388526
This. The amount of brainlets in this thread is unbelievable. Never thought I'd meet people worse at math than me.

>>16388323
I think you need to go back to literal pre-school.

>>16389382
He's doing basic algebra. (a - b)c = ac - bc

>>16389382
>>16389401
Lol fucking /lit/ tards

the absolute state of /lit/
yall get up on your high horse abt stemfags, call them bugmen, meanwhile yall are out here getting filtered by high school level algebra lmfao

>>16389515
i get the the proof but is it actually possible to substract infinities?

im not >>16389382 or >>16389401

>>16389567
But 0.999... is not infinite. 0<0.999... <2.

>>16389567
Be exact you're not subtracting infinities those are both clearly finite numbers with infinite decimal expansions or even more specifically infinite non-zero decimal expansions. And yes you can add and subtract such infinite decimal expansions with the natural method and have a well defined answer.

>>16389600
so
1/9=.111...
.111...*9=.999...
1/9*9=9/9=1
.999...=1
thats a simpler proof right?
sorry for being a retard

>>16389618
I don't think it's simpler because you might as well ask why is 1/9 the same as .111....
After all, each finite truncation of .111... is less than 1/9, so we're back to where we've started.
In contrast, multiplication by 10 is very easy and intuitive: you just shift the decimal point to the right.

>>16389618
Sure. A trick you learn in school is any integer divided by that same integer with every digit replaced by 9 equals an infinite repeating decimal expansion of that integer for example
16758/99999=0.1675816758... try it in google

>>16389567
>>16389391
>>16389382
>>16388672
>>16388586
>>16388541
>>16388530
>>16388476

>>16389666
Based Matlab autist

>>16389666
here you can see that even to 9E-99 term Matlab shows a real value != to 1, but an infinite series as the problem asks does converge to 1

>>16389666
Based, checked, and correct

>>16388137
You cannot add infinite 9's.
Imagine a machine adding 9's to a sequence since the begging of the univers to the end of it. Even if you achive optimal computing performance you still have the univers lifespan as limitation.
1=0.9... because its the closest thing reality allows us to do.
Also: 1/3(0.3...) multiplied by 3 is 1.

>>16389869
Take a fucking math class the sum of an infinite series is covered in high school pre-cal

>>16389869
It is not because it's the closest thing reality allows, it's because 999... is another way of expressing 1 just like saying 1.000... =1 or 4/4=1

>>16389727
additionally, .000...001 is not a real physical value as I will show you:
0.0 followed by an infinite number of zeroes, culminating in a 1 is the hypothetical answer to 1-.99...
This can be expressed as 1*10^(-infinity), or, 1 divided by 10 an infinite number of times. (1 divided by 10 is .1, divide by 10 again is .01, and so on unto infinity)
So we now have 1-.99...=1*10^(-infinity)
10^(-infinity)=1/10^infinity=1/infinity=0
1*0=0
Therefore we see that 1-.99...=0

>>16389869
0.999... is not a sequence of additions though. It's a single unchanging quantity.

>>16390136
wtf no you have to accept my new definition of a quantity and reject the rest of the mathematical community's collective understanding of recurring infinite decimals and/or limits of cauchy sequences

>>16390136
.99... can be represented as .9+.09+.009+... just like 10 can be represented as 5+5.
10 is not a sequence of additions, it is a single unchanging quantity, but it can still be represented as a sequence of additions. The concept of multiplication uses a series of additions, and math would not exist if concrete quantities could not be represented as a sum

>0.999 =/= 1 threads on /lit/ is even worse than the ones on /sci/

>>16388204
difference betweeen practical and theoretical.

>>16390329
Fucking shut up you don't know anything. Open any fucking calculus or real analysis textbook and they will all say 0.999...=1 THEORETICALLY.

>>16390219
ellipses in a mathematical context are often used to indicate the limit. In this case 0.99... refers to the limit evaluating at 1 (unless explicitly indicated beforehand that you are using a nonstandard system)
The limit of your sum is another representation of 1
If you want to 'terminate' your sequence of additions, then you can write them out in full or as follows
0.9 + 0.99 + ... + 0.999(how ever many nines you want in your last term)
This will communicate the 'concrete quantity' effectively

>>16390329
see>>16389727

>>16390329
mmmmmmhhhhhhh, disagree. isnt it a
The Tortoise and the Hare thing?

>>16389954
>It is not because it's the closest thing reality allows
> it's because 999... is another way of expressing 1
Almost if reality conditioned our way of expressing, specially in maths.

>>16389936
>The sum of infinite series
There is no such a thing in reality.
If there was an infinite number of decimals this means you can divide real objects infinite. Reality does not work this way.

>>16390694
>There is no such a thing in reality (as a sum of infinite series)
Are you mentally retarded? Did you fail your high school math classes? Do you understand calculus in ANY way?
>actually the slope of the curve at any point cannot be calculated since I don't believe in infinite series
That's you, retard

>>16389869
What is up with retards who try and argue with "this calculation is infinite by a process of adding each sum 1 by 1, therefore not real" well einstein thank god we have other ways of adding infinite sums other than 1 by 1

Seeing all these coping retards not understanding basic maths is pretty funny. No wonder you guys read garbage books.

>>16390793
People don't understand math freely give their wild guesses, and then double down by refusing to admit they don't understand math

>>16388785
So what's your point?

>>16390793
An infinite slope is simply a vertical line used to show the tendency of a curve, show me an example of an infinite vertical line, empirically.
>>16390793
It's not about the process of modification the number its about the number itself, doesnt matter the type of modification you do to a number. You cannot reach infinity.

>>16390992
>you cannot reach infinity
Of course not, but that does not mean that converging series do not exist. For example: the sum of 1/k^2 for values of k from 1 to infinity is pi^2/6, not infinity, even though it is being added an infinite number of times.

David Foster Wallace’s Everything and More is the only math I have ever experienced. I don’t know that his style is well-suited to it though. Starting his footnotes with “Shit. Ok...” and the like maybe made the material more approachable, and perhaps conveyed the sense that the mathematicians were themselves stumbling around trying to deal with infinity... ok I talked myself into seeing that as an effective tone.

>>16388204
As one of three posters on /lit/ who made it past calc 1 I can tell you that 0.9999... = 1. If you really want to know why look up dedekind cuts or Cauchy sequences or something equally autistic

>>16391103
>1/1+1/2+1/4+1/8... = 2
You need an infinite number of operations to reach 2. There is no such thing as infinite time to make infinite computation to reach 2. If we IMAGINE we have an infinite amount of time, then this makes sense, if not, it doesnt exist. Then 1/1+1/2+1/4+1/8...=2 because its the closest thing reality allows us to do.
>>16390992
The first one was ment to >>16390789

It's the top
1-0.9999999... = 0

>>16388137
x = 0.9999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x=1

Jesus Christ, this thread is giving me AIDS

>>16391339
=0.0...1

>>16391348
>10x = 9.999...
prove it

>>16388220
>0=1
were you born this stupid or did you pay private classes in being moronic? Because either way you have a professional level of profficiency at it.

>>16391405
See>>16390034

>>16391293
Wtf are you talking about? Your mindless babbling does not show that 1 != .99...

>>16391293
>closest thing reality allows
That is not true at all. Just because someone cant add up values one by one infinitely does not mean that we cannot determine real infinite sums. We don't need an infinite amount of time to calculate 1+SUM((1/2)^n),0,INFINITY)=2

>>16388137
if we took the construct of .999...., it presupposed the multiplication transform, zooming in and out, since it's a decimal. it's a zoom in, division. You are zooming into one and no matter how close you get to one the dot will not leave it's back.

>>16388212
>>16388204
>>16388157
retards
1/3 = 1 * 0.333333...
2/3 = 2 * 0.333333...
3/3 = 3 * 0.333333...

>>16388204

>>16391821
For all the retards out there: the upside down A symbol means “for all” and the backwards E means “there exists”

>16391789
Retard!
Circumlocution: you used the premise to prove the conclusion. You used the premise that .3 repeating is equal to the constant 1/3 to prove that .9 repeating is equal to the constant 1.


I hope you feel stupid, but of course you don't because you are too stupid to know you are too stupid to know you are too stupid to know...
.... Repeating.

>>16391821
Thank you. I've been trying to show these retards that 1-.9999... = 0 but there is no way to deny this

>>16389727
Could you refute Zeno’s paradox with this as basis?

>>16391879
When there was a Zeno thread I said over and over Achilles and the tortoise is explicitly covered in most calculus books and yes the sum of an infinite series explains the paradox.
http://homes.sice.indiana.edu/donbyrd/Teach/Math/Zeno+Footraces+InfiniteSeries.pdf
https://slate.com/technology/2014/03/zenos-paradox-how-to-explain-the-solution-to-achilles-and-the-tortoise-to-a-child.html
https://npflueger.people.amherst.edu/math1b/achilles.pdf

>>16391694
>Uses infinity to determine infinite
Sure OP, you are right.

>>16391616
>Your mindless babbling

There is no such a thing as 0.9... is 1 because 0.9... doesnt exist and cannot be computed empirically. Saying something is infinite means its not real.

Lets take Pi as an example
Pi has not infinite decimals, Pi has as much decimals as you can count untill the universe dies.
>Look at this retard saying pi is not infinite
The universe obviously had a beginning, and therefore there was no such thing as pi before the origin of the universe (where I use 'pi' to refer to some specific number). If you are talking about 'the value of pi', then that it not a real value at all. Real values require an observer or measuring stick, but in order for something like that to exist we would need something outside our own universe! Therefore there can be no meaning to saying whether pi has any actual numeric value because if it did have one, it could only mean that our universe exists inside another bigger multiverse where time itself doesn't flow linearly.
Furthermore, we can clearly see that the universe is expanding as time goes on. This means that it must have been smaller in the past. Therefore there cannot ever have existed a situation where pi had any meaning beyond our own universe.
Youcan calculate pi, but that is just a definition of the word 'pi' in terms of some other numbers. It does not describe any objective property of the universe.

>>16391934
Draw a line segment 1 inch long then draw another line segment 1 inch long perpendicular to the endpoint. The diagonal that connects the two remaining endpoints has a length of the square root of 2 by the pythagorean theorem. 2^1/2 is an irrational number with an infinite decimal expansion. Are you saying that you can't draw a line to connect those two endpoints?

>>16391934
So you're saying that irrational numbers do not exist and are just concepts? Is π different for me than it is for a computer calculating π? If the integer 1 exists in reality, what is the hypotnuse of a right triangle with legs of the value 1? Or can the triangle not exist?

>>16391934
Holy fuck please just admit you are making this shit up as you go and you have no foundation in math. You clearly have no idea what you are talking about and are just saying things that you think sound right

>>16391958
Jinx>>16391954

>>16391954
I'm saying that this relation is not achivable in reality. If its not achivable, It doesn't exist.
>But I can draw it
False, If you mesure it you would make an error.
If you mesure the diagonal to a sub atomic level, you will find out that this relation is not real because of how reality works. You cannot divide an electron, there is no such a thing as an infinite number of decimals.

>>16391961
Sure OP, inifinite decimals exist, I've told you, you are right, take ur meds and go to sleep.

>>16391958
The triangle cannot exist

>>16392005
>>16392018
So you claim reality is discreet and geometry does not hold true for the fundamental units, and there can be no measurements between each grid. There are no straight lines except across axis, which cannot be measures because everything exists along them.

>>16392010
>mathematical proofs
vs
>well I just don't think someone could count to infinity
Fuck you, you stupid fucking retarded mongoloid you don't deserve to breath my air

>>16392047
Unironically being triggered, you think and act like an animal.

>>16392005
So you don't believe in the pythagorean theorem?

>>16392044
>that last part
Lmao fuck

>>16388204
If a circle is big enough it becomes a straight line or something like that... That's how it was explained to me.

>>16392005
>You cannot divide an electron
What is this supposed to mean? You understand that atomic theory has the particles existing in space not that all of space is made of particles

0.999... and 1 are different objects and so cannot be equal. There is nothing to prove. This fallacy arose from Euler's Blunder:

https://www.linkedin.com/pulse/eulers-worst-definition-lim-john-gabriel/

1/3 has no measure in base 10, so 0.333... is just a consequence of this fact. The most important number theorem in mathematics is proof that 1/3 has no measure in base 10:

https://drive.google.com/file/d/1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH

It is possible that you will retort ignorantly that the theorem proves 1/3 has no "finite representation or measure in base 10". Well, there is no such thing as an infinite measure and it is nothing but wishful thinking on your part to believe that somehow "at infinity", 3 becomes one of the prime factors that divides (2x5)^n.

This gibberish has to end!

>>16392087
If it was explained that way it's fucking wrong because the bottom one
>0.999...!=1
is retard level

>>16388137
Hegel didn’t believe in infinitesimals. He also didn’t believe in atoms. He thought that both were a bunch of hocus pocus.

>>16392104
2/2 and 1 are different do you think that 2/2!=1?

>>16392104
John Gabriel is mentally ill

>>16392111
Clearly 1.00000...!=1 because someone cannot add an infinite number of zeros forever
>>16392104
>3 becomes one of the prime factors
4 is not a factor either, .25 is not an integer and therefore cannot be a factor. You do not know math. Shut the fuck up

>>16392111
>>16392128
aight thanks for clarifying im a retard who looked this up on youtube to try and glean even some understanding of this and wanted to see if this guy was for real

>>16392130
You didn't answer the question 2/2 and 1 are visually distinct symbols so do you believe 2/2!=1?

>>16392139
I was agreeing with you and saying the 1.00 sarcastically, I'm not him

>>16392044 also >>16392070
Text is right, pic is satire.
I think math is a powerful tool to understand the world and predict how it will behave in CERTAIN situations (and buy apples).
Math exists in our minds, its not part of the fabric of the universe.
>>16392095
0.24 nanometers is the size of hidrogen atom.
Tell me how can you draw the triangle with any combination of atoms.

>>16392188
Use whatever unit of measurement you want to draw the right triangle. With 2 legs of 1 unit the hypotenuse will still be 2^1/2. Or are you also saying that measurement is impossible?

>>16392188
>math exists in our minds, it's not part of the fabric of the universe
Not entirely true, math is how we define the universe around us, it's not arbitrary

>>16388137
FUCKING RETARDS ITT RIGHT NOW, I AM DISAPPOINTED /LIT/, OBSERVE:

1/3=1*0.333....=0.333....
2/3=2*0.333....=0.666....
3/3=3*0.333....=1 !=0.999....
0.999....!=3(1/3)
therefore, 0.999....!=1

>>16392215
You wont be able to make perfect triangle with atoms.
N is w/e value.
Both legs are 0.24 x N nanometers
The hypotenuse needs to be a multiple of 0.24 nanometers, because you can't divide the atom.

>>16392279
Fuck, this was ment for >>16392210
>>16392215
Math didn't exist 3000 years ago. It defines some of the universe arround us, so does language.

>>16392279
>>16392296
And this is in direct contradiction with the pythagorean theorem. That's like middle school math you don't understand

>>16392279
You seem fixed on making things with atoms, and use a hydrogen atom as the smallest unit. Space itself can
>you cant divide the atom
???
Atoms comprise of hadrons, which comprise of quarks, etc. A wave can have a much smaller wavelength.
If the universe were discreet, it must have some fundamental smallest unit, say for example | and _.
|_ <- this would form a triangle. You don't need to form a triangle out of something, you can define it with measurements on space.

>Atoms comprise of hadrons, which comprise of quarks, etc. A wave can have a much smaller wavelength.
Atoms are the smallest amount of matter than can be found as a something that makes up a unit. Hardons are found within the atom. Quarks are more like properties, not thigs we can see/measure.
You cant divide the atom into something smaller anon, it's called nuclear fission and it does not result in smaller units of measurement. Things in universe are made of atoms, so if you want to have the maximum accuracy with pithagoras theorem you need to use the,

>You don't need to form a triangle out of something, you can define it with measurements on space.
Can the universe interact in some way, is there real prove, if humanity didn't exist will the triangle still be there? No, It's a product of your imagination. It does in fact not exist.

>>16392433
>Things in universe are made of atoms, so if you want to have the maximum accuracy with pithagoras theorem you need to use the smallest individual thing that makes reality.

>>16392447
10 atom length legs the hypotenuse would be 10(2^1/2) an irrational number with infinite decimal expansion

>>16392467
What would the hypotenuse be made of?

>>16392477
So you don't think that hypotenuse can exist? Bizarre

>>16388137
>>0.9999... = 1
>or
>>0.9999... =/= 1
>which one would Hegel endorse?

hegel wouldn't care.

>>16391694
actually those equalities only held before obama switched us over to metric in 2014, now we still don't know if dedekind cuts can still construct the real numbers

>>16392433
>product of your imagination
>does not exist
thought experiments are and have been extremely important for humans to be able to understand the way the universe works. Just because matter breaks down into discrete blocks does not change the fact that the length of the hypotenuse of a 45 degree right triangle is irrational

>>16388204
decimal expressions are just representations of numbers, don't take them too seriously.

the representation (0.999 w countably infinite 9s) stands for the same value as "1." The representations are different because writing them involves different characters.

What doesn't make sense to me is that a limit has different properties than an integer, bc you can do operations with a limit that you can't with an integer, so when you equate the two, a mathematical property is removed. Is this why equals signs with 3 lines exist?

>>16388204
0.99... will not equal one until you take its limit at infinity. Its limit as the n of digits approaches infinity is 1. If you do not understand this look up what limits are and how they work. Infinity is not just "big number".

>>16393331
equal sign with three lines is an equivalence, it has nothing to do with limits. Mostly used to show that 2 equations are always equal to each other.

>>16393920
Thank you. My Prof never explained them

As long as the math problem gets solved logically he wouldn't care

>>16393680
0.99... is already a number defined through 'limit', how else are you gonna 'write' it otherwise? To be precise, it is itself a series which is Cauchy. The only time the latter is correct is when you exclude 1 in your set, then the set will be incomplete, and thus 0.99... tends to nothing. Look up how real number can be defined through Cauchy sequence, then 0.99... = 1 is literally a tautology under your usual real field axioms.

Fuck you /lit/ I and everyone who read this thread is now dumber for having done so.

>>16392257
>>16391789
>1/3=1*0.333....=0.333....
Wrong, retards. 0.33... is close to 1/3 but never reaches 1/3, just like 0.999.... and 1.

>>16388137
>>16388204
This thread is full of brainlets.
The reason why 0.999... = 1 is because of the very structure of decimal representations themselves. Decimal representations are just series of fractions. The number 0.875 for example is (8/10^1) + (7/10^2) + (5/10^2). That's how the idea of a decimal is defined mathematically. When we're defining an infinite number of numbers after the decimal, what we're really doing mathematically is defining an infinite series like the one above.
For example, 0.333... = (3/10^1) + (3/10^2) + (3/10^3) ... You cannot define a number with infinite decimal places without assuming the existence of infinite series is what I'm getting at.
The thing about infinite series is that some of them *converge*; which means that when you add up all the numbers in the infinite series they can be proven to equal to a finite number. Not just that they *approach* equality or get ever closer to a number; but that they *do* equal that number. Once you assume that these series can exist you can show that they converge. So 0.333... = (3/10^1) + (3/10^2) + (3/10^3) ... = 1/3. proving it is complicated as has to do with limits.

From this we can easily show that 0.999... = 1 as the decimal representation (9/10) + (9/10^2) + (9/10^3) ... converges to 1. There's other ways involving dedekind cuts and other weird stuff; but once you assume you can have infinitely large series this becomes easy to prove.

The problems with proofs that say 1/3 = 0.333... and therefore 3/3 = 0.999... is that they presuppose the existence of these infinite series and don't explain why 1/3 = 0.333... in the first place.

That being said Hegel would likely endorse the 0.999... = 1 as anyone with a child's understanding of Hegelian dialectics should realize that 1 is the thesis and 0.999... is the antithesis and they'll combine into the synthesis 1.999... so they'll finally be equal to each other.

God, /lit/ really is full of brainlets.

>>16388360
retard.

0.(3) is just another way of writing 1/3. it's just that.
1/3 + 1/3 + 1/3 = 3/3 = 1
0.(9) = 1

>>16394142
1 is a number. 0.999.... is a process. A number can't equal a process.

>>16394142
>1 is the thesis and 0.999... is the antithesis and they'll combine into the synthesis 1.999...
damn 1 = 2 now thank you hegelian dialectics

>>16394150
>0.(3) is just another way of writing 1/3. it's just that.
Ok, if 0.(3) is just another way of writing 1/3, then why should 0.333....=1/3? Protip: it's not. LHS gets closer to 1/3 but never reaches 1/3.

>>16394160
>LHS
It's not a fucking integral you mongoloid there is no left hand sum. 1/3=0.333... every fucking calculus book in existence will tell you that

>>16394160
>Ok, if 0.(3) is just another way of writing 1/3, then why should 0.333....=1/3?
Retard. 0.(3) is just another way of writing 0.3333... (ad infinitum)

>why should 0.(3) = 1/3?
because thats how we assumed to represent this fraction in the decimal system you retard

>>16391821
Computers are finite machines and are only capable of performing finite processes. There is no way to add infinite 9s so the computer approximates and tells you the answer is 1. In reality, it's a bit less than 1.

>>16394173
Gah holy fuck you guys are retards. That's a fucking proof taken from a textbook no computer involved you stupid mother fucker

>>16394173
I think you meant >>16389727

>>16394170
>1/3=0.333... every fucking calculus book in existence will tell you that
Prove it. Protip: you can't, because it's not true.
>>16394171
>Retard. 0.(3) is just another way of writing 0.3333...
Correct, retard. But that's not what you said. You said 0.(3) is just another way of writing 1/3. That's as dumb as saying 0.99... is just another way of writing 1 (the thing you're desperately trying and failing to prove).;
>>why should 0.(3) = 1/3?
That doesn't make them equal. There is no accurate decimal representation of 1/3. Every decimal approximation is either less or more than 1/3.
0.33... is strictly less than 1/3, but engineers use it because it's close enough.

>>16394182
https://openstax.org/books/calculus-volume-2/pages/5-2-infinite-series
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/08%3A_Sequences_and_Series/8.02%3A_Infinite_Series
https://www.shsu.edu/kws006/Calculus_2/3_Infinite_series_files/MTH143_3_2_IntroToSeries%20copy.pdf
https://fl01000126.schoolwires.net/cms/lib/FL01000126/Centricity/Domain/261/FDWK_3ed_Ch09_pp472-529.pdf
You mouth breathing fucking retard

>>16394190
Not gonna read all that retarded shit. Either provide an actual proof yourself or fuck off, moron.
I can't believe you don't realize how dumb your fucking proof is.
>Not convinced 0.999...=1? Well, let me divide by 3 and multiply by 3. Doesn't matter that 0.333....=1/3 poses the exact same problem of getting infinitely close to 1/3 but not reaching 1/3. Let's just presuppose that it's true in one case to prove it's true in an essentially the same case.

>>16394182
>You said 0.(3) is just another way of writing 1/3. That's as dumb as saying 0.99... is just another way of writing 1 (the thing you're desperately trying and failing to prove).;
It's not dumb, it's just how the fraction 1/3 is represented in the decimal system, and it's represented so weirdly because the decimal system doesn't handle non decimal fractions well (duh)

>there is no accurate decimal representation of 1/3
There is - 0.(3)
I suggest you go back to Math class.

>>16394197
You've got your own special math but in real math 0.999...=1 and 0.333...=1/3

>>16388157
>In an abstract mathematical sense the bottom would be right
Wrong. Read a book, retard.

>>16388291
>It must be denoting something different if it is itself different in someway.
Let's de-con-struct this.
>It must be denoting something different
Our primary clause here, note the verb "be", which is forming the phrase "be denoting something different". You use the adverb "denoting" in conjunction with the auxillary verb "must" to underline the state of existence having an evident property. In more terse terms, we can simplify this to merely:
>It is different
As the only reason to include the adverbs is due to the choice of case with the verb "be". By switching to the present tense third-person and losing the subjunctive case, we remove a semantic redundancy.

Now let's look at the other clause beyond the conjunction "if":
>it is itself different in someway.
Here we will note the verb is a case of be, "is". This clause uses the verb to connect the subject "it" to the assertion that it holds the property of "difference". You then specify that there is greater information with the preposition of "in", however "some way" yields none. The adjective of "some" precludes that the degree of difference in the "way" of "be"-ing is indeterminate. Ultimately this places the onus of meaning on the first clause, which denotes a definiteness, making this prepositional phrase meaningless.

Consider:
>it is itself different in someway
and
>it is itself different
They are fully equivalent in this case. Additionally, the inclusion of the extra "itself" adds nothing to the meaning of the sentence at all, so we can remove that as well.

In other words, you have written:
>It is different if it is different

Which is quite the astute observation. While this phrase is different from the one you have written, the meaning is the exact same. Nothing about what is communicated has changed, except for the form that it has taken. This form is merely less obscure in it's circular logic and surface-level observation than the other.

And this ties into the mistake that you've made. The sign is NOT the meaning communicated, the sign is only a sign. 1, 0.999... are both different signs, and yet they communicate the exact same meaning. They are the products of two different sign processes that happened around the exact same meaning. Your question of difference is not one of value, but one of shallow representation.

>>16388204
He cant, because HE is the MATHLET. Not you.
>>16388360
>>16388367
>>16388476
>>16390329
retards

>>16394217
>>16394212
The number pi is often represented by engineers as the fraction 22/7. Doesn't mean they're fucking equal though, does it?
In the same way 1/3 is represented as a decimal expansion as 0.3.... but that doesn't make them equal. It's just the closest decimal approximation.
>>16394217
If it's real math, you should be able to prove it. But you can't, because it's false.

>>16394236
I gave you four fucking textbooks that give the formula for the sum of a geometric series. Your fucking wrong and making the same mistake a first year calculus or lower level student would make

>>16394236
>The number pi is often represented by engineers as the fraction 22/7. Doesn't mean they're fucking equal though, does it?
Youre a fuckin retardo, bro. 22/7 isnt pi and pi cannot be represented with a fraction because pi is IRRATIONAL.

1/3 isnt irrational, by definition any fraction is rational (rational = defined as a quotient of 2 numbers)

youre such a retard dude. literally elementary school math

>>16394266
You sound so confident about it. Yet you can't prove it. Why? Because you don't understand it yourself.
>>16394269
Exactly. 0.999... is also irrational. It can't be represented as a fraction, only approximated. 1 is the closest fraction to 0.999... but it's more than 0.999..... .

>>16394280
>Exactly. 0.999... is also irrational
No, it's not. 0.(9) is rational because you can represent it as 9/9.

>>16394296
9/9 is the same fraction as 1. So you're presupposing the conclusion, but you can't prove it because it's false.

>>16394280
Are you fucking shitting me? I don't understand geometric series. They teach that shit in high school pre-cal. Sum of a geometric series is 1/(1-r) where r is the r^n of the geometric series. 3*.1+3*.01+3*.001...=.333... so r=.1 Since your starting at the second term .3 instead of 3 you multiply through by .1 so .1(3/(1-.9)=1/3. You're fucking wrong

>>16394224
>Consider:
>>it is itself different in someway
>and
>>it is itself different
>They are fully equivalent in this case. Additionally, the inclusion of the extra "itself" adds nothing to the meaning of the sentence at all, so we can remove that as well.
>In other words, you have written:
>>It is different if it is different
Wrong, it adds the meaning that we don't quite yet understand what part of it is different. And they as separate terms/things, "itself". Etc etc.

>And this ties into the mistake that you've made. The sign is NOT the meaning communicated, the sign is only a sign. 1, 0.999... are both different signs, and yet they communicate the exact same meaning. They are the products of two different sign processes that happened around the exact same meaning. Your question of difference is not one of value, but one of shallow representation.
But the words ostensibly meant something different, as do these numbers.

>>16394312
>Sum of a geometric series is 1/(1-r)
This is false. The geometric series gets very close to 1/(1-r), in fact closer than to any other rational number, but it never reaches 1/(1-r) ( assuming |r|<1). Thus you're using circular reasoning.

>>16394224
But I must say, very based post good sir.

>>16388137
Hegel would endorse
>0.9999... =/= 1
But then would say that for the self while being the creative self and not the observant one then >0.9999... = 1 would be true

>>16394301
>9/9 is the same fraction as 1
Yes, and as a matter of fact 0.(9) is the same fraction as 1. Same as 8/9 is 0.(8). And 7/9 is 0.(7). Therefore 9/9 is...... ;)

>>16394321
Omfg read the fucking textbooks I linked you goddamm idiot and stop relying on your own brain dead shit. You really think the fucking formula for the sum of a geometric series is wrong?

>>16394325
>0.(9) is the same fraction as
1.
[citation needed]
>Same as 8/9 is 0.(8)
false
>And 7/9 is 0.(7)
false.
You're literally just pulling "facts" out of your ass. You can't prove any of these.
>>16394326
>You really think the fucking formula for the sum of a geometric series is wrong
It's a good approximation, but you can't actually complete the sum and be it equal to a fraction.

>>16394335
So your denying all of calculus and real analysis. That's cool bro but why should I care about your opinion. Mathematicians have logical rigor and practical results what do you have?

If 0.999... < 1 then 0.999... = 1 - x
He would choose this one.

/thread.

>>16394335
>You can't prove any of these
But I can. Try dividing 7 by 9.

>>16394344
But you've provided no arguments from calculus or real analysis. All you're doing is appealing to authority and saying that I'm wrong. Repeating that I'm wrong doesn't make it more convincing. To prove something, you need an actual argument.
>>16394350
>Try dividing 7 by 9.
I did. I got the fraction 7/9. What's your point?

>>16394385
Wtf do you think the sum of a geometric series is from goddammit? Those were fucking calculus textbooks I linked

>>16394390
>>16394385

>>16394190

>>16394390
>read my book
How about you go fuck yourself. All of those books are wrong.
>Wtf do you think the sum of a geometric series is from goddammit? T
The sum of a geometric series is the addition of infinitely many terms which follow the geometric pattern. There is a formula for a good approximation of what the result is, but it's not equal. What more do you want from me?

>>16394396
All of those books are calculus and real analysis. All of calculus and real analysis says you're wrong

>>16394398
If you've actually read those books yourself and understood them, and if the books actually explain how I'm wrong you should be able to provide a good argument for why I'm wrong.
But you can't, because I'm not wrong and either those books are retarded, or you haven't read them or you've misunderstood them.

>>16394406
They give the formula for a geometric series. You say it's wrong calculus says it's right

>>16394412
I already said I acknowledged the formula as a good approximation to the actuals sum. In fact, it's as good of a rational approximation as you can get. But they're not equal.
You need to prove they're equal. But you can't, because they're not.

>>16394385
>I got the fraction 7/9. What's your point?
No, what I mean is, try finding out how many 9's fit into a 7. Decimally.

>>16394421
I don't need to prove shit the textbooks I listed say that the sum given by the formula is not an approximation and what I said is that calculus textbooks say your wrong

>>16394421
And this shows how fucking mathematically inept you are nothing about the formula says that it will be a rational approximation. I think it's because you saw the fraction 1/(1-r) but if r is irrational the formula result will be irrational as well

>>16394424
You're arguing like a woman.
>textbook say I'm wrong therefore you're wrong
The textbooks are wrong. You've provided 0 actual arguments for why I'm wrong. Because you're a moron.
>>16394422
0.77.... is the closest decimal approximation to 7/9, but it's not equal to 7/9, for the same reason that 0.99... is not equal to 1 and why 0.333.. is not equal to 1/3. What's your point?

>>16394434
What I've said is that calculus and real analysis textbooks say that you're wrong. Which you agree with and claim the textbooks are wrong

>>16394434
>it's not equal to 7/9
What is your proof? 0. followed by an infinite sequence of 7's is a logical conclusion to the question "how many 9's fit into a 7"

>>16394435
What I'm saying is that even if they did say I'm wrong, that's a shit argument. If they do say I'm wrong, and you've read them, you should understand why I'm wrong and should be able to explain it to me in your own words. Surely the reason they declare that I'm wrong is not arbitrary?
Or do you think mathematics is like dogma. Whatever the authorities say is true, is true. There are no higher reasons.

>>16394440
It's obvious to me that they're not equal. No matter how many 7s you add to 0.777... it will always be smaller than 7/9.
If you think they're equal, you should be able to provide a proof. But you can't, because you're a moron who doesn't know what he's talking about.

>>16394441
But you agree that all of modern mathematics says you're full of shit

>>16392188
Brain let how me where in you mind you can hold an infinite series you funking mongoloid. You can't you done even believe you can add them together because they are too big but somehow your mind made em up and they exist there.

>>16394441
https://en.wikipedia.org/wiki/0.999......
https://brilliant.org/wiki/is-0999-equal-1/
https://betterexplained.com/articles/a-friendly-chat-about-whether-0-999-1/
https://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

>>16394456
>>16394445
>appeal to authority
>random links
>0 actual arguments provided
It's like I'm arguing with beauty pageant constestants.

>>16394476
You're the one who can't understand high school level math. Do you even know what a limit is? Like the epsilon delta proof for functions from calculus. Or the epsilon N for sequences. If you don't go read about those

>>16394476
Some sequences you tell me what you think the limit is for each
[1,1,1,1,1,1,1,1,....]
[1/2,0,-1/3,0,1/4,0,-1/5,....]

>>16388157
1 - 0.999... = 0.000...
Now we just wait for the mythical 1 at the end that will never come.

>>16394524
It's going to come, or are you going to be the one who tells God you had to round it up?

>>16394443
This is dumb no matter 7s you add to 0.777 it will always be less than 0.777...
0.7<0.777...
0.77<0.777...
0.777<0.777...
0.7777<0.777...
so 0.777...<0.777...?

>>16394320
>Wrong, it adds the meaning that we don't quite yet understand what part of it is different.
Then the difference cannot be dealt with using definite cases. To understand that something holds the property of difference, it necessitates a comparison to another thing and for that comparison to yield meaning for both components of the proposition, and for those meanings to be understood as different, and thus inherently the definitive case comes with the preclusion of understanding. You have either abused the definitive case, or you have just gone back on what you have written.

>And they as separate terms/things, "itself". Etc etc.
This is false. "Itself" is a reflexive pronoun, it's syntactically binded to the nominal "it", as the object. For all of the examples to choose, picking the one syntactic element which solely exists as a coreferential part of speech seems to indicate that you have a tenuous grasp of the concept of "meaning" in the first place.

At any rate, I already laid out to you what this "difference" that you supposedly (in your own words) have trouble understanding. Perhaps a simpler example:
x = 1
y = 1
Both of these variables are stand-ins for the concept of signs, though the proposition is but a simulacra of signs and a heuristic for argument's sake. They both are assigned the meaning of "1", such that any operation on either of them is implicitly understood as an operation on the number "1", despite neither of them being the number one, and indeed being variables are not numerical literals. This is of course an analogy of the sign process, and that the sign is not the meaning (and a sign can never point to itself), but merely exists as the vessel of meaning. The meaning remains the same, only the vessel has changed.

Feel free to find a flaw in the algebra or first-order calculus, though. I've spent too much time responding to this bait already.

>>16394443
The sum of 7*(1/10^n) from n=1 to infinity is represented by 0.777... . For an arbitrarily small number there is a value of n such that the difference between 7/9 and the first n iterations of the sum (and all later iterations) is smaller than it. Therefore we can say that the sum converges to 7/9 as n approaches infinity, and since 0.777... is the completed representation with infinity "reached", 0.777... must be 7/9.

>>16388360
How dumb can /lit/ posters get? You're just straight-up begging the question. I honestly can't tell if it's satire at this point.

>>16394443
>No matter how many 7s you add to 0.777
I dont think you understand how infinite series work.

>>16394150
>>16394610
oops, I meant to respond to this post

>>16394424
you're a fucking idiot and the other guy is right. textbooks sometimes simplify things to help people learn them. when you were a kid you probably got taught that atoms were discrete as well, plenty of textbooks say it but its not fucking true.
if you can't provide a mathematical proof, then what you are saying is probably not correct.

>>16394610
>>16394727
I dont think you understand how math works. Read a book.

>>16394530
Just wait for the 1 bro. Its going to come, trust me.

Anon here who argued that 0.999... is not 1. I actually know it's fun but youre all fucking retarded for not being able to counter my simple arguments. None of you seem to actually understand why 0.999...=1. The 0.333... =1/3 proof is extremely stupid and just begging the question.
Perhaps if I get enough (you)s Ill explain why its 1.

>>16395226
>it's fun
Meant it's one. Fucking autocorrect.

>>16395216
1

>>16394150
1/3 + 1/3 + 1/3 = 3 * 1/3 = 3/3 = 1 but 0.(3) + 0.(3) + 0.(3) = 3 * 0.(3) = 0.(9) =/= 1

>>16388278
>so what is 1 - 0.9999... = ?
1/infinity, an infinitesimal

>>16394146
Lol that image is funny
>>16394345
>>16395294
1/infinity = 0, what are you guys retarded or something?

Why is it so hard for brainlets to understand that 0.9999... does not mean you keep on adding 9s to the end of the decimal place? 0.999... is a fixed number that contains an infinite number of 9s in it, no one is adding the 9s up or putting more 9s on. 0.999... can be represented by the sum(9/10^k) for values of k=1 through k=n. Simply take the limit of this sum as n->infinity and you will clearly see that 0.999...9 (n= 1 million, 1 billion, however many discrete 9s you want, and the highest number you can think of) is less than one, but the value of the number 0.999... (infinite 9s) is equal to one. Earlier I showed you a very very simple computer code that clearly illustrates this
Also, see the actual mathematic proof some anon posted above and then blow it out your ass

>>16395808
See these posts
>>16389727
>>16390034
>>16391821

Abstain from posting in this thread before reading this. https://plato.stanford.edu/entries/philosophy-mathematics/ Finitism (there is no actual infinity as in 0.99...) is a philosophical stance and therefore is not mathematics.

>>16395943
Wtf are you talking about 0.999... is clearly a finite number. Fucking hell this shit makes me doubt everything I've ever seen posted here if you shits can't even understand basic math

>>16396018
>>16396018
Yes, 1 is a finite number, but there is a infinite string of 0s in 1.000... and an infinite string of 9s in 0.999...

>>16396181
Yes, and the values of those 2 numbers are equal

>>16388204
https://www.varsitytutors.com/hotmath/hotmath_help/topics/infinite-geometric-series

Hegel supported multiple mathematical systems as being required to reach truth so he would be ok with both of them depending on the context

>>16388204
>Bottom
>Correct
It's really simple and I have no idea why it take 10 minutes for youtube mathematicians to explain why 0.999... = 1.

Just ask yourself a question. What is the number between 0.999... and 1?

The answer is... there isn't one.

0.999.... is a nonsensical number. It does not exist in reality, and unlike other numbers that don't exist in reality, as it has no theoretical use as there it's value is indistinguishable from 1.

Therefore it is just one.

I love when /sci/ crossposters come over with the bait questions and casually filter out all the pseud's here who think they're high iq but are dumbfounded as to understanding basic mathematical concepts, like the probability and the cuboid questions. The 0.999... = 1 is correct and you don't need to be taught any special math to understand why, you only need high IQ. Essentially if you put 0.999... on a number line it will be on the same point as the number 1 because there is no number in-between 0.999... and 1, so essentially 0.999... and 1 are the same number but just represented differently.

>>16396977
Also the argument from philosophy is; If two numbers are different, then you can fit another number between them, such as their average. But what number could you possibly fit between 0.999... and 1.000...?

>>16397027
0.999... < (0.999... + 1)/2 < 1

>>16397135
(0.999...+1)/2=0.4999...+.5=0.999...

>>16397135
>>16397210
Retard, go take a class in real analysis and come back.

>>16388137
. 9999... = x
9.999.. = 10x
9.0 + 0.999... = 10x
9.0 + x = 10x
9.0 = 9x
1 = x

>>16390992
what the fuck are you talking about? what is "reaching a number" do you know what numerals are. do you know that number =! numeral

>>16395049
confirmed troll
assuming what is in question is the opposite of math

>>16397362
thats a pretty nice proof

>>16398878
its the standard 'not real analysis' proof, anyone dicking about with 1/3 = 0.333... deserves to be trolled imo

>>16394280
>0.999... is also irrational
You have lost the argument.

>>16394335
no, the formula for the sum of the geometric series does not produce an approximation.

>>16394434
>0.77.... is the closest decimal approximation to 7/9
Do you not understand that the "..." refers to an infinite number of sevens? It is not an approximation. If I said 0.77, it would be an approximation, yes. But the "..." makes it not an approximation. Now, you can claim the "..." is sloppy form, and
that the number should be instead represented with a fraction, sure. But this does not mean it is not correct for 0.33... to equal 1/3.

>>16396977
You dont even need high IQ. Even that is an overstatement. It is such a simple problem that if you were to give the problem to an American grade 5 classroom the majority would get it right.

>>16388476
Wow.... what a rigorous proof... thanks for sharing your knowledge.

>>16388476
what, master, is the speed of this adding of nines? Is it possible to accelerate it?

>>16391103
>For example: the sum of 1/k^2 for values of k from 1 to infinity is pi^2/6, not infinity, even though it is being added an infinite number of times
the retardation of lit.

>>16388291
>it must be different if the notation is different
>2/6 =/= 1/3, they look different
pee pee pop poo

>ITT; Infinity and irrational number copelets

>>16388586
1 + 1/2 + 1/4 + 1/8 ... = 2
Read a calculus book to find out why. Apply the same method to the sum the other anon posted. Then you will understand.

>>16400392
How so? Prove it's rational. Protip: you can't.
>>16400403
Prove that they're actually equal though. Protip: you can't.
They're just very (infinitesimally) close. Infinitesimally close is still not equal.
>>16400437
>Do you not understand that the "..." refers to an infinite number of sevens?
Yes. 3.1444444.... (infinitely many 4s) is an approximation for pi. It's not the best approximation, but it's an approximation nonetheless. The fact that there are infinite 4s does not make it equal to pi. An approximation can have infinite decimals.
Similarly, 0.333... is an approximation of 1/3. It's the best decimal approximation possible, but it's not equal to 1/3, it's just infinitesimally close.

>>16391431
Did you miss the day of third grade when they covered multiplying decimals?

Opening this thread as a pure mathematics major is honestly the most depressing thing I've done all week. Almost 300 replies in and this is some of the most retarded shit I've ever read.

0.999... is equal to 1, there is no question to be had. There are infinitely many 9s, it never ends, so the difference 1 - 0.999... has to be zero. Yes, this can all be formulated and sorted out rigorously with the construction of real numbers. No, there is nothing practical about the number 0.999... with neverending nines, because infinities do not fucking show up in nature, ever. There is no way to interpret this, it is an abstract mathematical construction with ZERO fucking use and consequence. Fuck everyone in this thread. Fuck ever mathlet who thinks they're top shit for having completed one calculus course for their meme engineering or compsci degree.

1/3 = 0.3(repeating)
2/3 = 0.6(repeating)
0.3(repeating) + 0.6(repeating) = 0.9(repeating)
1/3 + 2/3 = 1
Therefore 1 = 0.9(repeating)

>>16391348
This is a dumb proof. You can't manipulate infinities like that.
Another example of such a dumb proof:
x= 1 + 2 + 4 + 8 + ....
2x = 2 + 4 + 8 + 16 + ....
x - 2x = 1 + (2-2) + (4-4) + ... = 1
-x = 1
x = -1.
But clearly that's ridiculous.

>>16401540
>0.999... is equal to 1, there is no question to be had. There are infinitely many 9s, it never ends, so the difference 1 - 0.999... has to be zero.
The difference is an infinitesimal, but not zero.
>Yes, this can all be formulated and sorted out rigorously with the construction of real numbers
Nobody cares. Cauchy sequences and Dedekind cuts were introduced much much after people were happily using the reals and doing real/complex analysis.
>No, there is nothing practical about the number 0.999... with neverending nines, because infinities do not fucking show up in nature, ever
This is the dumbest thing I've heard all week. pi shows up all the time in nature, and there is no way to define pi without resorting to infinite processes (usually integrals).
>it is an abstract mathematical construction with ZERO fucking use and consequence
How are you so sure about this?

>>16401542
clearly yours is false, because your infinity is not convergent,
whereas >>16391348 , the "infinity" here is convergent, hence the manipulation here holds truth.

this is high school calculus ffs

>>16388137
Hegel would endorse you being a retard anon

>>16388137
Recommend me a book on hyperreal number, foundation of mathematics, and surprising lack of care on foundation of mathematics of mathematicians.

>>16388137
>Ctrl F : hyperreal
>0 mention
What kind of wasteful dogfight have you been doing?

>>16401883
0.999...=1 in the hyperreals. Ever heard of the transfer principle?

>ITT brainlets
https://en.wikipedia.org/wiki/0.999......

>>16401952
>wikipedia say it's 1 therefore it's 1!

>>16401900
I learned it.
you can't say "0.999...=1 in the hyperreals". I know you meant it; real number is not changed, but the standard definition of the number 0.999... can be less than 1 in hyperreal

>>16401982
I didn’t claim it was 1. My intention was to make people aware of the Wikipedia article, which presents actual theories/proof instead of the garbage this thread is full of.

>>16388137
>300+ replies
The fucking state of this board

1/3 is not a number, its the closest equivalent to .3333 that humans can come up with.

>>16401540
tunnistettu

>>16391821
as if im going to read a proof where someone writes fix instead of let

>>16396229
Yes

>>16388137
>replies: 308
Guys? :(

>>16388157
>In an abstract mathematical sense the bottom would be right
You're a retard

If you're an engineer then 0.9999... = 1 because they're close enough for all practical purposes.
However, if you're a pure mathematician, close does not suffice, and you say 0.9999... is smaller than 1, albeit just infinitesimally smaller.

>>16403363
no, you don't, because you're not a retard.

>ITT math illiterate retards not realizing that they implicitly use limits when they fucking write 0.999...

Since when does Math go against logic and common sense? Did mathematicians run out of things to dwell on? If 9s in 0.9... go on infinitely, and a nine follows every subsequent nine, where exactly does it transition into 1? I have read 100 "FUCKING RETARD" replies and no one managed to prove how 0.9...=1.