this is why 0.9999... does NOT equal 1.

[@tristantheoofer2]

i just realised that around like 6 minutes i accidentally "prove" its 1 fuck 😭😭😭😭 anyways hopefully yall enjoyed this, so much shit has happened in the last 2 months, so im glad i was able to make something for yall lmao. and also this video was more my take on the 0.999... = 1 thing than anything else lmao also ofc sources and music are below sources en.wikipedia.org/wiki/0.999 - 0.999.. = 1 "proofs" www.askamathematician.com/2011/01/q-%CF%80-4/ - pi = 4 music atlantis - audionautix part 1 - douglas holmquist (from smash hit) cliffside hinson - c418 total drag - c418 beyond space - chill carrier a slow dream - emily a. sprague CORRECTIONS: ~8:10 i accidentally said "as n goes to infinity" instead of "as k goes to infinity" sorry- edit: this video has an 89.3 like to dislike ratio now- why am i not surprised lmao, especially with a topic thats so controversial edit 2: it dropped to 78 then stabilized at 81.4 lets go??

[@ItzSneakyMinecraft]

thanks for clarifying this is not the first

[@ItzSneakyMinecraft]

help i’m being araved

[@TheRealSillyWillyC]

@@ItzSneakyMinecraft???

[@Lazymediasiblings]

@@tristantheoofer2 why does IT SAY IT WAS FROM 1 DAY AGO THIS WAS UPLOADED AN HOUR AGO??!!

[@lalilolsu]

pov what you hear when your math teacher wants to say something

[@marivcenteno9444]

geometric series argument: 0.99... can be expressed as 9/10 + 9/100 + 9/1000 + ... we get the common ratio: a2 / a1 0.09 / 0.9 = 0.1 or 1/10 and the formula for the infinite sum of a geometric series is a1/(1-r) where a1 is the first terms (9/10) and r being the common ratio (1/10) so we substitute: (9/10) / (1-1/10) 0.9 / (1 - 0.1) 0.9/0.9 = 1

[@dafurious6457]

the fact that you brought up the pi = 4 thing as an actual argument shows a fundamental lack of understanding of what a limit is

[@Chris-5318]

The last five words of your comment are redundant.

[@dafurious6457]

@@Chris-5318 tbh yeah

[@Thisisdefinitelynotanalt]

As an absolute math nerd, I think the only way to appreciate this wonderful video that must’ve taken ages, is to try to argue against every point because I have nothing better to do lol. 1:06 - The ⅓ Rebuttal 0.3 repeating IS the actual exact value of ⅓. If the repeating 3s only repeated a finite amount of times, it would be an approximation. This however is not the case. There are 2 ways to prove this: Basic Division, if you were to divide 1 by 3, you would end up with 0.3 repeating And the more solid proof, Algebraic Proofs X = 0.r3 10X = 3.r3 10X - X = 3.r3 - 0.r3 9X = 3 X = 3/9 X = ⅓ 0.r3 / ⅓ 2:26 - The Number Line Rebuttal 0.r0…1 just can’t exist as it’s a contradiction within itself. The r denotes the infinite repetition of the denoted decimal places. It will never end. Adding a 1 at the end means well, there is an end, but there isn’t. Infinitesimals simply do not exist in the real number system, as they are somehow smaller than a real number while being greater than 0. This goes against the rules of the real number system. 5:54 - The “10x” Rebuttal I’m just going to repeat the previous equation I used as it essentially proves the same point as before: X = 0.r9 10X = 9.r9 10X - X = 9.r9 - 0.r9 9X = 9 X = 1 0.r9 = 1 The problem with the equation you used is multiplying both sides by a fraction doesn’t necessarily change the equation, it’s usually used for simplification. The 1 after the infinitely repeating decimal issue occurs again as well, as with this number, we can an equation like this: 9 = 8.r9…1 Which doesn’t make much sense. 6:54 - The Calculus Rebuttal Now I haven’t reached calculus, so feel free to correct me if I’m wrong. I'm just shooting my best shots lol. First, ignoring the calculus stuff for now, we run into the whole 1 after an infinitely repeating decimal problem again. Which is something that just cannot happen. From what I’ve gathered from random youtube videos like these though, this is what I would do: I would do the n = (amount of 9s) thing, but displayed as an infinite geometric series like so 0.r9 = 0.9 + 0.09 + 0.009 … First term would be 0.9 (a), and the common ratio being 0.1 (r) S = a/(1-r) The sum of our infinite series would then add up to 0.9/0.9 which would equal to 1. Limits still could be used, either with an infinite geometric series again, or even by the use of the equation debunked in the video! The reason being 0.r0…1 isn’t a valid solution to the limit as it can’t really exist, at least in the real number system. If you somehow made it here thanks for reading my random night time ramble about something pretty miniscule in the grand scheme of things, and I just wanted to make it clear this wasn’t to hate or put down any work done. It’s very cool to see someone put this much effort into editing and all the work for a math video. I just wanted to add my thoughts to it, that's all. 😁

[@chasingcheetahs5017]

A lot of the arguments in this video are also fallacious, with a few general patterns: Several of the arguments are misrepresentations (strawman) of mathematical ideas in order to refute them. Some of the arguments have conclusions that do not follow from the premises (non sequitur), rendering the argument incoherent. Several of the arguments are assertions based on intuition, with the assumption that because the video maker cannot understand how something were to be true, it must therefore be false.

[@memelobby0]

Ill explain why youre wrong here on the numberline The argument that "there must be a 1 at the end" of 0.999... misunderstands infinity. 0.999... means the 9’s repeat forever, so there is no end where a 1 could be placed. Infinity doesn’t work like that- you can’t finish an infinite sequence and then add something afterward. The idea of a "1" at the end (like 0.000...1) is nonsensical, as no such number exists in the real number system. Algebraically, 0.999... = 1, and there’s no gap between them. The supposed 1 "at the end" is simply not possible. The idea of a "1 at the end" of 0.999... is impossible because there is no end to an infinite sequence. By definition, the 9's go on forever, so there’s never a point where you can add a 1. The argument assumes infinity is something you can eventually reach, but infinity doesn't work like that-it keeps going without stopping. The concept of 0.000...1 (infinite zeros followed by a 1) is mathematically invalid because you'd never actually reach the 1 after infinite zeros. Plus, in real number math, 0.999... equals 1 exactly, with no gap. The same goes for you trying to disprove the algebraic proof, you cant jus stick a 1 at the end of an infinite series. and the problem with the calculus argument is already at the start.. the idea that 0.999... is only "approaching" 1 but never "reaches" 1 misunderstands how limits and infinite series work in calculus. Yes, 0.999... is an infinite decimal that gets closer and closer to 1, but the key point is that in the limit, it equals 1. In calculus, when we say a number "approaches" a limit, it means the value gets arbitrarily close to the limit and eventually equals it. There's no difference between 0.999... and 1 because the infinite sum converges to 1, meaning they are mathematically identical, not just "close."

[@tristantheoofer2]

fuck i thought approaching didnt mean legit eventually equaling something- but in that case... how would is equal EXACTLY 1?? and wouldnt that definition of approaching essentially mean "this is close enough to where we can say its this"? like thats a genuine question. because arbitrarily close doesnt seem like it *could* ever equal anything specifically

[@memelobby0]

@@tristantheoofer2 "approaching" a number means that as you get closer and closer, the difference between the numbers becomes so small that it's effectively zero. When u say 0.999... "approaches" 1, it doesn’t just get close to 1-it becomes 1 exactly because there's no real number between 0.999... and 1. It’s not a case of “close enough”-in the case of an infinite sequence like 0.999..., the sum converges exactly to 1. When we say "arbitrarily close," we mean that for any tiny gap you imagine, 0.999... will eventually fill that gap entirely. The difference between 0.999... and 1 is not just small-it’s zero. So, in mathematical terms, they are equal, not just approximately the same. It might seem weird, but that’s how infinite sequences work: they reach their limit, and in this case, the limit is exactly 1

[@MozzarellaWizard]

Holy essay

[@gandalfthemagenta7364]

@@tristantheoofer2 it is not true in all cases, like lim(x->0)1/x=1/0 is not true, but in the case of lim(x->infinity)1/(10^x)=0 is true because there is no paradox.

[@ChloeDaVoir]

I don't mean to sound like a smartass, but, what about ordinal numbers? With ordinals, you can have things like "infinity + 1", "infinity + infinity", and so on. To say you can't have infinity and then add something at the end is only a limit of cardinal numbers, not ordinals.

[@betterert]

me when the rigorously defined and universally accepted truths about limits and geometric series give me an answer i dont like:

[@tristantheoofer2]

whar

[@betterert]

@@tristantheoofer2 the step you dont like about the "calculus argument" is just a proven thing about geometric series

[@Ryann9]

This is literally everyone when they hear about the Four Color Map Theorem

[@bronsoncarder2491]

...This isn't a debate. This is a mathematically proven fact. Literally the only thing this video can possibly be about is how you don't understand it, so I guess I watch that. lmfao "I don't feel this is true." This is literally where you start. Your conclusions are flawed because they are based on your biases. Ok, and the first "argument" that you "debunk" is just an illustrative example and not an actual proof. And it's looking like the second one is too. I agree that there are flaws with these examples, but disproving them doesn't affect the larger argument in any way. Yep, third argument too. These are not proofs. You need to start with learning what a mathematical proof is, and how to understand them, because you clearly don't even have the basics of the background to be approaching tackling this problem. These are not proofs, they're illustrations, and yes, they're poorly constructed ones. If these are the only arguments you've seen, and you've never seen the actual proof... no wonder you don't understand or believe this.

[@andynilsennot4329]

ok no i am not going to start a argument again i am NOT

[@toastey9756]

@@andynilsennot4329 ok but it is literally not an opinion?

[@Invy-PT]

@@andynilsennot4329 It's not an opinion it's a wrong answer.

[@hata6290]

Parents no love 😂

[@GuyllianVanRixtel]

prove it

[@Bill_W_Cipher]

3:27 You're completely right in this part of your argument. After a finite number of iterations, no matter how incredibly large that number would be, you would always arrive at a number that is above zero. However, this process is not supposed to be finite. If you were to do this process infinitely many times, you would arrive at zero. However, you might object to this logic saying that you can' complete an infinite process. And that's a perfectly valid statement. So, let's try doing this process a finite number of times, like 3 times. You'd get 0.001. With 4 iterations you would get 0.0001. With 5 iterations you would get 0.00001. As you can see, we're continually subtracting numbers from 1, so we're either converging on a number or drifting off to negative infinity. We can prove that we are not approaching negative infinity with a pretty simple proof. Lets represent this process with the equation 1-x=h. x represents the number we are subtracting by and h represents the result. x is always going to be smaller than one, since all the digits to the left of the decimal place are always zero. And when you subtract any positive number by another smaller positive number, the result will always be positive. Therefore, this process can not drift off to negative infinity. The only other option is that it is converging on a number, and the question is, what is that number. Since the number in this process is getting continually smaller, once we drop below a given number, we will never again reach it. This implies that 0.1 is not the answer, since we get below this number on the 2nd iteration, with the result being 0.01. But that isn't the answer either, since we get below that on the 3rd iteration with 0.001. And neither is that the answer since we drop below that on the 4th iteration. So this means that if we can prove that 1. Zero is the highest number it will never drop below and 2. Once you drop below a number, you will never reach it or a higher number again. we have proven that 0.9 repeating is equal to 1. (This next part gets a bit difficult to follow) Lets take another look at that equation from earlier (1-x=h). What we need to show here is that h can never drop below zero given that x is a number between 1 and 0. This given statement can be written a bit more algebraically with 1>x>0. Well, since x is always less than 1, if we plug 1 into the equation, we should get a result that is less than or equal to zero. And if you do that, you get 1-1=0, which is obviously true. This implies that plugging in a number greater than 1 will give you a negative number, which is not allowed. Therefore, zero is the highest number it will never drop below. That just leaves us with the second statement to prove. Well, by definition of the problem, each number we plug in for x is larger than the number in the previous iteration. And if you take a constant and subtract it by a number that is getting larger, the difference will be getting smaller. Therefore, we have proven the second statement true. And just like that, we have proven that 0.9 repeating is precisely equal to 1. It's not an approximation to one. Its exactly one.

[@tristantheoofer2]

but how do you get EXACTLY zero??? like, genuinely exactly 0. i could see how its a very small amount ABOVE that, but not EXACTLY that

[@Bill_W_Cipher]

@@tristantheoofer2 You never do. No matter how many iterations you complete, it will always be barely above zero. And you can't finish an infinite process. But you can get arbitrarily close to 0, and remain at least that close to 0.

[@tristantheoofer2]

.. but thats not equal to zero in that case. how specifically is 0.999... 1 if zero doesnt *necessarily* mean zero in that case?

[@Bill_W_Cipher]

@@tristantheoofer2 I'm not exactly sure how to best explain this. I'm a calculus student, not a calculus teacher. All I can say is that limits have different axiom systems than normal arithmetic and algebra. I understand if you don't feel that answer is fully satisfying and coherent. I just don't know how to better explain it.

[@mausengonmned-5258]

Yeah this is why they say infinity isn't a number @tristain it is a concept

[@entityredstoneonyt]

Repeating decimals are just used to convey x/10 + x/10^2 + x/10^3 and so on, or maybe in special cases, 142857/1000000 + 142857/1000000^2. With this, you can't add a one to the end o an infinitely repeating decimal because that is not how they are defined. They are defined as the number that is approached by a finite number plus an infinite sum of a number over a power of and multiplied by increasing powers of a finite power of 10. If we put 9/10 + 9/10 * 1/10 + 9/10 * 10^2... so on and so on into the geometric sum, we get (9/10)/1-(1/10), which means the sum approaches 1. You are correct, simply the sum x/10 + x/10^2 + x/10^3 ... doesn't get you 1, but approaches it. However, the same can be said for 3/10 + 3/10^2... [approaches 1/3]. The way repeating decimals are defined, it is the number it approaches that is the final value. Nobody even says, '0.333333333 approaches 1/3,' but they say it IS 1/3. Therefore, yeah, 0.999999.... is one bc it's infinite sum approaches one. This sort of stuff is why i hate decimals and think fractions are better. We can't convey normally any fraction where the denominator isn't prime-factorized into only 2s and 5s, and the only way we can do so is making 'repeating decimals', and using infinite sums and stuff, when it would be much easier to just say, for example, 1/3. Also, in the 10x proof, you forgot to explain why 9x = 9. It is not a given, it is what was trying to be proven. if 9.9999 is 10x and x = 0.99999, in 9x we just remove the repeating 0.9999... from 9.99999.... and end up with 9.

[@Chris-5318]

That was twaddle. If 0.(N) represents the n digit decimal string N being repeated, than 0.(N) = N/(10^n -1). e.g. 0.(285714) = 285714/999999 = 2/7. As algebra confuses you, try this: 10 * 0.999... = 9.999... => 9 * 0.999... + 0.999... = 9 + 0.999... => 9 * 0.999... = 9 => 0.999... = 9/9 = 1 Try representing Pi as a fraction. Then explain why you prefer fractions to decimals.

[@hhhhhh0175]

one formal definition of the real numbers in math is equivalence classes of cauchy sequences, or if you haven't taken 2 years of mathematical analysis, basically the set of all ways to approximate a number using rational numbers. so cauchy sequences that could "belong" to the real number 0 could be (1, 1/2, 1/3, 1/4, ...), (0, 0, 0, ...), or (1, 2, 3, 0, 0, 0, 0, 0, ...). the fact that any finite decimal can't exactly equal most real numbers is practically built into this defintion, because mathematicians don't want to use a number system where there technically isn't 1/3, only approximations. so when people say 0.999... = 1, they're using the formal definition of equality for real numbers: do the cauchy sequences approximate the same number? and yes, 0.999... and 1 both approximate 1, so they are the same real number (in detail, the notation 0.999... is defined to mean the sequence (0.9, 0.99, 0.999, ...), which is cauchy because it's made of rational numbers and approaches 1)

[@tristantheoofer2]

ok

[@scares009]

This is probably the best explanation out of all the comments. A bit brief on the details, but of course you can't expect to teach people about completeness in a KZbin comment! For anyone curious to read more about this kind of stuff, you can try looking up some of the axiomatic constructions of the real numbers. They delve into all these sorts of things, and they give you the mathematical lifting power you need to dispel these sorts of confusions :)

[@jamielus]

if it equalled 1 then it would be called 1

[@tristantheoofer2]

i mean ok then-

[@HFIAPY]

Fr 0.999999… is not 1 bc it's 0.000000…001 smaller than 1 therefore it's not 1

[@POverwatch]

@@HFIAPY Except that the 1 at the end of those infinite zeroes doesn't exist because it's infinitely small. What else is infinitely small? 0.

[@melee-built_centipede]

2-1 isn't called 1 tho

[@gavengasper3456]

​@@POverwatch0.000...0001 /still/ is infinitely small, however, it is still bigger then 0.

[@ombrathefurry]

Every time you post a video like this, I understand little to nothing upon watching it, then it all suddenly clicks two days later when I’m trying to fall asleep at 11:00 at night - great work as usual, I always learn something new whenever you share these sorts of things! :)

[@tristantheoofer2]

ty lmao- ive had a shit ton of people roast me in the comments though cus apparently im kinda wrong or something

[@ombrathefurry]

@@tristantheoofer2 even though you might be wrong in their eyes, I found I still learned a lot anyways :)

[@omnirubix]

> tristangent uploads > watch video > understand nothing > still happy and joyful

[@tristantheoofer2]

lmao that is so real

[@EyeWasBored]

real asf

[@trueuniverse690]

@@tristantheoofer2 Also you can not consider infinite as a number, 0,999... does not have a number as a gap, there are bigger infinites but they are still infinites

[@felixtheanimator5516]

ok, what's next? 0.5 ≠ ½? 💀🙏

[@KananR-ns9jv]

I only knew the 1/3 and the 10x argument before this

[@AsiccAP]

0.999 repeating does equal 1, at least when working with real numbers. Easiest way is the 10x argument that you just "debunked", let x=0.999999999 repeating, then consider 10x. 10x=9.999999999 repeating. Now consider 10x-x. it is 9.99999999999 - 0.99999999999, which is precisely 9. as 9x=9, x=1. Contrary to what you're saying, it does not assume 0.9999999=1 to begin with, we simply let it be x and prove that x is 1. Again, we are working with real numbers, so the argument that 1-0.99999999 is an infinitesimal number does not work. Infinitesimal does not exist in the real numbers, therefore 1-0.9999999999 is regarded as 0 in the reals. 0.9999999999=1. Also, you are fundamentally misrepresenting the concept of limits. Look up the epsilon delta definition of limits. Using the definition, we can prove that limit of 1/10ⁿ as n goes to infinity does, in fact, equal to precisely 0, not some really really small number (again, there are no infinitesimals in the reals) TLDR 0.999999=1 in the real numbers, by the 10x argument and limit argument. the 10x argument doesnt assume 0.999999=1, and when in doubt, limits shouldn't be done intuitively, but rigorously using definitions. So what now? I'm right and you're wrong? Not exactly. I have just enough knowledge in the real numbers to confidently say that I'm correct and 0.9999999=1 in the reals, but you bring up an interesting concept: infinitesimals. Introduce that to the reals and you get new number systems, including surreal numbers and hyperreal numbers. And I don't know anything about them, and you may be proven correct in those number systems. You may be right afterall, just not in the real numbers.

[@tristantheoofer2]

honestly fair enough with that, especially the whole limits thing i suppose. this also would mean we are both correct but in seperate ways. in that case what would 0.999... be? a stupid representation of 1??

[@AsiccAP]

While I fundamentally disagree with you on this video, please keep in mind that this isn't personal, and I think it really echoes back to the community post you made about one or two months ago: that 1+2+3+... equals -1/12. It's a genuinely interesting to think about it and considering different worlds or definitions where the equality will be true. Same thing here. 0.999999=1 in the reals, but what if it isn't? We get infinitesimals and new number systems. You may have made some interesting points that while sadly doesn't work in the real numbers, work in some other systems.

[@AsiccAP]

@@tristantheoofer2 after some research, you will be right in the hyperreals, and I think indeed, there are infinitely many numbers between the two.

[@chrisharlem5912]

@@tristantheoofer2 exactly that, it's a stupid way to represent 1 (although it can have uses - a common way to give each decimal a unique representation is to choose a non-terminating sequence)

[@tristantheoofer2]

ok so this is a technically correct kinda deal

[@cheryldelguercio4177]

As a tristangent fan, I can confidently say that I understood about 0.999% of this video.

[@tristantheoofer2]

why is this so accurate bro 😭😭😭😭😭😭😭

[@wqrw]

same

[@cheryldelguercio4177]

@@tristantheoofer2 probably because I am, in fact, a fan of yours lol

[@jollytronvr4486]

So about 1%

[@Fire_Axus]

StGeSoEm

[@0777coco]

let me clarify first and foremost that i am all for critically developing mathematical intuition as it is one of my very own favorite occupations, however as it stands this video is next to dangerously misleading. going into any problem with the predetermined rejection of the result is a cardinal logical fallacy and may lead to viewers stumping their curiosity on a topic, stubbornly clinging to opinionated denial versus open-minded interest in learning. far were it from me to say i understood algebra, so maybe as a layman i can suggest the following gateway: 0.99... = 1 "for all intents and purposes". it is not exactly a fundamental principle of math, but more so a conclusion of set proofs. hence even disagreeing with their practices, if you wanna get philosophical about it, what they really proof is that in the respective mathematical fields there is simply no known reason whatsoever to detest the conclusive assumption for the sake of progressing research. furthermore having such baselines enables accessibility and an overarching agreement through which scientific findings can be compared and linked. the argument about how infinities work is also to be made, as others here have pointed out. there just is no end to the 0s where we could eventually put the 1. that's precisely why there is no gap to be found. i see where you're coming from with the argument regarding approaching terms - as far as numbers in-between go, it stands, but in presence of unfathomably large or the abstract infinitely sized, we circle back to the safety net of necessity. i really hope to not come across as condescending or so here, i truly enjoyed the vibe of this video! so hey maybe if you can find an instance wherein there is an important distinction to be made between 0.99... and 1, that could be quite revolutionary! it is still an ongoing field of research after all :) if you like, i can search and link some videos that i found helpful before as well

[@tristantheoofer2]

actually if you could link some videos that would be pretty awesome

[@tristantheoofer2]

also i did NOT mean to dangerously mislead people holy fucking shit-

[@tristantheoofer2]

@Spectral_RotD bruh im literally a nerd myself tf are you on about- you also literally walked into what is essentially an argument over a fucking number, of course the whole comments section will be nerds

[@soulsmanipulatedinc.1682]

My favorite proof for this is simple. Proof by contradiction. If 0.9999 != 1, then either 0.9999... < 1 or 0.9999... > 1 must be true. Since that is the case, there must also be an open set of points inbetween (0.999..., 1) that includes a values between 0.999... and 1. This is the "gap" you were talking about. To find the middle (which is guaranteed to be inside the above-defined set of points), we can add the numbers and divide the result by two. (0.9999... + 1) / 2 = (0.9999... / 2) + (1 / 2) = 0.49999... + 0.5 = 0.99999... Thus, the mid point in the open set (0.9999..., 1) is 0.9999... But, 0.9999... was excluded in the set (0.9999..., 1) [as it is an open set], so that doesn't make sense. How can an end point be the midpoint? Now, this is already a contradiction. But let's keep going. If (0.9999... + 1) / 2 = 0.99999..., then => 0.9999... + 1 = 2 * 0.9999... => 1 = (2 * 0.9999....) - 0.9999... => 1 = (2 - 1) * 0.9999... => 1 = 1 * 0.9999... => 1 = 0.9999... Hence, a clear contradiction. Our previous assumption that 1 does not equal 0.9999... must have been wrong. Therefore, by proof of contradiction, 1 = 0.9999... ...within the real numbers, of course.

[@tristantheoofer2]

woah, ok this is something i legitimately can see having merit. in a sense yeah i actually agree with that. good proof dude

[@soulsmanipulatedinc.1682]

@@tristantheoofer2 Also, similarly, ...99999999.0 = -1, since ...9999999 + 1 = ...000000 = 0, thus (subtracting 1 from both sides) ...999999 = -1. ...9999 * ...9999 = ...000001 also. Feel free to divide or exponent. It has the same value of 1 no matter what you do. Hence, ....9999999.99999999... = 0. :P Also, ....99999998 = -2. ....444443333 = 1/7. 0.499999999... = 1/2 = ...555555.5 = 0.5. Etc. It's like there is a form of built on infinite-base modulo to the real numbers themselves. It's counterintuitive, yes, but that's just how it works when you are working with infinity. Infinity is such a concept where you can say "I have infinite rooms, and all are filled. There is no more room for anyone else to enter" and, yet, someone else enters anyway. Infinity is such a concept that 1 - 1 + 1 - 1 + 1 ... = 0.5. Infinity is such a concept that infinity * 0 can equal anything. Even my mother (only half joking). Infinity is such a concept that all our mathematical operations are not defined to be capable of using it. ...because infinity is not a number to begin with. It's like adding one to an apple. We have to add extra definitions to even make it work. Then, if course, there is the nullity concept...which is even worse...somehow. *Edit:* Another increasing thing... ...5555555555.0 * 2 = ...0000000000000 = 0 However, ...555555555555.0 * 3 = ...5555555555555 So, if x = ...555555555555555555, and k is an integer, then... x * 2k = 0 and x * (2k + 1) = x. Yet, again, another example of why infinity makes everything weird.

[@tristantheoofer2]

ok so basically this number kinda acts as an overflow point for the reals??? fuck thats way cooler than i expected

[@soulsmanipulatedinc.1682]

@@tristantheoofer2 OH, WAIT! Sorry, I made a mistake. ...555555.5 * 2 = ..1111111111.0 = -1/9 So, ...5555555555.5 = -1/18. Also, ...55555555.0 * 2 = ...11111111110.0 = -10/9 Again, sorry for misinformation. This is just a confusing topic.

[@tristantheoofer2]

@soulsmanipulatedinc.1682 w h a t ok thats even more confusing than ...999.9... being -1. how the fuck

[@JamesMcCullough-lu9gf]

10:47 correction: NONE of these arguments can be used to disprove 0.r9=1. As for your numberline argument, I am going to use a slightly different one. Can you find any number between 0.r9 and 1? because if 0.r9 and 1 are real numbers and not equal, you should be able to. However, simply adding digits after infinitely many 9s breaks the literally definition of infinity: without end.

[@Chris-5318]

The video poster doesn't care that he is deluded and wrong.

[@tristantheoofer2]

@Chris-5318 dude youve commented on so many peoples comments that i think youre the one whose deluded atp

[@JamesMcCullough-lu9gf]

@@tristantheoofer2 what does atp mean

[@Chris-5318]

@@tristantheoofer2 LOL. That's vey funny. Try dealing with the math arguments that show that you are wrong, and that 0.999... = 1 is right.

[@Chris-5318]

@@tristantheoofer2 I'd be deIusionaI if, like you, I disagreed with several million degreed mathematicians, and made arguments that are pulled apart by anyone with a modest understanding of Calculus 2.

[@Wettham77]

Howdy, what you are describing appears to be the hyperreal numbers. While this is a valid number system it is a completely different number system to the one that most people usually use (standard real analysis). So the real answer to this question, like many in math is yes and also no. Yes, you can technically use Infinitesimals to get this result but saying that it doesn't equal 1 is probably a bit of a weird take in my opinion to call the more common math system "wrong", but it could be fair to conclude that in some ways it is kinda both (math can be weird like that). I'm not the most knowledgeable in this area so I would recommend looking into both systems to see the differences and how everything works for yourself. What I do know however is limits and a LOT of math relies on similar usages of limits which are considered by the entire math academic community to be well proven. Most of your arguments aren't necessarily the most sound and come from a misunderstanding of limits. To disprove limits you have to look at the reasons why limits exist and why they work and then disprove something there, which I would recommend to be an extremely tall task as something nearly unanimously agreed upon by mathematicians. Math often has situations like this, people assume its one field or that there is one true way to do math when this really isn't the case. *disclaimer* I am nearing the end of my second year as a math major in university and consider myself fairly decent at math, however, this is not a field I have studied. I looked into it a bit after watching this video but I could be incorrect, don't take my word as law, I would recommend looking into hyperreal and standard analysis yourself and seeing the differences there

[@tristantheoofer2]

before i dropped this i didnt even know the hyperreals were a thing- and also, why cant hyperreals and reals be in the same system? would it just... break shit? or what? and the fact that the actual answer is both is somehow not surprising to me actually... cus of course it is

[@AsiccAP]

I'm curious, what fields of math do you study? I need some advice in becoming a math major, so I'm wondering what courses I should take in University.

[@Spectral_RotD]

N E R D

[@ElPeloXD]

​@@tristantheoofer2 reals are contained inside hyperreals (every real number + infinitesimals and infinites = hyperreals)

[@Pixelgd_5821]

Maybe the real 0.r9 is the friends we made along the way

[@NeutronGD_OFFICIAL]

Pixel. I didn't expect you to comment here.

[@tristantheoofer2]

@NeutronGD_OFFICIAL this guys been watching me for a while

[@CuongTruong-cb3mk]

can you guys shut up

[@Pixelgd_5821]

@@CuongTruong-cb3mk no!

[@pixelatedguy]

Hello, ​@@Pixelgd_5821 .

[@Bill_W_Cipher]

A lot of your arguments here rely on the claim that 0.0repeating1 is greater than 0. So lets assume this is true. What would happen if we add this number to itself, which is the same thing as doubling it. We would get 0.0repeating2. Now lets repeat this process again. We would get 0.0repeating4. Now lets do it again, and again, and again. If this number really is greater than 0 like you say it is, it should eventually reach a number above 1 performing this doubling process a finite number of times. But it doesn't. No matter how many times you complete this process, it will have infinitely many zeroes before its other digits, meaning that it is less than 0.

[@tristantheoofer2]

"less than 0" how would this be less than 0? anyways.. i see how you have some point here actually... im starting to see how i may be wrong actually

[@cater_piler]

what is 0.000...1 times infinity then? would that just be 0.000...99999...??? how would having two repeating sequences in a decimal even make sense whatsoever???

[@Bill_W_Cipher]

@@cater_piler You don't multiply things by infinity in mathematics. Infinity is not a number, but an idea. But if you were to multiply it by infinity, any number above 0 would be a valid solution, which is a problem, because you could then "prove" that any positive number is equal to any other positive number.

[@Spectral_RotD]

NEEEEEEEEEEERRRRRRRDDDD

[@zander513]

@@Bill_W_Cipheralon Amit quora post Debunked you

[@cyancoyote7366]

I will have to disagree with you on this video. This is not an argument. I encourage you to dive deeper into calculus, and especially something called Real Analysis. Starting from a few, universally accepted axioms, the calculus proof is valid and consistent with the framework of mathematics underlying it. If you ever studied Real Analysis, heavily recommend it by the way, you will realize that limits, convergence, etc... are extremely rigorously defined concepts. If something approaches 0 as, let's say, x→∞, then the limit just equals infinity as it cannot technically be anything else! This is what the whole saga of ε-δ proofs are all about. They say that no matter how small of a value you throw, I can compute a formula that will always give you a smaller value. Therefore there is proven to exist a formula that will, if applied iteratively, will always give you 0, if the limit is 0. If you want to disprove these, you will need to disprove a few hundred years' worth of accepted theorems.

[@braincell2020]

his knowledge about calculus is basic calculus 1 knowledge, i wont really recommend real analysis too much to a person at that level..

[@zander513]

Why are you using infinitesimals? They aren’t real numbers they are hyper real numbers (which means that 0.R9/Infinitesimal = 0.R9/0 = Undefined) while 0.999999999999… is. Also 5:30 is finite because Just because a number has infinite digits doesn’t mean it’s infinite, I can add 1 to 999999999… and it will become 100000….. or multiply 1000…. By 2 to make 20000…

[@canadashorts7740]

"I'm breaking up with y-" BABE SHUT UP TRISTANGENT UPLOADED

[@tristantheoofer2]

lmaooooooo

[@jakfjfrgnei]

@@tristantheoofer2 did you know uranium glass is safe as long as you dont grind it up and snort it?

[@JahmazeJahmaze]

@@jakfjfrgnei worlds most wild acid trip

[@aTtsb]

​@@jakfjfrgnei but that is why uranium glass is fun

[@Plasma885]

Relatable

[@NoOne-zv8mc]

Honestly i think its just a quirk of how we do math

[@Chris-5318]

I suppose you're right if you think it's a quirk that 2/5 + 3/5 = 1 = 3/7 + 4/7

[@magma90]

These are good arguments if you assume infinitesimals, however the real numbers do not have infinitesimals. If you have a system of arithmetic with infinitesimals, you can arrive at 0.999…≠1. To properly work with this, we have to define what we mean by decimal expansions. If we define the decimal expansion of 0.a_1 a_2 a_3…=Σ_{i=1}^{infinity}(a_i/10^i), and we also assume that the real number the sequence of partial sums converges to is the value of the infinite sum, we end up with 0.999…=1. If we change from the real numbers to a system of infinitesimals, then we could have the sum not converge to any value and therefore not exist, or the sum might converge to 1-ε where ε is an infinitesimal number. The proofs that you said were not correct are false in the axioms you were using, however they are true in the standard axioms of the real numbers.

[@tristantheoofer2]

ok i see

[@Zejgar]

Yet another case of mixing up "arbitrarily many" and "infinitely many". Hopefully it's been a good learning experience for the author of the video.

[@Chris_5318]

The author has learnt nothing and has no intention of learning anything.

[@zensoh887]

If 0.9999… ≠1 then 1/3 is impossible

[@lolwutttzz]

exactly

[@Chris-5318]

@@lolwutttzz Please explain.

[@somedudewatchingyoutube9163]

@@Chris-5318 1/3 =0.333… 2/3 =0.666… 3/3 = 1 but since 3/3 is 2/3+1/3, or 0.33… + 0.66… which is 0.99… (Not 100% sure about this explanation)

[@Chris-5318]

@@somedudewatchingyoutube9163 I know the math, what I don't know is what either zensoh887 or lolwuttzz are actually saying. My current best guess is that they agree that 0.999... = 1 and 0.333... = 1/3. I have no idea what "1/3 is impossible" is supposed to mean. The problem really is they express themselves so badly (lazily) that I cannot easily decide what that are trying to say.

[@lolwutttzz]

@@Chris-5318 Im saying that if that 0.999... cant be one then 1/3 can be 0.333...

[@scares009]

While there are certainly problems with the video, I think you have a genuine talent for critical thinking and I encourage you to keep at this sort of stuff

[@tristantheoofer2]

hehe ty :3

[@Chris-5318]

@scares009 I hope you were being sarcastic.

[@scares009]

@Chris-5318 Don't you have anything better to do than continue to spread negativity in this comment section? You've already replied to, like, half the comments here; you've made your point. I'm a fourth year math/CS student. I'm well aware that this video is flawed. I'm also aware that thinking about these sorts of concepts is the only way for anyone to truly grasp them. The video demonstrates a lack of understanding in certain concepts, yes, but it also demonstrates that the creator is able to think deeply about concepts and present their ideas. No, it isn't perfect, but with time and some reading, it's clear to me that they could produce some seriously good stuff. You're not helping anyone by religiously correcting/mocking every comment this video gets

[@Chris-5318]

@@scares009 The video is not flawed, it is abysmally wrong. The author has not understood the topic at all and actively ignores any help offered. I'm not spreading negativity, I'm trying to stop the spread of misinformation and ignorance. Haven't you got anything better to do that encouraging the spreading of false information and very bad math and validating the perpetrators of that?

[@Chris-5318]

@@scares009 I note that you were too busy being condescending to the video poster to actually state what the problems are or provide any help.

[@maika405]

roblox youtuber versus decades of renowned mathematicians.

[@tristantheoofer2]

eh not really. its just my take on the whole thing and even then the entire reason the debate exists is because of how you can interperet the proofs different than someone else. either way the algebraic proofs are bullshit

[@maika405]

@@tristantheoofer2 at this point it's not really a debate among academics, more so the general population and mathematicians. the algebraic proofs are logically sound and easy to understand, but disagreeing with the logic of a proof obviously renders it false, anyone can do this. the algebraic proofs have their place, and I would certainly not discount them altogether. they serve as an easy way to conceptualize the issue based on widely accepted prior knowledge.

[@blocc0]

@@tristantheoofer2 the algebraic proof does kind of suck, but its because the algebraic proof is an artistic way of explaining it, most likely designed for people who are still learning algebra. you should also look how if you try doing ...999 + 1, you get 0. this means ...999 should equal -1 which makes no sense, which means the algebraic proof for 0.999... is also wrong

[@tristantheoofer2]

@blocc0 isnt that smth with p adic numbers or whatever theyre called

[@blocc0]

@@tristantheoofer2 i tried using it as an example on why algebraic proof makes no sense, as algebra is already flawed with numbers that use infinity

[@sinom_00]

Amid the comments pointing out mistakes, I want to say that asking questions and starting debates (with an open mind at least) is a good thing to do. Its an opportunity to think more critically and learn something new. I just hope people aren't to mean about it, and that you aren't discouraged from sharing what you think in the future. Its certainly not something I would be brave enough to do, and that's honorable in it's own right.

[@PFnove]

3:31 do not let bro know about calculus

[@oforkel]

Me after giving out fake info on the internet be like

[@oforkel]

Ok, I step back in my words, now I m actually confused and capable of losing my night searching for answers

[@tristantheoofer2]

@oforkel ... and this is why this is so controversial lol. you search for answers and depending on what makes more sense to you you go with it does or does not equal 1

[@trueuniverse690]

Watching veritasium's video about infinity will explain this question

[@senshtatulo]

Your intuition doesn't trump a mathematical proof.

[@theguywhoaskedyoutube]

these comments are just diabolical😭

[@tristantheoofer2]

FR BRO 😭😭😭😭😭

[@Dummigame]

Um, actually _puts on tinfoil hat_ *insert essay about how not one is one*

[@Fire_Axus]

StGeSoEm

[@gett_]

they kinda interesting tho

[@secondaryrainau]

very intresting

[@VoidInstructions]

i think you accidentally reinvented hyperreal numbers in this video with all those talk about infinityth decimal places lol did you know that there is actually a term for infinitely small values? they're said to be infinitestimal and is basically what dx means (take this with a gigantic grain of salt since i'm parroting wikipedia). the hyperreals basically add an infinite value - let's call it ω - to the reals and let you do algebra with it. i am not sure what 0.r9 would equal in this, but i think it's definitely not 1, and if we say that 0.r0...1 is 1/ω for now then we get a nice representation of 0.r9 as 1 - 1/ω that part where you mentioned 0.r0...r9 and 0.r9/0.r0...1 especially made me think of the number set, as if we use our prior assumptions they're easily representable as 1/ω - 1/ω² and ω - 1. there are indeed infinite numbers between 0.r9 and 1 here! that said, this explanation of your thought process falls apart during the 10x argument section, as 0.9(10 - 1/ω) is 9 - 0.9/ω, not 9 - 9/ω which is what 8.r9...1 would be. -9 - 0.9/ω requires that that 1 be at the "infinity minus 1st" position, which i have no idea how to represent in this ad hoc system.- nvm it's just 8.r9...01 all in all i think you should get a better understanding about infinity and stuff - a good starting place for gaining an intuition about infinity would be hilbert's paradox of the grand hotel, which ted-ed has a really good video about (that video opened my elementary school, precocious, deeply uncracked at the time eyes to the wonders of infinity. seriously you should give it a watch). love your vids still keep up the good work

[@VoidInstructions]

just realised immediately after writing this comment that many people already mentioned the hyperreals now i wanna bury myself in a hole

[@Chris-5318]

@@VoidInstructions FWIW dx is not usually considered to be an infinitesimal. It is much more common to treat it as a differential, and that is just a real number.

[@Ryan_Alt-p7n]

Genuinely it is the difference between theoretical and practical. Like theoretically 0.r9 does not equal 1. Practically it can, at least in a statistical sense . A probability of 0.r9 for example would be represented as “approximately 1” or “approaching 1”, and generally a probability cannot be 1 in any practical sense. The theory is sound that they are not equal, but of course practically approaching 1 is practically equivalent to 1.

[@tristantheoofer2]

ofc ofc, and i agree. 0.r9 PRACTICALLY is 1. but 0.r9 is not TRULY 1

[@Ryan_Alt-p7n]

@@tristantheoofer2 agreed

[@improvisedPilot]

@@tristantheoofer2 practically and truly 1

[@2tothe4th]

5:56 Also, for the 10x argument, you get 9x = 9 by subtracting x, 0.r9, from both sides of 10x = 9.r9. People learn this when converting repeating decimals to fractions.

[@Chris-5318]

tristan deliberately misrepresented that proof.

[@tristantheoofer2]

@Chris-5318 no i didnt

[@Chris-5318]

​@@tristantheoofer2 Liar. The proof says x = 0.999... => 10x = 9.999... = 9 + 0.999... = 9 + x => 9x = 9 You completely skipped the last steps, and replaced them with "9x somehow exactly 9 which makes no sense" and trying to make out that was ridiculous. It makes perfect sense. There is no way that you didn't do that wilfully. You then went on to ridiculous claims such as (9/10) * 9.999... = 8.999...1 instead of 8.999.... You cannot have a 1 at the non-existent end of a non-terminating decimal. If we multiply your 8.999...1 by 10/9 we'd get 9.999...0 and that is not 9.999... In fact your 8.999...1 notation is another con trick. The digit to the immediate left of the 1 is a 9. A slightly less dishonest notation would be 8.999...9991000.... Then (10/9) * 8.999...9991000... would be 9.999...999000... where the first 0 of the latter is where the 1 is in the former. It is now obvious that you are just pretending that 0.999... is 0.999...9, i.e. you are just claiming that 0.999... is not an infinite decimal. You also avoided writing 0.999...9 or 0.r9...9, again that is deliberate dishonesty. I know that you will ignore this because it doesn't fit in with your completely delusional belief that you are smarter than millions of degree mathematicians, and it exposes you for the fraud that you are. I have dealt with all of you mistakes in other comments. You ignore those. You fail to respond to every challenge put to you. You just dodge, duck, dip, dive and dodge.

[@riccardoguglielmini7840]

Bro proved litterally nothing 😭😭

[@Fire_Axus]

StGeSoEm

[@riccardoguglielmini7840]

what?

[@MichaelDarrow-tr1mn]

if 0.0000...1 exists, what's 10 times it?

[@Chris-5318]

You should also ask what is 0.1 times 0.000...1

[@Chris_5318]

He won't answer because it challenges his beliefs.

[@tristantheoofer2]

@Chris_5318 first of all im a her, and second of all i dont see all your comments or all the comments under this video. im not on youtube 24/7 my guy

[@Chris-5318]

@@tristantheoofer2 I was referring to your biological gender. Admittedly I only base that on your voice. Take a glance between your legs for a better determination. I'll refer to you as if you were a female if that is what you choose to believe you are. As predicted, you did not answer Michael's question, or mine. Here's a hint: infinite (i.e. non-terminating) decimals do not have a last digit. 0.000...1 has a last 0 (sneakily hidden using a notational con trick) and 1 at the non-existent end. Because of the endlessness, 1 - 0.333... = 0.666... (and not something like 0.666...7). But 0.666... = 0.333... + 0.333..., therefore 1 - 0.333... = 0.333... + 0.333... => 1 = 3 * 0.333... => 0.333... = 1/3 and 0.999... = 1. I'm quite sure that you will ignore that because it doesn't fit in with your deIusionaI belief that you know better than the mathematicians, and that they are incompetent. When are you going to publish in a reputable math journal (and become rich and famous)?

[@angelski3s]

i love how confident you talk in this video about such controversial topic, prob my favorite from all of those vids you have

[@tristantheoofer2]

fair enough lmao. and somehow im wrong to about 60% of the comment section-

[@ammenace2068]

There are plenty of other sources that might help with this problem. Overall, the main line of thought is that there exists no number between 0.9…9 and 1. I think least upper bound is an interesting concept. Thus, mathematically, I would say it’s one. Philosophically, however, you would be right to call it “different”. So I wouldn’t exactly say your thoughts are wrong per se as they reflect a more philosophical and metaphysical definition rather than a purely mathematical one.

[@ChezburgerLeaf]

There are infinitely many numbers between 0.99... and 1 Like what...? Genuine question

[@Enju-Aihara]

0.99... < x -> ∞ < 1

[@tristantheoofer2]

i mean if you think about it, theres ALWAYS slots to put in more numbers even if the decimal goes on infinitely. always. you can always add 1 more number to the end.

[@trueuniverse690]

@@tristantheoofer2 You should watch veritasium's video about infinity

[@realcinnamongold]

infinity goes on an infinite amount of time

[@xing._.]

think of it like this: there are two types of infinity: quantitative infinity and un-quantitative infinity. quantitative infinity is infinity you can count, like 1, 2, 3, etc. un-quantitative infinity is infinity you can't count, like the number of unique decimals between 0 and 1. if you try, what should the first number be? should it be 0 is 0.r0...1? but you can add infinitely many zeroes before adding a 1. it's kind of the same logic with 0.r9. you cannot stop between that number and 1, otherwise it isn't infinite. and there are infinitely many numbers in between 0.r9 and 1 because you can always add more. I'd also like to point out that infinity is not really a number, it's more of a concept. conceptually, there are infinitely many numbers between 0.r9 and 1, but no one can truly prove for or against that because these abstract concepts do not have real value due to the very nature of infinity.

[@brawlmemes7372]

idk how other countries use it, but it was so triggering when i had to see those fractions as 0.r9 instead of 0.(9)

[@Chris-5318]

You are easily tiggered.

[@therealdia]

I’d personally say you are correct, and that the majority of these proofs are merely the result of infinity not being a number. The way I see it, if a number involves infinity in any form, it is not a real number (including repeating digits). 1 is a real number, while .9r is not, so therefore they are not the same. I especially like your point about 0.3r being an approximation rather than a literal representation of 1/3. Infinitely repeating digits like that are the result of decimal representation rather than a genuine infinite real number (in base 3, “1/3” would be 0.1; no repeating numbers required.) At the end of the day, math is in many ways an abstract construct. Focusing on semantic concepts like 1=0.9r is much less useful than pragmatically finding the answer. 1 does not equal 0.9r because there should only be a single real representation of each number, and having redundant symbols for numbers will only cause confusion.

[@tristantheoofer2]

agreed honestly, thats why i suggested at the end that 0.r9 doesnt exist. just another thing to think about. personally i say it still isnt 1, especially cus of that possibility that it doesnt exist. also also with the fraction thing, 0.r9 simultaneously is and isnt rational lmao

[@pavelmatusu4457]

lets say 1 - 0.r9 = 0.r0..1 is a real number, it clearly has to be: 1. Not smaller than zero. 2. Smaller than any real positive number. Clearly the only real number that satisfies these properties is 0. Thus 1 - 0.r9 = 0 => 0.r9 = 1

[@Chris-5318]

That's far too sophisticated for the poster. OTOH, anyone with more than half a usefully functioning brain will see that your argument is solid.

[@ChanceYouTube]

Here’s an easier way to explain your point 0=0 ✅ 1=1 ✅ 0.9999=1 ❌ conclusion: 0.9999 isn’t 1, just dont think too much 👍

[@tristantheoofer2]

real???

[@ChanceYouTube]

@@tristantheoofer2real

[@strumblers3701]

Add infinitly more 9s then its 1

[@tristantheoofer2]

@strumblers3701 its still not

[@strumblers3701]

@@tristantheoofer2 Actually, 0.999... (repeating infinitely) is mathematically equal to 1. Here's a simple way to understand it: Let 𝑥 = 0.999... x=0.999..., then multiplying both sides by 10 gives 10𝑥=9.999... 10x=9.999.... Subtracting 𝑥=0.999... from 10x leaves you with 9𝑥=9, and dividing both sides by 9 gives x=1. So, 0.999... isn't just close to 1; it is 1 when you consider it as an infinite series.

[@carrot0013]

I have read some of the other comments and they explain the arguments prooving the equality correct quite well. I would like to focus on the notion that acts as a basis for all of your arguments. So, suppose there is a number x equal to 0.0000....1 (infinite 0, then an 1). Then: 10x=00.00000.....1 (infinite 0 then one) (we move the decimal point one place to the right). We can prove that there is the same ammount of 0 between the decimal point and the 1 in x, as there are in 10x. Let's number every one of those 0 in x with a natural number: {0,1,2,.......}. In 10x, the 0 tagged with "0" is moved to the right of the decimal point, so we get: {1,2,3,......}. To prove these sets have the same amount of elements, and therefore both x and 10x have the same amount of 0 between the decimal point and the 1, we have to find some way to map each element of the first set to exactly one element of the second set, so that no elecemts in the second set remain on their own. We can do that by matching each element n of the first set to n+1 in the second. Thus we have: 0->1, 1->2, 2->3 and so on, where the first number is from tthe first set, and the second from the second. I hope I have convinced you that there is the same amount of 0 in the decimal part of both numbers, because it is essentially for the next step. 10x=00.0000.....1 - x= 0.0000.....1 --------------------------- 9x=00.0000......0=0 The integer part is 0-0 which I hope we can agree is 0. We prooved that all 0 in the decimal part allign with eachother, so in each position we have 0-0=0, and then we have 1-1 which, again, is equal to 0. So, 9x=0x=0 or 9=0. 9 isn't equal to 0, so it has to be the case that x=0. But x is also equal to 0.0000......1. Therefore, 0.0000.......1=0.

[@areairv]

1 also the fact that you didnt align at the tightropes on f2 ToIE just HURTS DKGLRNXMZLRMDJ4SK

[@tristantheoofer2]

lmao i have no sympathy for you for seeing that

[@JamesMcCullough-lu9gf]

3:40 This disregards the literal definition of infinity, or the repeating bar, because they DO NOT END. In order for something to go after it, it would have to be finite, or in other words, have an end. 6:20 You did not entirely explain this proof, which actually starts with defining x as being equal to 0.r9, which would mean that 10x is equal to 9.r9. Your argument to disprove this also breaks the rule I already brought up, but it also doesnt make any sense because both x and 10x have an infinite and therefore equal amount of 9s after the decimal point. Infinity-1=Infinity. 10x-x=9.r9-0.r9=9x=9.

[@GuyllianVanRixtel]

Breaking News: Random af roblox youtuber solves mathematical arguement that has been going on for years.

[@tristantheoofer2]

looking at the like/dislike ratio (its 74%) it seems not- lol

[@Yatcha479]

The good old debate from when calculus was invented.

[@tristantheoofer2]

ngl, thats so real

[@ckogsh2585]

disagree, i'd not let that slide so, 0.999 .. . / me * me =No No = maybe maybe= icecream icecream = 3 3 = 1 which means 0.999 . .. = 1 its that simple

[@tristantheoofer2]

proof by words?

[@ckogsh2585]

@@tristantheoofer2 its a fact

[@CagnusMarlsen212]

fuck, that's a good proof

[@tristantheoofer2]

real???? (yes i know its sarcasm)

[@ckogsh2585]

@@tristantheoofer2 sarcasm? idk what you taling abt

[@yellomauz1]

a single digit repeating is often represented by a fraction, x/9. for example, 0.1 repeating is 1/9, 0.2 repeating is 2/9, etc. given this, as a fraction, you would convert 0.9 repeating to 9/9, which is one, since 9 is being divided by itself. 0.9 repeating, or 0.999... is equal to 1.

[@toastey9756]

Honestly, in our number system, .999...=1. You would have to expand the number system into hyperreal/surreal numbers, so that you define infinitesimals. (Otherwise, with only the basic real number system or extended number system, all the applied proofs would be true, as 1/infinity would mean a number is divided by infinity-defined as a number larger than every real number. In that case, yes, 1/infinity = 0 since you have infinite 0's before a 1, and since infinity is larger than any real number, you will never get an end to the 0's. If you want to argue that there is a .00...1, that's a hyperreal number😭. ) Basically every argument you counter is either on a straw man, a flawed explanation, or both. Your argument is both false and true, but mostly false. Mathematics doesn't deal in absolutes (unfortunately). Please take real analysis or like, any mathematical course if you haven't already, they usually offer some tools to deal with the proof. I'm not a maths major, but I can write a small documentation on this topic if you want. P.S. The pi=4 argument is true, somewhat. The square really approaches a circle, but the mistake is that you assume the function for the length of the square is continuous, which its not. Using that as an analogy is terrible, because the error of the circle argument never decreases until it is exactly a circle, while the error of the .999... function does decrease by the limit. 3b1b made a good video called "How to lie using visual proofs" that explains this in detail. Essentially, the limit of the length of the square does not equal the length of the limit of the square.

[@tristantheoofer2]

well shit alr then 😭😭😭

[@toastey9756]

@@tristantheoofer2 I'll try to get like documentation or a vid up about this, but its alg. Having more people getting interested in math is always amazing, and doubt of the established is what creates advancement.

[@Platinum_XYZ]

​@@toastey9756what a champ! you handled your initial comment, argument, and reply so well! +++respect to you

[@KaptainKovu]

Nice video, Keep it up!

[@aTtsb]

0.99999999 is not equal to 1 because they look like seperate numbers. i still have a lot to learn in math though, as i am not even halfway through high school. anyways this video was fun and interesting to watch even though i only understood about half of it.

[@DictatePM]

i mean in math something looking like diff numbers doesnt really mean anything

[@tristantheoofer2]

ofc ofc. once you get into calculus itll likely be easier to understand. my teachers have said that in calculus, limits are essentially just a number getting so close that you can essentially consider it as what you are looking for, which isnt really equaling anything now is it.

[@hydrange.a]

@@tristantheoofer2 you're so confused 😭😭😭😭

[@ultimatehusky5481]

waow (signed cloud from The Discord)

[@tristantheoofer2]

no way you just donated 25 bucks holy hell tysm :0

[@ultimatehusky5481]

​@@tristantheoofer2 i also boosted the server 4 times smh /lh

[@tristantheoofer2]

@ultimatehusky5481 what-

[@ultimatehusky5481]

@@tristantheoofer2 ya go check :3

[@tristantheoofer2]

@@ultimatehusky5481 i just saw

[@when-the-hrandomstuff]

Now do one about how [1+2+3...∞] doesn't equal -1/12.

[@tristantheoofer2]

that one honestly is way more annoying because that cant really be *defined.8 with the real numbers i think? i just know it has smth to do when you set the reimann zeta function to -1

[@nintendoswitchfan4953]

​@@tristantheoofer2 there are alternative ways to define distance between numbers. In the 10 adic metric ...99999=-1

[@starrekt2037]

Part 1: The 4 Arguments Part 2: The 1/3 Argument: this one is basically an argument about Fractions (e.g. ⅓, ⅔, ⅙ etc.) Being miscalculated/estimated and not the real answer. Part 3: The Numberline Argument: this one where you have a numberline with 0.r9 and 1. When you subtract these 2 (1-0.r9) = 0.r0...1 the 10x argument the calculus argument

[@loco4loco]

Well my brain just left…

[@tristantheoofer2]

lmao mine almost did making this thing

[@saladcat231]

“Man I got 9+ notifications to check out” First thing I see is this video and I immediately watch it, thank you for consistently making absolute bangers

[@benab3255]

I like to call those "math bugs". Like 1/0 which sometimes can be infinite and its confusinf or √1 can technically be -1 and 1 and trust me as someone who uses graphing calculators a lot it can get annoying that it doesnt equal to -1. Im just a math nerd and a computer science nerd ig. Learning what are "math bugs" can be useful since you can actually accept both values. Trust me, as a math graphing calculator nerd, you sometimes gotta accept both values. 1/0 is a great example. I work on a lot on math. Sometimes 1/0 can be infinite and sometimes its not. Really complex. Now, about your point, well I get it. However your videos does has some mistakes. While the argument of 4 is pi is false, it's really hard to explain what is acceptable and what is not. No hate at all. Some stuff are just "math bugs". Both are right. I totally get you. Accept math bugs sometimes. They are weird and beutiful. I'm not gonna go to the very details of your mistakes but I have a lot of experience on math. So yeah you're both right and wrong since it's a "math bug". By the way, this is all my theory. It's not proven that math bugs are a thing but theres lot of things that I know from my experience that aren't proven. I just use a lot of math.

[@tristantheoofer2]

fair enough and i completely agree. 1/0 according to computers is infinity but according to people its undefined. its like 0/0 which is somehow 1, 0, and infinity at the same time which counts as undefined cus theres multiple values it can represent.. just like 0.99... other people have said its just a different representation before which i dont really buy, cus that just feels like a cheat code to say theyre the same tbh. yk? honestly any recurring decimal i think could be said to be some kinda glitch in decimal representation, we just use other ways of number representation (eg fractions) to deal with that lol

[@kahafb]

@@tristantheoofer2 1/0 is undefined "according" to people because it goes to both infinity and negative infinity. You can see this visually if you graph 1/x

[@tristantheoofer2]

@@kahafb how the fuck does it go to negative infinity??

[@benab3255]

@@tristantheoofer2 he's got a point. Graph it yourself. It can also be -inf. I don't say it's undefined I say technically it can also be -infinite

[@lolwutttzz]

sqrt((+-)x^2) = x, its not a bug just that x^2 is always positive

[@TheRealSillyWillyC]

Awesome video as always. Have been here for a long time.

[@killing_gaming0973]

Never expected this from a 16 yr old, a very strong and valid argument right here, great work

[@killing_gaming0973]

Lmao this video come out 3am in my country

[@tristantheoofer2]

lmao ty.. though i apparently know less about calculus than i thought

[@killing_gaming0973]

@@tristantheoofer2 Welp calculus is a huge topics, there's Calc 1, calc2 and calc 3. Calc 1 would involve limits like you stated, differentiation and integration, they are very basic and general, which is the level im studying right now, The next semester i will be studying Calculus 2, which involves in differential equations, hopefully it's not that bad for me

[@killing_gaming0973]

@@tristantheoofer2 Conclusion is 0.999 repeating converges to 1. Which is just equal to 1. (1 - [limit of n approaching infinity 1/n]) means you substituted a number that get closer and closer to infinity until you substituted the ACTUAL infinity itself, which is defined to be zero. Since infinity is not a number, 0.999.. doesn't actually exist. It just become 1 due to there is no more real between 1 and 0.999... repeating. You did a very good job on explaining, as a grade 12 math major i am satified

[@killing_gaming0973]

@@tristantheoofer2 forget about the like ratio, no one can judge your point of view

[@christiandevey3898]

Will Achilles ever pass the tortoise

[@sammyjpeg8322]

Is this troll bait? 0.999.. = 1 is a fact not an opinion

[@tristantheoofer2]

its not and now im slowly coming to the realisation that im fuckin dumb-

[@RudyTheCannibal]

Man, fuck you! Leave my man alone.

[@Surperpeca]

as somebody who knows nothing about this stuff i could confirm that 0.999999 is not 1 because its just not 1. there's a difference between 0.9999 and 1 and unless your estimating or rounding, 0.9999 is not equal to 1. i agree with you on this one, and i understand all of your arguements.

[@Chris-5318]

Obviously 0.999999, with only six 9s is less than 1. The easily proven math fact is that 0.999... with infinitely (i.e. endlessly) many 9s is equal to 1. If you agree with his arguments, then you do not understand them. Every reason he gives, that the mathematicians are wrong, is wrong. If you meant 0.999..., then what is the difference between 0.999... and 1 that you claim exists? I calculate it to be 0.

[@Surperpeca]

@@Chris-5318 no matter how many nines are in it, it's not equal to 1. the gap theory is terrible and unaccounted for there being the same number of decimals in 0.000... so there's always going to be a gap no matter what.

[@Chris-5318]

​@@Surperpeca There are infinitely many 9s. You are thinking of the cases with only a finite number of 9s and just assuming that's true with infinitely many 9s. What is 1 - 0.999... according to you? Show how you arrived at your conclusion. Meanwhile consider this. If 1 - 0.999... = g > 0, then there are only log10(1/g) consecutive 9s in 0.999... and that means there is a last 9, contradicting the definition that there isn't a last 9. I used g for "gap". A big giveaway is that you said, "so there's always going to be a gap no matter what". That tells me that you, like the video poster, is thinking of the sequence 0.9, 0.99, 0.999, ... that never "gets to" 1. What you both fail to realise is that none of the terms in that sequence gets to 0.999.... either. As you probably don't understand logarithms, here a schoolchild level calculation for 1 - 0.999...: For 1.000... - 0.999... consider the digits in the n th decimal place after the decimal point. Because 0 < 9, we need to borrow from the n-1 th place so we can do 10 - 9 = 1. But by symmetry that means we will have a carry into the n th place from the n+1 th place. So we end up with (10 - 9) - 1 = 0 in the nth place. That is true for EVERY place after the decimal point (and there isn't a case where it fails). For the units digit (to the left of the decimal point), we have a carry in, and so we end up with (1 - 0) - 1 = 0, and there is no borrowing or carrying to the next decimal place (the tens position). So we end up with 1.000... - 0.999... = 0.000... = 0. PS I believe that your reasonng is as follows: 1 > 0.9 1 > 0.99 1 > 0.999 ... ergo, by magic, 1 > 0.999... Now replace 1 with 0.999... to see the problem with that argument: 0.999... > 0.9 0.999... > 0.99 0.999... > 0.999 ... ergo, by magic, 0.999... > 0.999...

[@chrisgaming9567]

@@Chris-5318 "Now replace 1 with 0.999... to see the problem with that argument" Here you're basically saying "If we assert that 0.999...=1, then we can show that 0.999 can't be less than 1"

[@Chris-5318]

@@chrisgaming9567 That is not what I did. It didn't occur to me that anyone could misinterpret what I said so badly. Hint: I showed that the argument is fallacious. More generally, you cannot induce over the naturals to infinity. Here's another example that might help you to realise what I actually did: 1 is finite. 1 + 1 is finite. 1 + 1 + 1 is finite. ..., ergo 1 + 1 + 1 + ... is finite (and that is absurd).

[@andynilsennot4329]

0.999999999... doesn't equal 1 in my opinion because look! theres literally a 0 at the beginning of the number! how could they mess that up!?

[@paolarei4418]

I worked for Mathis RV, he's a frauf

[@lolwutttzz]

this is not a 'opinion debate'. 1 = 0.99... because as it goes, 0.9, 0.99, 0.999 so on goes it turns into a smaller difference and when its infinite it turns into a difference = 0

[@andynilsennot4329]

@ i only said "in my opinion" because i know there are several claims proving its 1, just in my mind its its own thing because that just feels more correct

[@lolwutttzz]

@@andynilsennot4329 is mathematically 1. you cant just say something is false because you want to

[@andynilsennot4329]

@ ok fine

[@stoneguy150]

Ok, then how is 3/3=1 instead of 0.99999… if 1/3 is 0.33333… smarty!?

[@Chris-5318]

He doesn't accept that 0.333... = 1/3.

[@stoneguy150]

@ because he is so ⬛️⬛️⬛️⬛️⬛️⬛️ dumb

[@Chris-5318]

@stoneguy150 You got that right. He also intends to keep it that way.

[@ErrorSmiler]

why did i understand everything...

[@tristantheoofer2]

cus youre very smart fr

[@TheOlidosOfficial]

i understood all of it up until the huge equation

[@TheOlidosOfficial]

cause i havent done it in school yet. man, that one bit was confusing.

[@braincell2020]

(I'm not exactly proving your arguments wrong as 0.99999 being 1 is a somewhat controversial "fact" in mathematics. I do believe it is not, but i will take a more neutral approach and not let my biases play here) 1. I dont exactly know what you mean by "cant be expressed in decimal forms" for 0.r666 and 0.r333, Both of these are rational numbers (they match the prerequisites for a rational number, it can be expressed in form p/q and it is either a whole number, a non-infinite decimal number or an infinite repeating decimal number, like 0.r3333 and 0.r9999), but you only need 1 of these to define that a number IS a rational, so a repeating decimal can be expressed in form p/q, (where p and q rational numbers, this works because the group of rational numbers are closed in the case of division). Also 0.r999 does exist, atleast in the set of rationals, reals and complexes. This does open another door in the fact that if adding some numbers repeatedly until n number of times is not the same as multiplying that number by n, so your argument might make more problems. 2. Now i'm going to be kinda philosophical for this one, because atleast in this case, there is a barrier of "should make sense" in mathematics. If we define a number that is endless and say at some point in it's end that it has a different value, we are basically contradicting ourselves. Philosophically, infinity is an amount of items that is endless. So if we say that something endless has an end, we are contradicting ourselves. Therefore, the infinitesimal is basically just 0. It should have no end as 1, therefore it is basically just 0. Mathematicians still consider it more than 0, for the case of calculating the instantaneous rate of change of specific physical things like velocity and acceleration, you might also know about the derivative, used to calculate the rate of change at the infinitely small change of delta x for a function. 3. I'm not going to check this because i don't exactly like this argument. (The 0.r999 = 1 argument) 4. The same argument from the numberline proof extends here but another thing is that the values of a rational function (like 1/10^n) approaches 0 when n approaches infinity IF the function has a denominator greater than its numerator. it's still only infinitesimally close to 0 though. Now, even if the infinitesimal is greater than 1, The philosophical barrier combined with the logistics of calculus makes it basically 0. Another thing is that the infinitesimal does not exist in the real numbers set OR the complex numbers set (sets with irrational and complex numbers respectively) because to definite the infinitesimal, you have to define the first infinite ordinal, or omega onto the real number/complex number system. Because the infinitesimal will be 1/omega. We normally make functions with both the domain and co-domain sets all containing real numbers, so having this system won't exactly make sense for most functions, so we just approximate it to 0 because THAT is what it is (for confusion, refer to my numberline argument). But all of this could be wrong, im no mathematician just a dude who does math and talks about math for a hobby.

[@BlarbEgg3104]

a

[@nonsensicalramblings9167]

You always choose the best music for your videos. Love the Smash Hit soundtrack cameo in there!!

[@tristantheoofer2]

lol ty

[@KayePalma-d8l]

1÷3? 0.333333333... so 0.33... + 0.33... + 0.333... is 1? It's 0.99...

[@Arrowgu4]

im come backand 1:39 0.333… isn’t an appropriation of 1/3, it IS 1/3 we can just divide 1 by 3 and we will get 0.333… (fractions are just division.) now if we do (1/3) * 2 then we get 2/3, or 0.666…. 3/3 is one like you said, but (1/3) * 3 for some reason isnt? 0.333… * 3 would be equal to 0.999… or 3/3… which is 1…. if i did smth wrong pls let me know

[@Chris-5318]

You cannot use the division algorithm alone to prove that 0.333... = 1/3. You need to use limits.

[@Arrowgu4]

@@Chris-5318ok

[@ThatobjectArtist]

Hey! Mathematician here. 1. First I'd like to state that these are not approximations, they are called "infinitely repeating" for a reason. You just let them go on until oblivion, thus "precisely" representing the number. In the contrary, in base 3, we can represent 1/3 as 0.1, which is a terminating decimal in base 3. It does not make sense for a decimal to be an approximation in one system, and yet when converted into another system which is supposed to be essentially the same, save for a few digits, is a precise representation. 2, 3 & 4. most of these are based on the fact that there can exist a 0.00....000235828578943895 or something like that. And you can let it exist. Just not in the actual real numbers. If we're talking about the real numbers, there is a fact that you physically cannot add a digit to the end. Because since it is at the infinitieth place value to the right of the decimal point, it is equal to 0. It can't equal to a finite value, because each place value 0.1, 0.01, 0.001, 0.0001, etc. is already taken up by literally all of the other place values to the left of it. Logic really breaks down over the infinities, that's why most people can't wrap their head around it. Edit: MtF trans detected? :P

[@tristantheoofer2]

honestly based take. and yeah i forget that in every multiple of 3 base, infinite decimals like 0.r3 and 0.r6 can be represented as some shit like 0.1 and 0.2. also yes you have successfully detected a transfem :3 and NO WAY ANOTHER TRANS PERSON :0000

[@ThatobjectArtist]

@@tristantheoofer2 yeah it's easy to forget that base 10 is arbitrary ALSO TRANSTRANSTRANSTRANSTRANSTRANSTRANSTRANSTRANSTRANSTRANSTRANS

[@tristantheoofer2]

@ThatobjectArtist frrr and :333

[@ThatobjectArtist]

@@tristantheoofer2 :333

[@Chris_5318]

@@ThatobjectArtist 1/3 = 0.1 (base 3) = 0.0222... (base 3) and 0.bbb... (base b+1) = 1 for every natural b.

[@goldenNOTfraud]

The thing is to me, whenever I was bored at school, I actually thought of something, if you placed a brick very close to a wall, and you can't fit any bricks, you make the brick smaller, and place a smaller brick, but there's still a finite space, so you keep adding smaller and smaller bricks, seemingly so close, but never touching, literally 0.999 ≓ 1. You always have a finite space, tyring to fill it in, but you never seem to actually reach the wall.

[@tristantheoofer2]

i mean if 1/infinity worked amazingly like that then yeah theoretically that would totally work

[@Im-Not-Actually-A-ScamBot69420]

it's ≠

[@hainer9440]

i cant tell if this is a crazy troll bait or youve never touched calculus but regardless neat vid

[@tristantheoofer2]

yeah im just dumb

[@RudyTheCannibal]

This is not troll bait. I think it's that you're just an asshole for no reason, hainer9440

[@altair-tf8fp]

the wish for perfect precision takes another life...

[@tristantheoofer2]

real

[@nega-guy]

Wait this was actually debated? Like no matter how many nines there are after 0.9999... it's still not equal to 1. Like wtf.

[@tristantheoofer2]

yep, and the proofs are... so dumb. theres also contradictions with some of them (and also my rebuttal which just proves even more that they arent the same imo). its like... adding 9/10 + 9/100 + 9/1000... etc etc doesnt equal 1. there will never be an end to the adding of 9s.

[@hydrange.a]

@@tristantheoofer2 the only valid proof there is the limits proof. The rest are not rigorous and are simply elementary methods to show 0.999... = 1 without any actual credibility.

[@lolwutttzz]

@@tristantheoofer2 theyre not dumb. you just dont want to believe a debate that has been over for over 100 years

[@nega-guy]

@@lolwutttzz What?

[@Ескендір-б5р]

Okay, there's a 100% proven theorem, that states that between two different numbers there is at least one number, try and find a number between 0,(9) and 1 if they are different

[@YEWCHENGYINMoe]

stay out of my territory

[@jelenasusic2914]

Nah

[@MarIsRandom]

i agree

[@TheOlidosOfficial]

nah, id trespass.

[@ðim]

the answer is there would be exceptions. You made this very clear but look: Since 1/3 =0.333 and 3/3 =1 depends on how you read fractions. Because it’s “ 3 divided by 3 “ it would be 1 but in Decimal form (not converted from fraction) it would be 0.r9 so it is a super value aka it can hold multiple value but that’s not entirely true. It all depends on from where you started.

[@ðim]

also because 3/3 is our way of representing a decimal. We use a so called “law” that can be used to convert “all” decimal numbers but it cannot be used for 3/3 because we used division to represent it which yeah, 3/3 equals 1, but does not equal 0.r9.

[@thetaomegatheta]

1/3 = 0.333... 1 = 0.999... There is no 'this thing can hold multiple values' nonsense going on. The author is just wrong.

[@ðim]

@ you’re wrong. 1 does not equal 0.9999 If you want to take this further I we cns take to dms

[@thetaomegatheta]

I have a degree in math, I can provide you with both the proofs that I have written specifically for KZbin, and with references to textbooks that cover this topic. 0.999... is exactly 1. In particular, x = p/10^n+x/10^n => x*(1-1/10^n) = p/10^n => x = (p/10^n)/(1-1/10^n) = p/(10^n-1) For x = 0.999... and n = 1 we have 0.999... = 9/10+0.999.../10 => x = 9/(10-1) = 9/9 = 1.

[@ðim]

@ now, your equation is correct. However it does not show 0.99 equals 1. The reason 3/3 could be these value is not because it is a super value. The reason is because us humans have created “fractions” a way of showing decimal numbers in a different form but that form has a “law” that fails to properly convert 3/3 to 0.99 because it uses a/b to find d (decimal).

[@crLmsin]

I used to say it did equal 1 but there is just too much ‘evidence’ against it lol

[@tristantheoofer2]

ive never viewed it as equaling 1 simply because all the arguments really dont point to it being 1, even the thing where you cant "find" a number between 0.999.. and 1. in that case your options are 1. yes there is, or 2. theyre right next to eachother lmao.

[@bubbacat9940]

So for the 10x example, I'm going to give what is in my opinion a better demonstration. x = 0.999... Multiply both sides by 10 10x = 9.999... Subract x from both sides 9x = 9.999... - x Substitute in 0.999... for x on the right 9x = 9.999... - 0.999... 9x = 9 x = 1 Also, in the calculus approach, they define 0.999... as lim 0.{9} k times k-> infty This is the definition, and the definition says "this is a limit. The expression will never actually equal this value, but it will get infinitely close." The expression never equals 1, but its limit is 1 because it can get arbitrarily close to 1. Because repeating decimals are defined as this limit, this proves that 0.999...=1 given this definition of repeating decimals.

[@bubbacat9940]

Also, I would like to add This is arbitrary. All of math is arbitrary. Mathematicians pick the definitions that are most useful, and the most useful definition of recurring decimals defines 0.999... as equal to 1

[@tristantheoofer2]

i was gonna say lmao. i guess mathemeticians be mathin

[@tristantheoofer2]

ooooooh ok so limits 1 because it can get whatever "arbitrarily close" is??? tf

[@bubbacat9940]

@@tristantheoofer2 Arbitrarily close means that whatever distance d you chose from 0, there will always be a value e where with e or more 9s, it is within that distance of 1 for any arbitrarily small value of d. That is how a limit is defined in calculus. In this case, it is guaranteed that with at least _ceil(log_10(1/d)) + 1_ 9s, the value is guaranteed to be within d of 1. That is how a limit in calculus is defined. 0.999... is equal to 1 because of the definitions that are standard in calculus and in mathematics.

[@pra_ta_ta]

"There is no number between 0,99999... and 1! Me: " 0,infinity "🗿

[@iispacedustii]

the video was enjoyable, but i think the 10x argument has a slightly different reasoning: let x = 0.r9 then 10x = 10 * 0.r9 = 9.r9 if we subtract x from 10x we get 10x - x = 9x = 9.r9 - 0.r9 = 9 implying x = 1

[@tristantheoofer2]

but this also implies that youre kinda just tacking another digit on the end of the end of the string of digits... though i guess infinity doesnt care does it i think that argument is stupid regardless

[@Dummigame]

I say bullshit with a side of bird shit

[@doc.chocholousek3378]

@tristantheoofer2 The whole point of periodic numbers is that the last sequence repeats forever. There is nothing like the last digit and nothing like adding another nine to the end. That's also the reason why your concept of 0.r0 1 is just just a pure nonsense in real numbers because the zeros simply repeat forever. There simply can not be anything after the zeroes because that would require the zeros to end somewhere, which is the exact opposite of the definition. Having a 1 at the end means there must be a last zero, but that means you can count all the zeros from the first one to the last one, so there isn't an infinite amount of them. An intuitive but probably non rigorous way of thinking about it is that infinity is the biggest number, so when you want infinite repeating 0, you want the most zeros you can get. When you have an end of a sequence that is .....0001, you can always get more zeros by inserting a zero between the last zero and one. The problem is that you then get ....0001, and you already know this isn't the sequence with the biggest number of zeros because you can add one more zero to it, so you can't write that number down as your final result with the biggest number of zeros either, nor can you any number in the form of ....0001. If you would be able to write number in the form of 0.r0 1 with infinite zeros between the period and 1, you would then be able to get a number arbitrary larger than infinity which is impossible so the number 0.r0 1 can't exist to avoid this contradiction. 0.r9 doesn't mean you have an infinite list of 9 that ends somewhere, and there are zeros after it, or you can put there anything you like, it's meaning is closer to simply having a function "return 9" for getting the nth place after the decimal point. You simply get 9 for any place you ask. There in fact are rigorous ways for defining infinitesimals like dual numbers, 0.r0 1 is just not one of them

[@CookieMage27]

Infinity by definition has no end, so 0.9r is literally equal to 1 because of the concept of infinity. Going the other way is also interesting, let’s say you have a bunch of 9s extending infinitely in the other direction, like …999999, adding 1 to it turns the first digit into 0 and this propagates the entire way up, since infinity is literally unending, it won’t finish propagating, ever. This, makes it into zero, so funnily enough, makes it fundamentally equivalent to -1. Yeah that’s right, I said it, an infinite amount of nines extending upwards is the same as -1, because adding 1 to both of them makes it zero, the only reason this works is due to the fact that adding one doesn’t end up with a bigger number, just infinite zeros. You can think of it as a variation of the real world example of computer science where when you have only a set number of digits, for instance, 4 of them, like so 9999 You can’t add one and get 10,000, you get 0000 Does this make sense?

[@SarahTheAmbiguous]

when you don't know how limits work and then assert you know how limits work 1/infinity = 0

[@Chris_5318]

He doesn't care. He just wants to believe he knows better than the mathematicians.

[@yablomas_]

Hey, I see everyone in the comments disproving him, but can someone explain to me this? I’m not saying y’all are wrong, but I don’t understand because the main argument is that no number can fit between 0.999… and 1, so they must be the same; but if you multiply 0.999… by 2 it becomes 1.999…9998, which means that SOME number can fit in there, therefore it’s disproven. Atleast in my mind, can someone tell me why I’m wrong?

[@tristantheoofer2]

apparently with infinity no??? or some shit like that idk 😭😭😭

[@Chris-5318]

@yablomas_ 0.999... * 2 = 1.999... not 1.999...9998 1.999...9998 / 2 = 0.999...9999 and that isn't 0.999... as would have to be the case IF you were right. How did you come to the bizarre conclusion that 2 * 0.999... = 1.999...9998? Why didn't you say 1.999...8 or 1.999...9999999999999998 or some other random variation? Whatever, your 1.999...9998 has a last digit, whereas 0.999... doesn't.

[@thetaomegatheta]

'but if you multiply 0.999… by 2 it becomes 1.999…9998' It doesn't. 0.999...*2 = 1.999... = 2. Consider the fact that, in '1.999...98', that digit '8' has to be at some nth position. Whichever natural n you pick, when you divide your number by 2 you get 0.999...99, rather than 0.999..., meaning that you made a mistake.

[@yablomas_]

@@Chris-5318 huh? Why are you talking about how I said 1.999…9998 instead of something else, why does it matter?

[@Chris-5318]

​@yablomas_ Duh! I'm talking about you saying 2 * 0.999... = 1.999...9998 because YOU ASKED people to explain why you are wrong for saying it? I told you that 2 * 0.999... does NOT equal 1.999...9998 but DOES equal 1.999... I also pointed out that 1.999...9998 / 2 does NOT equal 0.999... but DOES equal 0.999...9999 and that is not the 0.999... that you started with. I'm ignoring the fact that 0.999...9998 is not a valid decimal. It most certainly is NOT an infinite decimal because it has a last digit. Infinite decimals do not have a last digit. If such decimal were allowed, then it'd be 2 * 0.999...9999 = 1.999...9998. Why isn't that obvious after I had pretty much spelled it out for you? FYI "infinite" is just a fancy word for "endless", not "big". You have also chosen to ignore theatomegatheta's reply which gives another way for you to see that you are wrong.

[@miniyoshiyt1178]

If you assume there are infinitely many zeros and you add 1, are there still infinitely many zeros with one behind them or a huge amount of zeros with a 1 behind them? If it is assumed that there are infinitely many zeros and a 1 behind them, then would we be in the world of infinite ordinals? I mean that if there is a quantity W of zeros and a 1 there would be W+1, since we have infinite zeros and we add a 1 we could add more and more zeros going through all the ordinals but never reaching infinity so there are never infinite zeros

[@Chris-5318]

Tristan's 0.r0...1 and similar are nonsensical.

[@miniyoshiyt1178]

@Chris-5318 ik

[@Chris-5318]

@@miniyoshiyt1178 ik

[@Muchsperner]

“Why should 9x = 9??” Here’s why: 9x = 10x - x, 10x clearly being 9.9r, with x being 0.9r 9.9999999… -0.9999999… ____________= 9.00000000…

[@Caerwyn-z5o]

0.r9 can be represented as an infinite geometric sum S = 0.9 + 0.09 + 0.009 + ... on into infinity. A bit of high school math will tell you that a geometric sum with a common ratio r < 1 can be found using the formula a / (1 - r), where a is the first term. In this case, the common ratio is 0.1 (because we take the first term, 0.9, and multiply it by increasing powers of 0.1, such that the sequence becomes 0.9 x 0.1^0 + 0.9 x 0.1^1 + 0.9 x 0.1^2 etc.), and the first term is 0.9, obviously. By using the formula, a / (1 - r) , we find that the sum S = 0.9 / (1 - 0.1) = 0.9 / 0.9 = 1 Therefore, by proof of the sum of an infinite geometric series, 0.r9 is equal to 1

[@Caerwyn-z5o]

Also, with the "10x" argument, it actually states that: x = 0.r9 10x = 9.r9 10x - x = 9.r9 - 0.r9 9x = 9 x = 9 / 9 = 1

[@tristantheoofer2]

@Caerwyn-z5o ... but that shouldnt even work due to the number having literal infinite digits, thats just tacking on 1 more digit to the end of it for the funnies then subtracting the original number. its like making up the very slight 0.r0...9 difference by saying it basically doesnt even exist in the first place

[@Caerwyn-z5o]

​@@tristantheoofer2 By saying the number has "literal infinite digits", while yes 0.r9 has infinitely many 9s after the decimal, this doesn't mean there is a final digit to get to. The infinite sequence of 9s means that as you go further and further to the right, the difference between 0.r9 and 1 becomes infinitesimally small, effectively 0. Also, you saying "tacking 1 more digit to the end" suggests that the belief that adding another digit to an infinite sequence changes its value, but it doesn't. In a repeating decimal like 0.r9, there isn't a final digit to "tack on" because the 9s go on forever. If we did tack on a 1 onto the end for example, there would be a long string of 9s followed by a 1, but not an infinite string. In calculus, an infinite sequence can converge to a specific value, which in this case is 1. So, there is no "extra" or "missing" digit, 0.r9 is another way of representing 1. Finally, by saying there is a "slight 0.r0...9 difference", you are implying that there is an infinitely small difference between 0.r9 and 1, but that's not true. 0.r0...9 is an attempt to express an infinitesimally small number, but mathematically, this is exactly 0 because there is no measurable difference. There is no extra digit or tiny difference being ignored, it just simply doesn't exist because it can't. And when there is no difference between two numbers, they are equal. Hence why 0.r9 is exactly 1, and not "infinitely close but not quite"

[@zushyart]

I still like to think 0.r9 = 1, but I enjoy seeing your take on the topic! I think a lot of the debate comes from the fact that maths gets confusing when dealing with infinity.

[@tristantheoofer2]

ngl, agreed, i say it makes more sense for why it doesnt equal 1 by a LOOOONG shot but i think both sides have merits SOMEwhere lol

[@limenarity3141]

In reality, just like .0repeating1, you can always walk towards the one and be getting closer, this argument will go on forever, with no true answer. It's just semantics, and it doesnt matter which argument people believe in, as we cant apply this to anything in real life, as if the difference is not real, it is just one, but if it is real, then we have to aproximate iti anyways, as the difference is so close to 0 that it is literally impossible to calculate.