Have the mathematicians of /sci/ figured this out yet?
.999 does not equal 1 but .999(9repeating) does
>>16937683it does nott.hyperreal enjoyer
>>169376839 equals 1
im tired of normies and midwit human calculators treating mathematics like a unified domain
>>16937708normies and midwits SHOULD treat math as a unified domain. That's how its most useful to them
>>16937723aught they to embrace a linguistics than that departs magnitude and temporality? Several cultures in sub-saharan africa did perfectly well without. Just enough mathematics to use money, but not enough to understand how money works? useful to whom?
>>16937683headline is decpetive:https://www.scientificamerican.com/article/mathematicians-cant-agree-on-whether-0-999-equals-1/
Claim: [math] 0.999_{\dots} \neq 1[/math]Proof: We use induction. The base case is trivial: [math] 0.9 \neq 1[/math]. Next we introduce the notation that [math]0.9_n = \underbrace{0.9999999}_{n-\text{many nines}}[/math] is the decimal with n-many 9s.Now the inductive step: we assume [math]0.9_n \neq 1[/math]. Then trivially [math]0.9_{n+1} \neq 1 [/math]. It might help to notice that [math] 1 - 0.9_{n+1} \neq 0[/math]. This implies that [math]0.9_n \neq 1 \qquad \forall n\in \mathbb{N}[/math]Finally, we define [math] 0.999_{\dots} := \lim_{n\to\infty} 0.9_n[/math].[math]\therefore 0.999_{\dots} \neq 1 \qquad \square [/math]
.001 is still a fraction of a something, ergo it is still a thing, ergo it is a one (1)
>>16938008Gottem
>>16937683>0.999... = 1ok so then>0.888... = 0.999...>0.777... = 0.888...>0.666... = 0.777... and so on....>0.000... = 0.111...Therefore 0 = 1
>>16937989retard
>>16937974>scientificamerican.comOh. This is one of the magazines cobbled together by litcritters to feed politics-brained shit to white boomer lawyers and accountants who enjoy the flavor of science extract in their mouths.>>16937683Not clicking that shit. What's the best argument for and the best against this equality?>>16937698>hyperreal enjoyer0.999... does in fact = 1 in the hyperreals I'm sorry to say. pic related
>>16937989and how is limit defined in your argument, hmmm?should only take a sentence or two to clarify that small detail.
>>16938037>0.999... does in fact = 1 in the hyperrealsHuh?Is it not the case that [math]0.999... < 0.999... + \epsilon < 1[/math]
>>16938043Not according to the bible of 0.999... ≠ 1>https://arxiv.org/pdf/1007.3018see page 6; it follows that0.999... = 0.999... + 0.999.../∞ + 0.999.../∞/∞ ... = 1
>>16937727>useful to whom?Useful in territotializing themselves into capital, ideological, or biological reproduction of course. That's what DNA craves
>>16938019retard>>16937989Conclusion does not follow from the argument, because convergence and limit haven't been defined.
They would've reach a place where the numbers are so small they would cross over to 1 according to physics.
>>16938059Once you're talking physics rather than pure mathematics the question shifts over to the act of measurement itself rather than the "quantity" in a vacuum
>>16938059math isn't physics
>>16938046Alright, at least it's just a matter of confused notation/definition/etc. which the authors acknowledge (see the end of page 8), and not me just being flagrantly incorrect
>>16938050NTA but you don't need limits or convergence to prove the equality, just finite induction and a unique additive identity.>>16938059Physics is mostly famous for not knowing how very small things behave.
>>16938059>>16938061If a number doesn't hold any weight or size then it's imaginary and made up. That's why it has to cross over at some point. Supercomputers with large values would have at some stage have a movements with it being comprised from a physical property.
>>16938079it doesn't matter because this is the 200 time this shit has been posted.#DeadInternetTheory.
>>16938088Wait until you go outside for the first time and check the vitals of offline theory. It will blow your mind.
>>16938080i repeat, math isn't physics
>>16938019Right. And I can prove this with any number. Take, for, instance 12 and 59.>12.121212 = 13.131313Eventually means 12.121212 = 59.595959
>>16937683it's not a number and can't equal 1, no
>>169381701 in decimal notation is 1.000...Why can 1.000... be a number but 0.999... can't be?
>>16937683
>>16937698if you enjoy them so much, how come you don't know about the transfer principle?
Disgusting midwit here. When mathchads say 0.999.... = 1, is it in terms of aproximation, as in "eventually it reaches a point where the difference essentially does not exist, so we call it 1", or does it literally equal 1 at some point, with no difference at all?Like, if in reality I had .9 grams of something, then added .09, then .009, and so on and so forth and kept going on infinitely (ignoring the limitations of planck scale and pretending we can go below), will it literally equal exactly 1 gram at some point?
>>16942944That makes sense. Thanks for the explanation
>>16942874>>16942850
Genius here. Any number beginning with 0. is automatically less than 1. Clear now?
>>16937683>bitter disputesounds retarded. and countless online forums makes it a psyop, distraction. some wall to bash your head against
>>16937683in school i was taught that it equals 1 because0.(3) is the decimal representation of 1/3and 0.(9) is the decimal representation of 1/3 + 1/3 + 1/3and 1/3 + 1/3 + 1/3 = 1and that makes sense to me.i was taught it's just a flawed peculiarity of the decimal system rather than a real flaw/question in mathematics
>>16938049thats for the 300 families, not the 6 billion that are given just enough math to be convinced money is 'real', but not to their level so as to witness the racket operate in real time. Is ford alluded too, if the 6 billion understood the more one person works the more everyone has to work, and the less everyone works the less everyone has to work, and that its mathematically impossible for everyone to be debt free, and that that game of musical chairs is determined by who gets new loans, then they know the quickest and surest path to the territorialization into capital, ideological and biological reproduction- a successio plebis, a homesteading actgold is the money of kingssilver is the money of gentlemenbarter is the money of peasentsand debt is the money of slaveswe can appoint ourselves the duty of becoming peasents under the true LandLorde- He Himself Almighty
shut the fuck up please
>>16938108AI-generated gibberish.Thanks for proving my point retard bot.
>>16943377Also a bot, probably the same build that also generates "Cult of Passion" spam.
>>16938088>>16943397>>16943399This must be the bot version of a retarded black dude walking around calling everyone else a nigger.
>@16943404>"No u">Fails to provide counterexamples.>Simply comes up with an insult and for some reason slanders blacksObviously, a disinfo network utilizing thousands or even millions of bots to manipulate public opinion would not openly admit to being just that.
>>16943412>a disinfo network This isn't up to debate, btw. If someone claims the contrary, there's probably a reason for that...The other issue; half the comments in here are meaningless incoherent babbling typical of poorly trained bots who will respond to previous comments with something that, in fact, does not relate in any meaningful way to what is said. And the break down has been notable since 4chan's recent "relaunch".
In technical terms no. In practical terms yes.
The people who still don't understand it aren't mathematicians. Simple as.
>>16943412>@16943404Indian reply syntax
>@16943460>Keeps on "no u">Racist accusations for some unknown reasonAlrighty, you're a bot though no (you)ing.
>>16943479>@16943460Indian reply syntax
>>16943510
Shouldn't 0.999...+0.0...01=1?
>16943491no idea what I'm supposed to do with a malfunctioning bot.
>>16943534No, then0.999... + 0.0...01 = 1.0...00999...
>>16943571Note how the Indian reply syntax bot is programmed to mimic the lowest class of poo, untouchable, forbidden to reply directly.
Ye, there's no point in arguing with >>16943591because 1. it's obviously a bot and 2. it's a bot specifically meant to incite racial hatred so it must bring race into it.Very sloppy work, overall and you would expect bots by now to have become better than generating meaningless babbling like >reply syntax bot.Very obvious, very sloppy work.
>>16943611
>>16943614>it's a bot specifically meant to incite hatred
>>16943634for you
0.999... = 0.999...1 = 10.999... ≠ 1
>>16938019Bait ?Sure, but let's correct this bshit.0.999... < 10.999... + 0.000...1 = 11.000...1 - 0.000...1 = 10.999... (base 10) =/= 0.888... (base 10) =/= 0.777... (base 10) =/= 0.666... (base 10) etc.But :0.999... (base 10) = 0.888... (base 9) = 0.777... (base 8) = etc. = 0.111... (base 2) = 0.FFF... (base 15)
>>16943764Sure, but let's correct this bshit.0.999... = 10.999... + 0.000...1 = 1.000...0999...1.000...1 - 0.000...1 = 1
>>16943787I've a problem with>0.999... = 1For me, 0.999... , 1 and 1.000...1 can be 3 different things :f(x)=1/(1-x)If x = 1 , f(x) is undefined.If x = 0.999... , f(x) is +infIf x = 1.000...1 , f(x) is -infAm I stupid if I think that with those arguments, then :0.999... =/= 1 =/= 1.000...1 ?>Yeah, but +inf or -inf is like de Austrian Painter card... it's irrelevant.
>>16937683It obviously does not equal one, that’s retarded. By definition .9999… repeating is infinitely close to being 1 without actually being 1. It approaches 1 “asymptotically” but never reaches it. Otherwise it would be 1, not .9 repeating. Obviously. This whole debate is stupid as fuck.
>>16943796An integer is defined to have a 0 in whatever decimal place you need it to have a digit. You can resolve your problem the same way. 0.9... means that any digit you need beyond the ... for whatever reason is always 9
>>16943800With continuous variables, no value is equal to another value
>>16943817>An integer is defined to have a 0 in whatever decimal place you need it to have a digit.But some numbers can be written with infinite decimals and finite decimals :1/3 (base 10) = 0.333... (base 10)1/3 (base 10) = 0.1 (base 3)
>>16943822No problem. 0.1 in any base is defined to have a 0 in whatever digit you want after the 1. Same as writing 0.10... or 0.1(0) for clarity. Just like 0.3... or 0.(3) has a 3 wherever you need it.
>>16943827In the case 1/(1-x) ,How can you prove :0.999... = 1 = (0.999... + 0.000...1) ?
>>16943834No, I disagree with that.0.999... = 1but0.999... + 0.000...1 = 1.000...0999...
>>16943787>>16943764malfunctioning ChatGPT framework.>>Yeah, but +inf or -inf is like de Austrian Painter card... it's irrelevant.???>>16943800???>>16943820???>>16943822Not actually relevant to >>16943817>>16943834>>16943840>malfunctioning ChatGPT framework.
>>16943840Let's make it clear : f(x) = 1/(1-x)f(x) = f(x) obviously.You say :0.999... = 1So, you should have this :f(0.999...) = f(1)But :f(0.999...) = +inff(1) = undefinedThere is a problem here.
>>16943847>>>16943820 (You)>???All measured values presume a certain amount of precision. Precision is theoretically infinite. Therefore all measured values are theoretically not equal to any other values.
>>16943847Please insult Mohandas Karamchand Gandhi right now in the most heinous and racially insensitive terms; the speed of your reply and its base of vulgarity will both determine how successful you were in your response.
>>16943851Both are undefined. 1 - 0.999... = 0 is the same statement as 1.000... - 0.999... - 0.000... Both are equal to the integer zero.
>>16943855>>16943856Bot-generated gibberish.
>>16943861Failed.
>>16943860>Both are undefined. 1 - 0.999... = 0 is the same statement as 1.000... - 0.999... - 0.000... Both are equal to the integer zero.Is ChatGPT still malfunctioning over this issue. Expect more spam. Btw. this thread will be screenshot and I will forward it to a blog documenting and monitoring bot networks on the internet. I should technically not even write here.
>>16943861You really can't understand the theoretical limitations of precision in measurement? Maybe try /tv/ or /v/
>>16943864Non-sequitur comment is posted to disengage commenter. Usually, racial slurs will be used for no clear reason.
>>16943860>Both are undefined.That's wrong."+inf" is well defined, and totally different from "undefined".Claude is malfunctioning here too. Weird.
>>16943866Irrelevant, non-sequitur -> bot which now uses preprogrammed patterns to engage user in a meaningless discussion -> typical demoralization attempt which implies US build.
>>16943868>Claude is malfunctioning here too. Weird.Bot references previous comments including mine, however fails to integrate them which is typical of LLMs. -> Generates gibberish.
>>16943871Do you hate thinking? Or are you struggling with the difficulties of learning a new language?
>>16943874???
>>16943851>>16943860My nigga. Me and you. Skip the bots. Goto>f(x) = 1/(1-x)Both are undefined. 1 - 0.999... = 0 is the same statement as 1.000... - 0.999... - 0.000... Both are equal to the integer zero.
>>16943876I'm sorry I didn't mean to confuse you. For me it's fun to explore ideas and frameworks
>>169376839+9=18.99 = 1.8Therefore .9999 ~=2
>>16943935>Therefore .9999+.9999 ~=2
>>16937694It doesn't though.Proof:give me any no matter how large or long 0.999... number and I'll find you the large enough corresponding 0.001 number that's missing to make it a full 1Q.E.D.
[eqn]0.\bar{9} := \sum_{k=1}^\infty \frac{9}{10^k} :=\lim_{n\to\infty} \sum_{k=1}^n \frac{9}{10^k}= \lim_{n\to\infty} 1 -\frac{10}{10^n} = 1.[/eqn]Without the first definition ([math]:=[/math]), 0.99.. is meaningless notation, so accepting it necessarily accepts the concept of infinite summation which in the framework of real numbers is taken to mean the second definition. People wouldn't be upset if they were taught number definitions in middle school rather than vibes. You can't define infinite decimal representations without introducing limits, and if you did in a non-equivalent way then all of calculus and analysis needs to be recast and you effectively create a number system that is distinct from the reals.It is that simple. And if the above is difficult to parse then you are simply mathematically illiterate and need to read up on what you are talking about.
>>16944508so what you're saying is>I know 0.999... is not 1 but due to the definition and necessity we have to pretend like it isdon't get me wrong I don't have a problem with pretending that .999... = 1 or that trannies are women I have a problem with us pretending like we're not pretending
>>16944518>I don't like the definition because the vibe upsets meYou are given three choices>accept 0.99.. = 1 simply by definition of 0.99.. in the conventional context it is used invalid>categorically reject 0.99.. as a concept and consider decimal notation ill-defined outside of the rationals (basically a finitist lite approach)valid>reject 0.99... = 1 by defining infinite decimals in a different waythis is what you want I suppose, because you claim it is "pretend", which implies there is a "real" definition of 0.99... that disagrees with the conventional one. So, go ahead: define it.
>>16937683This is just like rounding up with money.
>>16944525that is to say that [math]\mathbb{R}[/math] as a whole is "playing pretend" on a fundamental level. The real numbers have unfathomably many warts in their framework. Almost all real numbers are not computable, for example. That is much, much more horrifying than 0.99.. yet it requires some basic idea of what a Turing machine is to make sense.
>>16944533>accept 0.99.. = 1 simply by definition of 0.99.. in the conventional context it is used inLet's settle it on this one. We will accept that in the context of doing math we, by definition, pretend that 0.999... = 1 BUT in the context of reality and everyday life we admit to each other that we're just pretending because otherwise math would collapse so we're forced to play pretend is this a deal?
>>16938079>Physics is mostly famous for not knowing how very small things behave.on the contrary. physicists re very confident in knowing how very small things interct
>>16937683what the fuck is 0.999...?show me 0.999... of an apple, or a cow.made up numbers are not real.
>>16944480No matter what 0.001 number you find, it has the 1 too early so you get 1.000999... you can never get farther out than the nines tail
>>16944562They say a small thing you found in the room with you can randomly be found on the moon if you try to find where it is again
>>16944588>>16944636>>16944664>>16944560>>16944533>>16944531It's all AI-generated slop.#Quit4channow
>>16944685
>>16944685Are you insinuating that I am a bot, or talking to a bot?>t. this post is dual-licensed under the AGPL+NIGGER and WTFPLv2.0+NIGGER license
0.3333... = 1/30.9999... = 3/3queue ee dee
>>16937989
>>16945050>0.3333... = 1/3nice try
>>16944885bot.Btw, weird how Israel/the US which is so obsessed with advancing black rights implements bots spamming the internet with slurs.
>>16944508>>16942850
>>16945411Wholeheartedly agree that you can see it as [math]0.\bar{9} :=\sup\{0,0.9,0.99,0.999,\dots\}=\sup\{\frac{10^n-1}{10^n}\vert n\in\mathbb{N}\}=1[/math]. You're basically using Dedekind cuts at that point, and realize that some lead to objects not contained in the rationals.
[math]0.\overline{9} \cdot 10 = 9.\overline{9}[/math]subtract both sides by [math]0.\overline{9}[/math]:[math]0.\overline{9} \cdot 9 = 9[/math]divide both sides by [math]9[/math]:[math]0.\overline{9} = 1[/math]
>>169452421/3 = 3/10 + 1/30= 0.3 + 1/30= 0.33 + 1/300= 0.333 + 1/3000:= 0.333... + 1/inf= 0.333... + 0= 0.333...
>>16937683>a = (0.9 ; 0.99; ... ; 0.999.. )>b = 1>invoke pythagoras>a^2 + b^2 == 2b^2 for every a>doesn't apply>????>profit
>>16944508limits aren't real
>>16946159You can't write an infinite decimal without implying infinite summation. Because a decimal number is a sum of integer powers of 10 times the corresponding digit. So if you write "..." you imply a limit, or you need to equip infinite summation with a strict definition that does not imply limits.
