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# /sci/ - Science & Math

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I know that a big part of this board is troubled by this simple fact. I do not wish to condone, in fact, I am very empathetic and actually SUPPORT everyone who doubts even the most popular assumptions. Sceptics are the policemen of science.

Therefore, I wish to assure every last sceptic here that 0.999... = 1, so that their energy could be directed at more noble tasks, which they deserve.

---

Let's say you have a bottle on 1L of liquid.
If you pour it into three glasses, equal amount each, you would have 1/3L in each glass. As we know (or can be convinced by simple manual division), 1/3 = 0.333...
So, if we were to pour all liquid back into the bottle, we would have 3*0.333... = 0.999... L in the bottle.

Since we started with 1L, didn't lose any liquid (since this is a mental experiment), and we have arrived to the quantity of 0.999...L, we can safely claim that 0.999... = 1.

Any questions?
Remember anons, there are NO stupid questions!

 >> Anonymous Sun Apr 12 09:46:58 2020 No.11557372 >>11557356Actually, you can divide 1 L in three only in base 9, of you define 1L as 9 mL. I used L but you could call this base 9 unit something else.With regular base 10 L, if you do that, you will get 0,3 + 0,3 + 0,4 L. Now if pay extra attention you might push the 4 way back, and obtain 0,33333 + 0,33333 + 0,33334 for instant, but if you measure it with somethibg precise enough, you will find a 4 somewhere.This stems from the fact base 10 unit system is ill suited for divisions by 3.If an alien species has 9 appendices and a base 9 unit system, they would find no problem with this, but would struggle with dividing by 5 for instance.A true intelligent species would be able to switch between bases at will using widely available computing power at their disposal, but I do not expect such thing from modern math enthousiasts (from top to bottom).
 >> Anonymous Sun Apr 12 09:53:45 2020 No.11557383 >>11557372>Inb4 you can divide the last infinitesimal unit in 3 foreverNo, at some point you would have to separate a single H2O (or any other liquid) in order to achieve the perfect equality of 3 + 3 + 3 (+ 1 to be divided in 3 again) which makes no physical sense.Same goes for spatial units, unless you're a continuous space faggot in which case kys you fairy.
 >> Anonymous Sun Apr 12 10:05:17 2020 No.11557403 No one has been able to argue against these two proofs:Via Cauchy sequences:0.999... = (0.9, 0.99, 0.999,...) = lim as n-> inf of 1-1/10^n = 1Via Dedekind cuts:Assume to contradiction that x is a rational number such that0.999... < x < 10.999... is greater than any finite string of 9s so for any natural number n1-1/10^n < 0.999... < x < 11-x < 1/10^n10^n < 1/(1-x)n < log(1/(1-x))Let n = ceiling(log(1/(1-x)))+1ceiling(log(1/(1-x)))+1 < log(1/(1-x))This is a contradiction, so x does not exist and 0.999... = 1.
 >> Anonymous Sun Apr 12 10:41:06 2020 No.11557511   >>11557403if 0.999... = 1then 0.9 = 0.8999...0.999... = 0.9 + 0.0999...0.9 = 0.8999...0.999... = 0.8999... + 0.0999...0.0.8999... + 0.0999... = 0.9998...0.999... = 0.9998...
 >> Anonymous Sun Apr 12 10:42:34 2020 No.11557514 >>11557511>0.0.8999...nice try retard
 >> Anonymous Sun Apr 12 10:50:38 2020 No.11557535   >>11557514Are you saying 0.9 != 0.8999...?
 >> Anonymous Sun Apr 12 10:52:26 2020 No.11557539 >>11557535>>11557514Nevermind, I see the typo.Corrected:>>11557403if 0.999... = 1then 0.9 = 0.8999...0.999... = 0.9 + 0.0999...0.9 = 0.8999...0.999... = 0.8999... + 0.0999...0.8999... + 0.0999... = 0.9998...0.999... = 0.9998...
 >> Anonymous Sun Apr 12 11:00:59 2020 No.11557559 >>11557372Your measuring device, regardless of the basis, has only a limited precision. Always. Let's say the basis is 10 and the precision is up to two decimal places. Then if your instrument shows 0.33, it means that in the glass is33/100 litres + R litreswhere the error R is, in absolute value, surely smaller than 1/1000. You can measure 0.33+0.33+0.33 no prob, it just means that the error terms add up to 0.001L. If you take a measuring device which uses base 3 and 2 places, then you will probably measure 0.10 but you can't conclude that there's exactly 1/3L in the glass. You can only conclude that there's1/3 litres + R litreswhere the error R is surely smaller than 1/27 (because 27 = 3^3).
 >> Anonymous Sun Apr 12 11:18:58 2020 No.11557599 >>11557559(cont)The exact amount 1/3 L is characterized as follows: If you take any measuring device which uses base 3, then no matter how precise it is, it will always show 0.1000...00.The exact amount 0.333...L is characterized as follows:If you take any measuring device which uses base 10, then no matter how precise it is, it will always show 0.333....3. These statements are equivalent by an easy argument using long division. This is the meaning of the equation 1/3 = 0333...
 >> Anonymous Sun Apr 12 11:21:32 2020 No.11557602 >>11557372>only in base 9the tree exists only if I look at it from this angle...hurrrr durrrr
 >> Anonymous Sun Apr 12 11:26:03 2020 No.11557617 >>11557539>0.8999... + 0.0999... = 0.9998...Incorrect. Learn how to add.
 >> Anonymous Sun Apr 12 11:33:09 2020 No.11557646 >>11557356Some guy posted it in an earlier thread but.if .999... = 1then it's safe to assume that.899.. = .999...But does .899... = 1?If the first rule were right numbers wouldn't exist at all
 >> Anonymous Sun Apr 12 11:33:16 2020 No.11557647 File: 18 KB, 410x566, Hmmmmmmm.jpg [View same] [iqdb] [saucenao] [google] [report] >>115576170.8999... + 0.0999... = 0.999...8
 >> Anonymous Sun Apr 12 11:33:22 2020 No.11557648 >>11557599You're dishonest.0,1000... = 0,1 just like 3 = 3,000... in regular base 10, or any base.>>11557602Retard
 >> Anonymous Sun Apr 12 11:33:56 2020 No.11557650 File: 141 KB, 640x480, 12889019025.jpg [View same] [iqdb] [saucenao] [google] [report] >>11557599Your explanation seems flawed, because you're mixing real life margin of error in measurements with the limitations of representation of an abstract concept, which is Math.The fact that we can't come to a conclusion about this issue proves Math, a virtual concept humans created, is flawed.
 >> Anonymous Sun Apr 12 11:36:50 2020 No.11557658 >>11557646That was me, I revised the argument a bit here>>11557647When you add 0.8999... to 0.0999... you repeatedly carry the 1 over to the left which gives you and infinite number of 9's following by an 8, which you can represent with bar notation or by ellipses as 0.999...8
 >> Anonymous Sun Apr 12 11:42:20 2020 No.11557677 >>11557599If you apply math to measure units in a discrete plane, 0 is an absence of unit, so 0,1000...000... makes no sense, infinitely repeating 0s are not written down.So yes, 1/3 in base 9 = 0,1 full stop just like 1/5 in base 10 = 0,2 full stop. To divide 1 unit in three perfectly equal lesser units you need a base to do so in the first place, because 1 is the smallest unit unless the scale is off and a smaller unit, of which 1 is comprised, exists. So you need a base, and that base is 9. There is no reason to reason to do so in base 10 and obtain the retarded 0,333... + error besides convention and the fact de have 10 digits. That's literally it.>>11557650Thank you, you get it.
 >> Anonymous Sun Apr 12 11:44:18 2020 No.11557684 >>11557403Now do it via almost homomorphisms of the integers (see Eudoxus reals).
 >> Anonymous Sun Apr 12 11:44:36 2020 No.11557686 >>11557646Retard. 0.899...=0.9, not 1.
 >> Anonymous Sun Apr 12 11:47:52 2020 No.11557700
 >> Anonymous Sun Apr 12 11:48:41 2020 No.11557703 >>11557658>>11557686I fucked that up ignore that
 >> Anonymous Sun Apr 12 11:52:06 2020 No.11557714 >>11557677And we use base 10 because we have 10 fingers.Mathfaggs clinging to 1= 3 X 1/3 = 0,333...X3 = 0,999... = 1 are literally ugga bugga apes unable to fathom the fact you can construct units with a base that does not use all of and only their 10 niggerfingers to count.
 >> Anonymous Sun Apr 12 11:56:19 2020 No.11557733 >>115576771/3 = 0,3 in base 9 not 0,1 sorry.
 >> Anonymous Sun Apr 12 11:56:46 2020 No.11557735 >>11557677>To divide 1 unit in three perfectly equal lesser units you need a base to do so in the first place,In the material world, you will never know if you managed to divide a unit into three equal lesser units. Only up to arbitrary precision. It's totally independent of the base. Don't tell me you're disputing this.In mathematics, things get abstract, and 0.333... = 1/3 becomes simply a logical formula which happens to be true. There's no discussion here. Your only chance is to reject a part of mathematics for some personal reason.
 >> Anonymous Sun Apr 12 12:01:30 2020 No.11557749 1 - .999... = 0?
 >> Anonymous Sun Apr 12 12:04:11 2020 No.11557762 >>11557714Nothing wrong with choosing to represent a number in base 10. Just because it's arbitrary doesn't mean it's incorrect.>you can construct units with a base that does not use all of and only their 10 niggerfingers to count.So according to you, what is 0,9999... in some other base besides 10?For example,0,333.... in base 10 = 0,4 in base 12.0,999.... in base 10 = ? in base 12.What replaces the question mark in the previous line?
 >> Anonymous Sun Apr 12 12:04:16 2020 No.11557763 >>11557735>In the material world...Our inability, for now, to measure perfectly well X or Y doesn't mean our maths shouldn't function as if we did.But again, you're wrong, an atom is an irreductible unit, for instance. We could measure it.
 >> Anonymous Sun Apr 12 12:06:50 2020 No.11557771 >>11557700I saw that argument too, it’s still shit. There’s no contradiction, you’ve only proven that 0.999...8=1, which is correct as can be seen from your line of reasoning.
 >> Anonymous Sun Apr 12 12:13:33 2020 No.11557792 >>115577620,333... is the wacky result of a ratio in a base that doesn't support that ratio, as in 1/3 in base 10.0,999... is a constructed abstract concept that does not exist and that represents nothing.All numbers are constructed and abstract, but they all derive from the first primary assumption / convention that 1 is a unit that exists and 0 is the absence of 1. All the other numbers are derived from 1, by one way or the other. You can't obtain 0,999... by any natural operation other than adding 0,9+0,09+0,009+... to Infinity which makes it a limit, a function, represented as 0,999... by convention. You cant take 1 and use it do obtain 0,999... You can't do 1 - 0,000...1. You can't divide it by a certain number either, etc..
 >> Anonymous Sun Apr 12 12:17:01 2020 No.11557800 >>11557792>0,999... is a constructed abstract concept that does not exist and that represents nothing.Well then, I suppose that frees us to choose something for it to represent.I choose for 0,999... to represent the same quantity as 1.
 >> Anonymous Sun Apr 12 12:20:01 2020 No.11557816 >>115577620,333... =/= 0,4 in base 12, 1/3 does.1/3 is a ratio, 0,333... is not a ratio, it's the representation of an approximation because that ratio can't be properly defined in base 10. You could hace used another convention that ..333... if you wanted.0,999... represents no known ratio, in any base, so there is no need to express by this convention something that can never occurr in the material world and does not exist. It confuses you because 0,999... unlike other concepts in maths, uses really common symbols, but it is an impossibility, it can't exist.
 >> Anonymous Sun Apr 12 12:22:57 2020 No.11557830 >>11557792Consider base n.In base n, 1/(n-1) is represented as 0,111...We know that (n-1) * 1/(n-1) = 1.And we know from arithmetic that (n-1) *1/(n-1) = 0,{n-1}{n-1}{n-1}... where each {n-1} represents a digit.So in any base n, 0,{n-1}{n-1}{n-1}... = 1.
 >> Anonymous Sun Apr 12 12:23:48 2020 No.11557834 >>11557800Feel free to do that, you can also say ° = 1 I don't care man. It's just not practically true, and even theoretically it makes no sense and can easily be debunked by deconstructing the base 10 convention of 10 fingered apes. It's a childish "fun" thought to have that 0,999...=1, it has no real implications, no real consequences in ANY field.
 >> Anonymous Sun Apr 12 12:24:00 2020 No.11557835 >>11557816>0,333... =/= 0,4 in base 12Read carefully, I never implied that 0,333... = 0,4 in base 12.I said that0,333... in base 10 = 0,4 in base 12.
 >> Anonymous Sun Apr 12 12:25:07 2020 No.11557844 >>11557763>>11557763>Our inability, for now, to measure perfectly well X or Y doesn't mean our maths shouldn't function as if we did.But our math does function this way. This actually speaks in favor of infinite decimal expansions, not against. So what exactly is your problem with 0.333... ?>But again, you're wrong, an atom is an irreductible unit, for instance. We could measure it.Obviously we're talking about quantities which are modelled well by the continuum.
 >> Anonymous Sun Apr 12 12:27:29 2020 No.11557856 >>11557830You're wrong on you second line. It does not equal 0,111...Try your assumption with a n=9 or n=5 and find out.Also use a paper + pen, because I doubt your calculator lets you switch bases like that.
 >> Anonymous Sun Apr 12 12:31:07 2020 No.11557869 >>11557856In base 9: 1/8 = 1,0/8,0 = 0,1 R1 (8 goes into 9 once)= 0,11 R1 (8 goes into 9 once)= 0,111 R1 (8 goes into 9 once)etc.In base 5: 1/4= 1,0/4,0 = 0,1 R1 (4 goes into 5 once)= 0,11 R1 (4 goes into 5 once)= 0,111 R1 (4 goes into 5 once)etc.
 >> Anonymous Sun Apr 12 12:33:42 2020 No.11557878 >>11557844There is no evidence for continuum, I personally think space is discrete.Anyway it's another debate but I find It gay that math decided in favor of continuum theory, even moreso that even if true, continuum theory wouldn't impacto anything besides fields way below what we notice and use everyday. Discrete space makes practical sense for 99% of our activities yet our primary tool, maths, uses continuum as truth.
 >> Anonymous Sun Apr 12 12:36:43 2020 No.11557889 >>11557869Now do base 2 :^)
 >> Anonymous Sun Apr 12 12:39:34 2020 No.11557904 >>11557403>No one has been able to argue against these two proofsApart from all the times it was debunked, sure.
 >> Anonymous Sun Apr 12 12:39:40 2020 No.11557905 >>11557830That's where you got me wrong. 0,111... is never a valid representation. You shouldn't use it for operations, use the ratio instead, or the approximation sign.Anyway 1/n-1 can be resolved and expressed in non ratio form in base 2 only.
 >> Anonymous Sun Apr 12 12:41:14 2020 No.11557910 >>11557889>>11557856lolIn base 2:1/1= 1
 >> Anonymous Sun Apr 12 12:44:35 2020 No.11557925 >>11557878It's not about discrete = true, continuous = wrong. It's about what's useful for the problem in hand. The water consists of a finite number of particles, no doubt, but fluid mechanics is still modeled by PDE. Why do you think this is?
 >> Anonymous Sun Apr 12 12:46:54 2020 No.11557936 >>11557910So in base 2, 0,111...=1 :^) clown world indeed.Very sound theorem anon.>>11557830
 >> Anonymous Sun Apr 12 12:50:47 2020 No.11557953 >>11557925Because the number of particles in a volume where fluid mechanics occur is so great that an approximation is enough to correctly predict stuff with a very small infinitesimal error. Again, an approximation working for all useful purposes is a whole different statement than "=".
 >> Anonymous Sun Apr 12 12:50:50 2020 No.11557954 >>11557936Unironically yes
 >> Anonymous Sun Apr 12 12:53:38 2020 No.11557962 So I'm confused on the .999....=1 situation.They say "There's no number between .9 repeating and 1, so they are equal". But then in probability you have the concept of "almost 0". Like if you select a random number from the set of all reals, what is the chance you'll get 4? Well it's not 0, it's almost 0. Isn't that Almost 0 the number inbetween .999... and 1?
 >> Anonymous Sun Apr 12 12:54:48 2020 No.11557968 >>11557647>0.8(9)+0.0(9) = 0.(9)8This is incorrect, it's just 0.(9). Look up the algorithm for addition from the left.This is also irrelevant to what you're replying to. Show that 0.8999... + 0.0999... = 0.9998...
 >> Anonymous Sun Apr 12 12:56:02 2020 No.11557972 >>11557904>all the times>can't even name one
 >> Anonymous Sun Apr 12 12:58:30 2020 No.11557980 >>11557953And you do realize that both PDE and infinite decimal expansions are parts of one theory which either works as a whole (including small annoying technical details like 0.999...=1), or doesn't work at all, right ?
 >> Anonymous Sun Apr 12 12:59:28 2020 No.11557984 >>11557962You’re trying to apply a measure theoretic concept and *almost* use Erdös’s probabilistic method, but that’s not what this means. 0.999... = 1 is a simple consequence of the construction of the reals by completing the rationals either by classes of Cauchy sequences or by dedekind cuts. Also this concept of “almost” doesn’t apply except maybe to infinitesimal numbers..but the reals are constructed in a way such that 0 is the *only* infinitesimal number. This is exactly the Archimedean property.
 >> Anonymous Sun Apr 12 13:02:03 2020 No.11557993 >>11557953>infinitesimal error Dude the only infinitesimal in the real field is 0 by construction, since it’s the Archimedean property that shows this. The only unmeasurable distance in the reals is something satisfied by a number b such that for every nonzero real r, b < r, and the basic Archimedean and order properties of the reals ensure you can always find a smaller nonzero b.
 >> Anonymous Sun Apr 12 13:02:19 2020 No.11557996 >>11557984So what, if you're a statistician you get a special set of reals that don't have the properties of the regular reals?
 >> Anonymous Sun Apr 12 13:02:56 2020 No.11558001 >>11557984It's all conventions all around man. All purely math-related conventions have 0,000... use in other fields so nobody cares. Otherwise a physics guy would have btfo this retardation at some point.
 >> Anonymous Sun Apr 12 13:05:02 2020 No.11558007 >>11557962>But then in probability you have the concept of "almost 0".No, in probability you have the concept of almost impossible, which is just p=0.>Like if you select a random number from the set of all reals, what is the chance you'll get 4?What does that mean? >Well it's not 0, it's almost 0.LOL, it's undefined because you haven't explained what you mean by randomly choosing a real number. You don't even know if it's possible.
 >> Anonymous Sun Apr 12 13:07:22 2020 No.11558017 >>11557996...no, the regular reals you speak of all have this Archimedean property. This is like the first chapter of any elementary analysis book. Youre complaining about something that’s counter intuitive yet ultimately follows almost immediately by the construction of the reals that everyone uses but people don’t study unless they take analysis...and statisticians generally hit at least one analysis course before grad school.
 >> Anonymous Sun Apr 12 13:07:24 2020 No.11558018
 >> Anonymous Sun Apr 12 13:08:16 2020 No.11558021 >>11557962those are two things which are completely unrelated. there's nothing else to say.
 >> Anonymous Sun Apr 12 13:09:15 2020 No.11558025 >>11557993What if space is discrete nigger?Your field presumes X then deduces Y then wonders why retardation like 0,999...=1 sees the light of day and instead of revising the theorem / definitions plunges its head further down its ass and never really demonstrates anything because "muh maths don't exist in the real world" when any experiment based on geometry, mass or light speed could be imagined to put it to test. That's why you're not a science but glorified philosophy.
 >> Anonymous Sun Apr 12 13:10:48 2020 No.11558031 >>11558001Nothing here is “about conventions.” This is the simple fact that the reals field does not have unique labels for rationals given its structure, which we see both by classes of Cauchy sequences and by dedekind cuts. A physics guy cannot generally btfo people at math because they apply math on a need to know basis - so they’re the last guys, unless we’re talking about mathematical physics in the math department, who could help doing a proof problem
 >> Anonymous Sun Apr 12 13:14:01 2020 No.11558045 >>11558031Whatever.Maths are just a tool, I reject your faggoty bullshit out of rational integrity but don't give a fuck one way or the other. 0,999...=1 has no impact whatsoever in any field outside of maths, and I'm fine with it.
 >> Anonymous Sun Apr 12 13:15:45 2020 No.11558055 >>11557658You can't have an infinite number of nines, show me anywhere in the world where there is an infinite number of nines
 >> Anonymous Sun Apr 12 13:16:51 2020 No.11558058 >>11558025>what if space is discrete Discrete in what sense? The reals do not have the properties you desire, ie, there is no neighborhood of a real number lying in the set of all reals that is empty. >Your field My field is what? What exactly is your field?>presume X deduces YExactly what are X and Y here, or do you have a problem with basic implication structure? I think you’re probably the guy who hates nonstrict inequalities too>retardation like 0.999... = 1A simple non intuitive fact about the real field is suddenly the end of the world? >muh maths Lol europoor >doesn’t exist No...it’s that these labels refer to the same object. You don’t need an ontology to confirm or refute that. The issue at hand is pure and no “real world evidence” has the power to refute or corroborate it.>not a science Math produces stronger results than science that are used comfortably everywhere lol. You’re probably also the crowd that hates imaginary numbers but has no issue about how they work magically in circuits problems.
 >> Anonymous Sun Apr 12 13:20:38 2020 No.11558073 >>11558045>whatever You made the wrong argument and want to brush it off?>maths is just a tool Trivializing the topic at hand is a clear way to try and downplay you’re lack of reasoning, I get it, but why are you so visibly salty?>out of rational integrity No; you have a feeling these things can’t be equal likely out or a lack of understanding the canonical construction of the reals or what they aim to “complete” in the first place. Any effort to say this has been met with “muh dogma.” >has no impact I mean I agree that this result is not the big life changing theorem. But it is the stepping stone to nontrivial topics. I bet if you took measure theory you’d shit your pants at “the bullshit” even though even in application, everything works out precisely as expected.
 >> Anonymous Sun Apr 12 13:23:37 2020 No.11558087 >>115580250.999... = 1, or more generally the fact that a number may have two distinct decimal representations, is a minor technical abnormality of the decimal system, which otherwise works just fine. If you have a better idea what should we use to represent real numbers, feel free to share.
 >> Anonymous Sun Apr 12 13:26:55 2020 No.11558104 >>11558045>Maths are just a tool, I reject your faggoty bullshit out of rational integrity but don't give a fuck one way or the other. 0,999...=1 has no impact whatsoever in any field outside of maths, and I'm fine with it.see >>11557980
 >> Anonymous Sun Apr 12 13:28:11 2020 No.11558113 >>11558058Discrete in that you can divide it in smaller boxes up to a certain point where you can't divide anymore, therefore rendering an infinite number of X like on 0,999...999...impossible.>Your fieldMaths I presume.>My fieldLaw. I have an interest in "science", or more specifically physics and biochemistry.>Define X and YX = continuous space that makes Y = infinitely repeating 0,xxx... possible in a vacuum.>EuropoorMy country (Switzerland) is superior in every indicator to the USA>No real world evidenceJust like religion and philosophy, agreed.>Not a scienceStill not a science if you aren't willing to put it to test. Some mathematical theories, most of them actually, are sound and produce results. But others are not and you lack the integrity AND vision to reconsider them or to put them to test. Philosophers were right about most things too, even some religions for some things right, still not scientists.
 >> Anonymous Sun Apr 12 13:30:38 2020 No.11558124 >>11558087It works, It just occurs to me that the approximation sign should be used out of integrity. 0,997 € = 1 € for all useful purposes as well, same should apply here.
 >> Anonymous Sun Apr 12 13:32:23 2020 No.11558133 >>11558073>Canonical constructionAgreed.>Muh DogmaYes.
 >> Anonymous Sun Apr 12 13:32:51 2020 No.11558136 >>11558018Almost surely = 1So what?
 >> Anonymous Sun Apr 12 13:34:12 2020 No.11558140 >>11558136Make up a new sign for almost surely and stop using = nigger.
 >> Anonymous Sun Apr 12 13:41:18 2020 No.11558161 >>11558113>Discrete in that you can divide it in smaller boxes up to a certain point where you can't divide anymoreYeah that’s the same as claiming there’s a neighborhood of a real sitting in the reals such that it’s empty - and this is NOT true by construction lmao. So no, the reals are not a discrete space as you claim >my field is law >interest in physics and biochem That’s great and all but neither of those equip you with the necessary tools to even address this argument. You’re using a 3rd grader’s understanding of the reals lmao and then trying to overfit empirical misunderstandings.>X = continuous space that makes Y = infinitely repeating 0,xxx... possible in a vacuumLOL it’s not continuous spaces that imply this alone. It’s continuous + completion + least upper bound property + Archimedean property + completely ordered field + rational subfield + equivalence classes of Cauchy sequences of rationals / dedekind cuts = one small quirk about the unique (up to isomorphism) field called the reals about the labels of rationals.>Swiss And yet still wrong, so your education didn’t do much for you >not a science Math is math, and as such science cannot make statements about mathematics, but mathematics is needed for the advancement of science, much to the chagrin of experimentalists. That being said, scientists do this in a collaborative manner - many do not understand the mathematics past its basic description, which makes many of them them clearly ill equipped to even start doing proofs
 >> Anonymous Sun Apr 12 13:42:33 2020 No.11558164 >>11558140But we have equality by the way measure theory works Imagine not understanding the generalization of length via measure and trying to argue about the reals
 >> Anonymous Sun Apr 12 13:44:00 2020 No.11558173 >>11557647Wrong, retard. The 0.999...8 is not infinite because there's an 8 AT THE END.
 >> Anonymous Sun Apr 12 13:45:01 2020 No.11558178 >>11557749What do you expect me to say other than "duh"?
 >> Anonymous Sun Apr 12 13:53:11 2020 No.11558215 >>11558161The construction you have is wrong in nature then. You go from 1 unit to breaking it into smaller units. Your construction is the result of humans not comprehending what the smallest unit could be at the time so every unit we made up could be broken by a base. It does not mean it's true for all units.
 >> Anonymous Sun Apr 12 13:55:55 2020 No.11558224 >>11558215You’re crying foul because you think the reals behave in a way they don’t...so then someone tells you that by definition you’re wrong...so then you double down and say nature is quantized so math should be as well. Don’t you see the folly? I know the (You)’s are addicting, but you’re making claims way outside your expertise / experience here and it shows
 >> mylotyrena Sun Apr 12 14:00:31 2020 No.11558239 >>11557800no you cant make u maths 0.9999... = 1 because1/9 = 0.111111...2/9 = 0.22222...therefore9/9 = 0.99999...9/9=1therefore 0.99999... = 1or more abstractly the more 9s you wright the smaller the difference between your number and 1 theirfore if you wrote an infinte number of 9s the diference would be 0 making 0.99999... = 1retard
 >> Anonymous Sun Apr 12 14:01:10 2020 No.11558240 >>11558215>>11558161Follow me on this.1 Atom is the unit, lets call this unit mAtm.1 Atm = 1000 mAtm.0,9 Atm exists, so does 0,99 Atm, so does 0,999 Atm, but everything past that, let alone 0,999..., makes no sense.Now imagine every unit ever is comprised of the equivalent to an Atom, something so small it can not be divised any further, which is what every evidence points to, do you see why 0,999... makes no sense now?>B-but It works for fluidsYeah so does Newton's law of Gravity for most things, doesn't make it a sound system, just a useful faulty system.
 >> Anonymous Sun Apr 12 14:06:57 2020 No.11558256 >>11558240your analogy breaks down because you cant get decimals of an atoms (excluding sub atomic particles). by your analogy 0.75 wouldn't exist either ps different atoms way different amounts google relative atomic mass
 >> Anonymous Sun Apr 12 14:09:19 2020 No.11558264 >>11558224There is an interaction of units in nature that exists without a human observer. You do not hold a monopoly on how to retranscript them and the Reals theory is not a natural law that can't be circumvented. It's just right 99,9999999% of the time so there is no need for a new system, however, you seem to not understand the implications and the ideas behind what numbers and decimals are. You just know a lot of "how" but have no clue on "what". Understanding the nature of "what" is not technical, anyone can do it by logical thinking, no technical skills involved.
 >> Anonymous Sun Apr 12 14:12:33 2020 No.11558276 >>115582560,75 can or can not exist depending on the unit. 0,999... we are certain can not exist was my point.>Muh atom weightA neutron, a quark, doesn't matter, it stops being possibly broken down at some point.
 >> Anonymous Sun Apr 12 14:14:35 2020 No.11558284 >>11558276you can have 0.9999... of an atom its the whole thing
 >> Anonymous Sun Apr 12 14:17:02 2020 No.11558290 >>11558284You're a faggot running in circles unable to escape his conditionning. There is no hope for you Anon...
 >> Anonymous Sun Apr 12 14:19:33 2020 No.11558295 >>11558290what youve got to realise is that when the whole world disagrees with you your probably wrong.
 >> Anonymous Sun Apr 12 14:28:17 2020 No.11558317 >>11558239You CANT WRITE an infinite number of nines!!!!You can only write a FINITE NUMBERE!
 >> Anonymous Sun Apr 12 14:39:32 2020 No.11558351 >>11558295Ok mister the Archbishop.Take my children and spread the good word now.>>11558317The Infinite is not the problem dishonest fagg. The "infinitely" small is.
 >> Anonymous Sun Apr 12 15:10:10 2020 No.11558432 >>11558317$0.\bar{9}$
 >> Anonymous Sun Apr 12 16:04:04 2020 No.11558581 >>11557968>>11558173Was playing around with this some more. I thought that by 8 being after the 0.9bar would weaken the equivalence between 1 and 0.9bar but it actually makes the argument stronger because the 8 has virtually no arithmetic effect because a 9 always precedes, meaning arithmetically 0.9bar8 is equivalent to 0.9bar. in fact you could put any number after the 0.9bar and it wouldn't have an arithmetic effect because the 9's would always precede whatever you put after them rendering it ineffective when adding left to right. So weird.
 >> Anonymous Sun Apr 12 16:15:02 2020 No.11558602 >>11557356We have been through all of this, all the retarded mental gymnastics, all the lies and intellectual dishonesty, all the parroting and indoctrination,It has already been proved that 0.999... DOES NOT EQUAL 1.You SODOMITES were beaten. The HOLY CHURCH of the FINITE was victorious. FACT: The Universe is finite and it is discrete. Its time to give up. Stop making these ridiculous troll threads.
 >> Anonymous Sun Apr 12 17:16:18 2020 No.11558767 >>11558602Based
 >> Anonymous Sun Apr 12 17:20:49 2020 No.11558779 >>11558602This. It's settled. The sophists have lost.
 >> Anonymous Sun Apr 12 17:22:41 2020 No.11558788 File: 40 KB, 410x598, 1586195557718.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sun Apr 12 17:24:13 2020 No.11558794 >>11557686If 0.9999999...=1 and 0.899999999......=0.999999999999Then if a=b and a=c then you’d assume a=c
 >> Anonymous Sun Apr 12 17:26:27 2020 No.11558801 >>11558794>0.899999999......=0.999999999999delete this nephew
 >> Anonymous Sun Apr 12 17:27:16 2020 No.11558808 >>11558794Sorry a=b and a=c then b=c I mean
 >> Anonymous Sun Apr 12 17:27:28 2020 No.11558809 >>115587940.89...=.9 You fucking mongoloid.
 >> Anonymous Sun Apr 12 17:29:06 2020 No.11558813 >>11558801Oh shit def see where i fucked that up.
 >> Anonymous Sun Apr 12 17:30:43 2020 No.11558817 >>11558317Correct, which is why we write '1' instead.
 >> Anonymous Sun Apr 12 17:31:44 2020 No.11558819 File: 97 KB, 1654x2339, For 1 tards.jpg [View same] [iqdb] [saucenao] [google] [report] >>11558602Wrong, retard.
 >> Anonymous Sun Apr 12 17:36:00 2020 No.11558825 >>11558819Stop posting gibberish
 >> Anonymous Sun Apr 12 17:40:58 2020 No.11558837 >>11558825It's literally a mathematically rigorous proof that 0.999...=1Just because YOU are too stupid to understand the argument doesn't mean it's true.
 >> Anonymous Sun Apr 12 17:43:42 2020 No.11558849 >>11558837""""""""rigorous"""""""">assuming that 0.9999...=1, then 0.9999...=1that's how dumb you sound
 >> Anonymous Sun Apr 12 17:43:49 2020 No.11558852 File: 73 KB, 554x400, dab.png [View same] [iqdb] [saucenao] [google] [report] >>11558837Show me 0.999... in nature or your """proof""" is nonsense.TIMES UP.Sorry, 1-0.999.. = Almost 0. Deal with it homo
 >> Anonymous Sun Apr 12 17:50:33 2020 No.11558875 >>11558849Where does it do that? Give me the line. Show me how "dumb" I am by showing me that line.>>11558852I'm holding up 1 middle finger at your post. Since point nine repeating equals one, I'm flipping you off with point nine repeating fingers. Give me an actual math disproof. The Reals are dense, thus if 0.999...<1 then there exists a 'c' such that 0.999...
 >> Anonymous Sun Apr 12 17:51:19 2020 No.11558878 >>11558875Cringe. This is the state of American "debating"
 >> Anonymous Sun Apr 12 17:52:58 2020 No.11558882 >>11558878You're right, I should've just said they're 'cringe' and left it at that. *rolls eyes*
 >> Anonymous Mon Apr 13 00:22:11 2020 No.11559797 >>11557356Infinity is only a potential, not an actual existent.
 >> Anonymous Mon Apr 13 00:28:32 2020 No.11559810 >>11559797Stop typing stuff as though you actually know what you're talking about.
 >> Anonymous Mon Apr 13 00:40:28 2020 No.11559840   >>11558878You're the one saying that 0.999 =/= 1So, this means you're assuming that there exists some number x such that $0.999 < x < 1$proof or gtfo
 >> Anonymous Mon Apr 13 00:44:29 2020 No.11559844 >>11558878You're the one who's saying that $0.999... \ne 1$That means you're assuming there exists some number $x$ such that $9.999... < x < 1$So, post proof or gtfo
 >> Anonymous Mon Apr 13 00:51:54 2020 No.11559866 >>11557356You can't pour it into 3 glasses equally you faggot.
 >> Anonymous Mon Apr 13 00:56:09 2020 No.11559873 >>11559844>That means you're assuming there exists some number x such that 9.999...
 >> Anonymous Mon Apr 13 01:06:01 2020 No.11559902 File: 112 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report] >>11559873>How does that supposed to prove anything?Don't be such a brainlet. $0.999...$ is, in fact, equal to exactly $1$ and this can be proven with simple algebra.Just because the alias doesn't look alike, doesn't mean they don't share the same *value*, in the same way that $0.5$ doesn't look like $\frac{3}{6}$.
 >> Anonymous Mon Apr 13 01:51:17 2020 No.11559982 >>11557356Prove that 1/3=0.333...>>11557403Literally doesn't know the definition of limit. 1/10^n never reaches 0
 >> Anonymous Mon Apr 13 01:59:10 2020 No.11560001 >>11559902You can't multiply and infinitely large number by 10. Prove that 1/3=0.333... protip you can't. Prove the formula of sum of an infinite geometric progression.
 >> Anonymous Mon Apr 13 06:06:03 2020 No.11560390 >>11558240The math itself isn't and cannot be "faulty". The only thing that's faulty is that it doesn't model reality 100% correctly. But NO physical theory does this and no theory ever will. There's no theory of everything. So does that mean ALL of math is faulty? You have already acknowledged that continuous math is used for fluid dynamics, simply because it's useful and easier than the alternative. So the question is: should we not use it, because the fluid is not actually continuous ?You can say "yes", it's a perfectly valid stance. But then you're practically saying that all of math should be finite, discrete, there is some largest integer past which we shouldn't count, there is some smallest fraction past which we souldn't divide. Again, ultrafinitism is a perfectly valid stance, it's just that your issue with math is much much bigger than just "0.999... doesn't exist". Or you can agree that even though spacetime is probably discrete, continuous math is still plenty useful, but then 0.999... = 1 is an irrefutable consequence of the theory.
 >> Anonymous Mon Apr 13 06:24:28 2020 No.11560421 >>11560390First high IQ post itt.Yes, this is my stance.0,999... = 1 is no more valid than pic related, but the non-valid system producing it is useful indeed.I still think we will switch to a more complete, "true-in-nature" (in the sense physics are, I know we will never get ris of the subjectivity attached to the observer) model as our computing power will increase and the simplification needed and brought by continuum in maths will no longer be necessary. Then 0,999...=1 will no longer make sense. Or maybe space is Indeed a continuum or maybe there is a God that created maths, but I don't see either of those being proven correct, it's counter-intuitive and it would make for an irrational world in the physics sense.
 >> Anonymous Mon Apr 13 06:27:16 2020 No.11560424 File: 154 KB, 2000x1400, 2000px-NewtonsLawOfUniversalGravitation.svg.png [View same] [iqdb] [saucenao] [google] [report] >>11560421>>11560390Forgot pic related.This is an equivalent to the continuum maths theory, a valid system if you don't look too close.
 >> Anonymous Mon Apr 13 06:35:13 2020 No.11560442 >>11560390I think there is no upper bound but there is a bottom bound past which we can't divide.It's part of the same reason why Time travel in the future is theoretically possible but time travel in the past is not. Time freeze is also impossible, that's why the current model of black holes is incomplete, we don't know the smallest time unit / lapse possible yet, and will probably never will.
 >> Anonymous Mon Apr 13 06:36:33 2020 No.11560444 >>11560442>>>/x/
 >> Anonymous Mon Apr 13 06:41:27 2020 No.11560455 >>11560444https://en.m.wikipedia.org/wiki/ChrononWe're still far from being able to form a 100% correct theory, the continuum model is the best we have so far, knowing fully well it most probably isn't the correct model, and by extent that 0,xxx... makes no sense.
 >> Anonymous Mon Apr 13 08:07:08 2020 No.11560569 >>11559982>Literally doesn't know the definition of limit. 1/10^n never reaches 0Wrong and irrelevant. Try again.
 >> Anonymous Mon Apr 13 08:42:39 2020 No.11560613 I see the SODOMITES still have not given up, despite being proven wrong time and time again. GOD will punish them in due course.Lets make this abundantly clear. 0.999 does not equal 1. There is no further argument. We are moving on now.The Universe is discrete and finite. So are numbers.The biggest number is MOAN ( Motherfucker Of All Numbers). Nothing can be added to MOAN. There is nothing left in the Universe to add to it. It lies at the end of the number line. Attempting to go past MOAN results in you sailing off the edge into non-existence. Our mission now is to rewrite all the textbooks, cleanse the Earth of Heresy and shout DEUS VULT very loudly, seeing as those faggots at Paradox have lost their balls.
 >> Anonymous Mon Apr 13 08:47:53 2020 No.11560624 >>11557650>The fact that we can't come to a conclusion about this issue proves Math, a virtual concept humans created, is flawed.I disagree.. It actually proves humans are flawed.
 >> Anonymous Mon Apr 13 09:41:13 2020 No.11560691 guys guys what if 1 isn't even the smallest representation of a unit and all numbers are actually fields, in the same way that quarks make up atomsAnd and then even though using the numbers the way we always have is fine, breaking down a number into its constituent patterns, then running those bits through sub-calculations, then putting them back together (or N O T ) gets rid of all the inconsistencies in coǹventional math?And also the light-bearing aether field they thought was required for light to travel through is actually just the pattern of very small things to suddenly round themselves up?
 >> Anonymous Mon Apr 13 09:44:24 2020 No.11560696 >>11560455>0,xxx... makes no sensehttps://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
 >> Anonymous Mon Apr 13 09:45:39 2020 No.11560699 >>11560691Interesting idea. I still stand by my statement that space is quantised and so should be numbers, but you gave the first real argument for the opposite and for 0,999...=1. The other faggs just parroted b-but it is the way it is even though it isn't but it was made up to be with no valid theory or reason grounded on any real science.
 >> Anonymous Mon Apr 13 09:49:15 2020 No.11560706 >>11560696I know about that. It's a mathematician jerking himself of and aiming for his mouth. A common thing among mathematicians.
 >> Anonymous Mon Apr 13 09:50:55 2020 No.11560709 >>11560696Here's another equally valid thought experiment.Imagine an infinite hotel where only the last three rooms are occupied, because lol why not fuck logic.
 >> Anonymous Mon Apr 13 09:51:06 2020 No.11560710 >>11557936yes1/2 + 1/4 +1/8 + 1/16 +... = 1
 >> Anonymous Mon Apr 13 09:53:03 2020 No.11560712 >>11560709go tell hilbert and wikipedia immediately !your fields medal is in the mail
 >> Anonymous Mon Apr 13 09:53:28 2020 No.11560713 >>11557372>Actually, you can divide 1 L in three only in base 9Lmao
 >> Anonymous Mon Apr 13 09:54:39 2020 No.11560715 >>11560706>t. 4chan schizo shitposter jerking himself off and aiming for his mouth.
 >> Anonymous Mon Apr 13 09:55:09 2020 No.11560716 >>11560710Hello based department?>>11560712Mother Theresa has a Nobel prize. Those things are no better than Oscars.
 >> Anonymous Mon Apr 13 09:56:30 2020 No.11560720 >>11557648>>Retard>i have no argument
 >> Anonymous Mon Apr 13 09:57:32 2020 No.11560724 >>11560713Remove "only" and I stand corrected. Stop being a pedantic fagg.1L can't be divided in a unit made up of 10 smaller units. It can be if you use a unit made up of 3, 9 etc smaller units.
 >> Anonymous Mon Apr 13 09:57:34 2020 No.11560725 >>11560716>Nobel prizelrn2read
 >> Anonymous Mon Apr 13 09:58:47 2020 No.11560729 >>11560725There is no Nobel prize in mathematics so you have a cope second rate prize.Even economics have their Nobel lmao
 >> Anonymous Mon Apr 13 09:59:12 2020 No.11560731 >>11560724or infinite units1/3 = 0.3...
 >> Anonymous Mon Apr 13 10:00:15 2020 No.11560734 >>11560729nah, a fields medal is solidwatch less tvread a book
 >> Anonymous Mon Apr 13 10:03:36 2020 No.11560739 >>11560731>Infinite unitsMy point and argument was you can't do that. Feel free to correct me by providing a unit that can be divided infinitely.
 >> Anonymous Mon Apr 13 10:08:51 2020 No.11560754 >>11560734Well it's made of metal but otherwise it's bullshit back tapping.Anyway Abel Prisen is much more comparable to a Nobel prize.>Before 40 yoGay award tbqhf
 >> Anonymous Mon Apr 13 10:35:58 2020 No.11560805 >>11560754>ignorant ramblingthe dumb, they're never wrong
 >> Anonymous Mon Apr 13 10:37:02 2020 No.11560808 >>11560739>providing a unit that can be divided infinitelyany real number
 >> Anonymous Mon Apr 13 10:37:23 2020 No.11560809 >>11560805K whatever fagg
 >> Anonymous Mon Apr 13 10:38:28 2020 No.11560810 >>11560808A number is not a unit. It represents a unit.
 >> Anonymous Mon Apr 13 10:44:26 2020 No.11560822 >>11557356if .999... = 1Using the x = .99910x = 9.99..9x = 9x = 1analogyHow would you prove .00...1 = 0?
 >> Anonymous Mon Apr 13 10:51:18 2020 No.11560833 >>11560822It does not stand in any base other than 10.It's just because the 9 is the last digit you add before you obtain 10. 0,111... does not equal any number because you can always add a 2 anywhere and prove there is a C in between A (0,111...) and B (hypothetical).If a unit = 7 smaller units for instance, 0,666... would be equal to 1 because 7 would not exist.It's a stupid concept that only works because chimps have 10 fingers. An alien intelligence would laugh at us.
 >> Anonymous Mon Apr 13 12:01:03 2020 No.11561021 >>11560001infinitely large != infinitely long
 >> Anonymous Mon Apr 13 12:13:36 2020 No.11561055 >>11560810welcome to math
 >> Anonymous Mon Apr 13 13:09:16 2020 No.11561198 >>11561055Well it's very gay, bye.
 >> Anonymous Mon Apr 13 13:13:08 2020 No.11561204 >>11560390>>11560421>>11560424Mathematical theories and physical theories are not the same thing.Math theory is about abstract objects, which are defined solely by their properties and relations to other objects. Using formal logic you deduce more relations from these definitions. A math theory is "valid" if it's consistent, i.e. if the axioms don't lead to contradictions.Physical theory only uses math theory as an instrument. To material objects you assign the abstract math objects, the theorems give you relations which should hold, you check them with an experiment. If the theory doesn't work, it doesn't mean that the math is faulty in any way. It literally means that this sort of math used in this sort of way isn't suited for this problem. It's always the case that not everything in the math has a direct physical counterpart. A physical theory uses only a small part of the mathematical theory, the physical part. This doesn't render the unphysical part obsolete or invalid. It's what makes the useful part possible in the first place. If you took it away, all the inner logical structure would disappear and you would be left only with statements which you take for granted.
 >> Anonymous Mon Apr 13 13:54:56 2020 No.11561295 >>11561204Well put.I can agree to that.
 >> Anonymous Mon Apr 13 14:01:53 2020 No.11561310 >>11560822>.00...1 = 0I've thought about this. So basically the issue here is whether any numbers come before, but not after the ellipses, or bar if you're using bar notation. Earlier I thought that by showing that 0.999... = 0.9 + 0.0999...0.9 = 0.8999... 0.999... = 0.8999... + 0.0999..0.999...8That this would show the equivalence to be wrong. But when you actually try adding this number 0.999...8 to anything, the 8 has no effect, because there is always a 9 preceding it. Likewise, in the case of 0.000...1, there is always a 0 preceding, thus 0.999...8 is effectively the same as 0.999... and 0.000...1 is effectively the same as 0.Any arithmetic operation on 0.999... produces the same effects as if it were 1, but with a different decimal representation. for example:2 * 1 = 22 * 0.999... = 1.999...8You might again say that, well 1.999...8 is not the same as 2, but, once again, if you realize that anything after the ellipses has no effect, then you are left with 1.999... which means that0.999... + 0.999... = 1.999...Which could only be true if 0.999... were equal to 1.So, since 0.999... has the same arithmetic effect as one, it must be equal to 1. It's interesting this debate is actually is a good segue into abstract algebra because it forces you to determine whether two numbers are equal based on their effects on other numbers rather than just what they "look like," i.e. this is a unit because it behaves as a unit, rather than, this is a unit because it looks like one.
 >> Anonymous Mon Apr 13 18:12:44 2020 No.11562054 Those who think 0.99... = 1 are like lawnmower mechanics. They can follow instructions very well and are capable of diagnosing and fixing small mechanical problems. In many respects they are useful people, although not absolutely essential. Left to themselves they are very capable of surviving but would never invent anything.
 >> Anonymous Tue Apr 14 06:30:46 2020 No.11563435 >>11561295well, that's my argument against:>math is faulty>math is invalid>"you just define it to be true, that doesn't make it true">0.99.. = 1 has no real world implications>0.99.. doesn't exist>infinity doesn't existand moreby the way the math behind quantum mechanics is actually continuous
 >> Anonymous Tue Apr 14 06:54:10 2020 No.11563482 >>11563435Well yes because we're still operating at a relatively speaking "huge" scale in physics.And as I already admitted, 0,999... is so close to 1 it practically equals it so everything works, this being of course the case for other repeating to Infinity digits in continuous maths.Continuous maths might default when applied to further practical applications of quantum mechanics in a distant future.
 >> Anonymous Tue Apr 14 13:22:17 2020 No.11564315 >>11557356This entire stupid debate is contingent on the notion that there must be one correct answer. Truth is that it entirely depends on the context of which we are thinking. If you're only concerned about real numbers then sure, you can define 0.999... to be 1. But if you're also concerned about surreal numbers (look it up), then you begin to see that they might not always be the same.It's the same thing with the sum of all positive integers, whether it diverges to infinity or becomes -1/12 is entirely based on the context of which you are speaking. Both sides are right in some way, and both sides are wrong about the other side being wrong. Unlike science, in maths the rules are made up, they're built up of axioms which defines the fundamental rules, rules we take for granted without needing to be proved. Because if we had no axioms, no things we could fundamentally accept as true, there would be no way to prove anything,you cannot prove anything without using logic to derive implications from things you already take to be true. What I'm trying to say is that maths is about as arbitrary as anything we humans have ever made, it's just a language we've made to describe abstract logic, and just like any language the definitions can vary depending on context.For some 0.999... = 1, and that's fine, you can logically justify it with the axioms of which you operate with. For others, 0.999 =/= 1, and that's also fine, because they can also logically justify it within the context of their own axioms.I hope this settles it.
 >> Anonymous Tue Apr 14 13:29:57 2020 No.11564342 >>11559902>You might thing infinitely small numbers (0.000...01) exist. The don'tThey do, surreal numbers. They exist just as much as complex numbers and negative numbers; while they might not have any real-world equivilent, they do exist in theory. You can divide 1 by 0.000...01 and get infinity, whereas if you were to divide 1 by 0 you would get undefined.
 >> Anonymous Tue Apr 14 13:47:55 2020 No.11564383 File: 60 KB, 783x897, 1586885468628_Reimann_Proof.png [View same] [iqdb] [saucenao] [google] [report] >>11557356Here's your proof
 >> Anonymous Tue Apr 14 13:57:39 2020 No.11564417 .9...=x9.9...=10xsubtract9=9x1=xtada
 >> Anonymous Tue Apr 14 14:14:57 2020 No.11564466 >>11564315-1/12 is what happens when you apply a type of smoothing function to the infinite sum of consecutive natural numbers. it is a technique for assigning unique values to divergent series.If you read my post here >>11561310You'll see that I can demonstrate that due to the infinite expansion of 9's, despite obviously being less than 1, it has the equivalent arithmetic effect as 1, because any of what you would "lose" from adding or multiplying it to another number is rendered ineffective by the infinite expansion.This makes it a very strange number and makes me tempted to classify it as something that is not 1 even though it is effectively the same as 1.To show that it was not equivalent to one you would need to show that there is some operation on it that would yield an amount that is "less than" it but no such operation could exist because of the infinite 9s and the effect they have on any operation you throw at them. Each operation you can attempt on 0.999... must first be applied indefinitely to the 9s which ultimately will just lead to the same 9s again, even if trailed by something less than 9.Imagine you had a set with two infinite sequences, {1, 2, 3, ... 0, 1, 2, ...}If you fed this into a product function, where each consecutive element of the set was multiplied by the previous in the usual ordering, it would always be non-zero because it would never reach the 0 after the ellipses. The same situation with 0.999... You can multiply it, exponentiate it, add it, doesn't make a difference because anything that comes after the 9s from the first step will never be used in later operations. You'll always be starting off with 9's after each operation.
 >> Anonymous Tue Apr 14 14:16:24 2020 No.11564473 >>11564342Irrelevant because we're not talking about the surreals, retard.
 >> Anonymous Tue Apr 14 14:19:09 2020 No.11564482 >>11564315>For some 0.999... = 1, and that's fine, you can logically justify it with the axioms of which you operate with. For others, 0.999 =/= 1, and that's also fine, because they can also logically justify it within the context of their own axioms.Let's pick a random 0.999... = 1 poster and a random 0.999... != poster. Ask them to describe the axiomatic system they're working in and to logically deduce their preferred answer. What do you think will happen ?
 >> Anonymous Tue Apr 14 14:42:08 2020 No.11564545 File: 30 KB, 813x132, Input interpretation.jpg [View same] [iqdb] [saucenao] [google] [report] How do you define .9999...? If you define it as pic related, then you can't deny that it equals 1, since you can use the definition of a limit to prove it
 >> Anonymous Tue Apr 14 14:44:29 2020 No.11564551 >>11564417>clunky$\displaystyle1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0. \bar{3} = 0. \bar{9}$
 >> Anonymous Tue Apr 14 15:00:09 2020 No.11564599 >>11564466Again, look up surreal numbers. It's essentially the point you're trying to illustrate here.
 >> Anonymous Tue Apr 14 15:07:40 2020 No.11564619 Math is made up and not real.
 >> Anonymous Tue Apr 14 15:08:04 2020 No.11564620 >>11564619that's kind of the point
 >> Anonymous Tue Apr 14 16:04:28 2020 No.11564787 >>11564599Will do anon, thanks.
 >> Anonymous Tue Apr 14 17:00:25 2020 No.11564969 File: 40 KB, 570x450, ooga booga.jpg [View same] [iqdb] [saucenao] [google] [report] >>11558825>grug no understand math symbols
 >> Anonymous Tue Apr 14 17:01:32 2020 No.11564975
 >> Anonymous Tue Apr 14 17:02:48 2020 No.11564979 File: 58 KB, 898x790, brainchad.jpg [View same] [iqdb] [saucenao] [google] [report] >>11557356x = 0.999...10x = 9.999...9 + 0.999... = 9.999...9 + x = 10x10x - x = 99x = 9x = 1
 >> Anonymous Tue Apr 14 17:04:17 2020 No.11564989 >>11559873>I mean there are infinitely numbers between 0.999... and 1.Name one.
 >> Anonymous Tue Apr 14 18:14:52 2020 No.11565186 >>11564979>9 + x = 9xAnon...
 >> Anonymous Tue Apr 14 19:56:49 2020 No.11565538 File: 680 KB, 1900x1766, Sri-yantra-Mandala.jpg [View same] [iqdb] [saucenao] [google] [report] >>11557356What people miss about this vital equation is that it is a simple proof of the principle of non-duality. All you need is finity and infinity and all numbers become non-dual. 1 and 2 are both 0% of infinity. Infinitesimal numbers just show that the non-dual union of numbers works via continuum.Its actually highly redpilled.
 >> Anonymous Tue Apr 14 20:11:55 2020 No.11565577 1/0 = x10/0 = 10x(10 / 0) / 10 = (10x) / 1010 / (0 / 10) = (10x) / 1010 = 10x / 00 = 10xx = 0
 >> Anonymous Wed Apr 15 05:00:41 2020 No.11566740 File: 260 KB, 4122x3030, Le ebic animes.jpg [View same] [iqdb] [saucenao] [google] [report] >>11557356Ok so what about this?
 >> Anonymous Wed Apr 15 05:09:33 2020 No.11566750 >>11565186he's right tho
 >> Anonymous Wed Apr 15 05:11:30 2020 No.11566752 >>11565577This kind of proof is what Pauli meant by "not even wrong"
 >> Anonymous Wed Apr 15 05:16:00 2020 No.11566759 >>11566740this guy knows the problem. equating this that are BY DEFINITION different entities, is an "phase fallacy". the point where you do the subtraction, you are manipulation variables that are in different "phase" or "information set" of examination
 >> Anonymous Wed Apr 15 05:25:47 2020 No.11566774 >>11565577(10/0)/10 = 10/(0*10)
 >> Anonymous Wed Apr 15 05:58:24 2020 No.11566829 >>11566740not really
 >> Anonymous Wed Apr 15 05:59:35 2020 No.11566831 >>11566759>equating this that are BY DEFINITION different entitiesyou seem to know a lot about this topic, can you please tell me the definition of "1" and "0.999..." ?
 >> Anonymous Wed Apr 15 06:15:17 2020 No.11566854 >>11557356I think writing fractional numbers as decimal doesn't make sense. All these problems go away if you stop trying to handle infinite decimals.Just like having sex.
 >> Anonymous Wed Apr 15 06:36:50 2020 No.11566885 >>11566854what problems ?
 >> Anonymous Wed Apr 15 07:31:18 2020 No.11566957 Those who think 0.99... = 1 are like lawnmower mechanics. They can follow instructions very well and are capable of diagnosing and fixing small mechanical problems. In many respects they are useful people, although not absolutely essential. Left to themselves they would never invent anything. Its generally best to let them keep believing in simple things, they can get very upset if their ideas are challenged in any way. As they are usually incapable of changing their world view educating them for the better is usually not worth the effort.
 >> Anonymous Wed Apr 15 07:40:55 2020 No.11566974 >>11557646Numbers DONT exist at all. Congrats on taking the red pill. Our universe is all ratio based, not quantity based.
 >> Anonymous Wed Apr 15 07:42:12 2020 No.11566975 >>11566957Those who think 0.99... != 1 are like lawnmower mechanics. They can follow instructions very well and are capable of diagnosing and fixing small mechanical problems. In many respects they are useful people, although not absolutely essential. Left to themselves they would never invent anything. Its generally best to let them keep believing in simple things, they can get very upset if their ideas are challenged in any way. As they are usually incapable of changing their world view educating them for the better is usually not worth the effort.
 >> Anonymous Wed Apr 15 07:44:02 2020 No.11566976 >>11566957>Those who think 0.99... = 1 are likepeople who know that the LHS is the representation of 1 in decimal expansion.
 >> Anonymous Wed Apr 15 07:50:02 2020 No.11566982 File: 1.93 MB, 4032x3024, 437FE6CC-E147-4F96-8B15-1622EB327039.jpg [View same] [iqdb] [saucenao] [google] [report] This board sure has a lot of replies for something that gets covered in the first week or two of a real analysis class.Can you define a real number between .999... and 1? .999... and 1 are not distinct. They are equal.
 >> Anonymous Wed Apr 15 15:37:10 2020 No.11568264 >>11566974Subtle.
 >> Anonymous Wed Apr 15 16:36:43 2020 No.11568490 >>11557356I think the problem most people have with this is actually very simple but often not addressed: There's this assumption that every number that starts with "0." has to be less than one; that whatever comes after the comma can never make up for the fact that we start with "0.". And that just means they don't understand the notation of infinite decimals and actually work from different assumptions. So there's no use trying to convince people that 0.999...=1 based on all kinds of arguments. The actual issue is just in how you actually define the notation of infinite decimals.Once everyone agrees that 0.999... has to be the limit of 0, 0.9, 0.99, 0.999, ..., the conclusion is inescapable.
 >> Anonymous Wed Apr 15 16:57:05 2020 No.11568565 File: 20 KB, 372x240, 1527881187078.jpg [View same] [iqdb] [saucenao] [google] [report] CAN WE PLEASE JUST USE FRACTIONS INSTEAD OF DECIMALS TO RETIRE THIS DUMB QUESTION
 >> Diracula Wed Apr 15 18:24:38 2020 No.11568811 you guys will love this one:So take this purely true fact about arithmetic:take any number and divide it by the 9's as long as the number has digits and you will create an infinite repeating decimal of that number.for instance 123/999 = 0.123123123...or 1/9 = 0.111111111...or 100/999 = 0.100100100100100you get the point, it creates the infinite decimal of the number.now lets see the infinite decimal of 9's by the same method:9/9 = 1
 >> Diracula Wed Apr 15 18:28:34 2020 No.11568824 >>11566957dude im literally creating proofs from pure intuition and random bits of math i know and youre calling me the uncreative one. youre just parrroting some supposed common sense about non terminating digits not having a terminable value. wow well done, we invented something called convergence to satisfy this problem. you should probably look it up.
 >> Anonymous Wed Apr 15 18:32:15 2020 No.11568840 >>11568565Sure thing Slim. lets hide the truth by just using fractions, which are unsolved equations. You do know that, dont ya?3/2 is 3 divided by 2. What is 3 divided by 2? Nah, lets not solve that, lets just leave it as 3/2
 >> Anonymous Wed Apr 15 18:46:26 2020 No.11568901 >>11564466 Any good decent God fearing person can look at something like 1 + 1 = 2 and know that it is both true and ordained by God.But when we are expected to believe that in obviously BATSHIT insane bullshit like -1/12 crap, that's where we get pissed. For obviously that can not be true. Any convoluted proof that supports such nonsense is obviously the work of the DEVIL and SODOMITES! Smug faced greasy little SODOMITES sitting in fluro-lit little offices, fiddling with their tiny little penises and thinking up more mathematical OBSCENITIES with which to plague the sanctuary of a FINITE AND DISCRETE Universe. Laughing as they release their EVIL creations upon an innocent and unsuspecting world,.Well, we have had enough. Now we are fighting back. We are reclaiming the mathematical world for the GLORY of GOD and RIGHTEOUSNESS. We shall prevail. DEUS VULT! DEUS VULT!
 >> Anonymous Wed Apr 15 19:06:07 2020 No.11568958 >>11565186>can't read
 >> Anonymous Wed Apr 15 19:07:35 2020 No.11568963 >>11566740epic xD
 >> Diracula Wed Apr 15 19:39:59 2020 No.11569071 >>115689010.9999.. being one im ok with, but the -1/12 people are witches plain and simple.
 >> Anonymous Wed Apr 15 20:14:05 2020 No.11569217 >>11557356Your conclusion is correct, but your reasoning is wrong. How do you know 3 * 0.3333... = 0.999...?
 >> Anonymous Wed Apr 15 20:15:46 2020 No.11569223 >>11569217by induction and by the fact that R is a field
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