Talk:0.999.../Archive 10

message: Should the archives be moved, as well?
:Talk:Proof that 0.999... equals 1/Archive01
:Talk:Proof that 0.999... equals 1/Archive02
:Talk:Proof that 0.999... equals 1/Archive03
:Talk:Proof that 0.999... equals 1/Archive04
:Talk:Proof that 0.999... equals 1/Archive05
:Talk:Proof that 0.999... equals 1/Archive06
:Talk:Proof that 0.999... equals 1/Archive07
:Talk:Proof that 0.999... equals 1/Archive08
:Talk:Proof that 0.999... equals 1/Arguments/Archive 1
— Arthur Rubin |  (talk) 22:49, 14 September 2006 (UTC)
replies: text: Meh. I guess it couldn't hurt. Melchoir 22:52, 14 September 2006 (UTC)
replies: text: There's no need, as long as the links from this page are ok. Mariano(t/c) 09:51, 15 September 2006 (UTC)
thread_title:  Move from [[Talk:Proof that 0.999... equals_1]] 

message: I liked this article, it made me think.
For what it's worth I think this equation should make everything clear:
0.999... + (⅓ - 0.333...) = 1
Or in other words the assertion that 0.333... = ⅓ is also wrong and hence the fractional proof is rubbish.
simonthebold 23:48, 25 October 2006 (UTC)
thread_title: Great Article

message: Hey WTF is with the stupid pictures.  They make no sense and add nothing. —Preceding unsigned comment added by 82.93.10.238 (talk • contribs) 
:The pictures are a visual representation of a difficult-to-visualize mathematical concept.  If you're unable to understand them, it is not because they "make no sense", it is because you haven't been taught how to interpret them.  Melchoir was kind enough to explain it to me here.  By the way, you can sign your comments using four tildes (~~~).  Also, additions to talk pages are supposed be appended at the bottom of the page.  Thanks. Supadawg (talk • contribs) 21:59, 28 September 2006 (UTC)
replies: text: I'm not _quite_ as dumb as that.  I meant the other two specifically, in fact, the pathetic "artist's impression" (WHY?) and the jocular(??) and pointless calculator image.82.93.10.238 22:09, 28 September 2006 (UTC)
replies: text: Hmm, didn't see those; thought you meant the other picture.  It might have helped, though, if you had provided specific examples and reasons why you thought the pictures should be removed.  Having said that, I completely agree: they add no information whatsoever to the article.  The artist's interpretation of 0.999... does not help one grasp the concept of 0.999... equaling 1, and the calculator image is of a syntax error, not a problem with the calculator. Supadawg (talk • contribs) 22:16, 28 September 2006 (UTC)
replies: text: I've never been sure what to do with :Image:999 Perspective.png, and I didn't add it to the article, but I'll defend it anyway: It is the only depiction of the infinite decimal itself, and the clearest indication that the 9s repeat infinitely. The calculator image accompanies text about the usefulness of calculators. What's wrong with images that illustrate the topic without trying to make some point? Melchoir 22:25, 28 September 2006 (UTC)
replies: text: I think that if the article was still "Proof that ...", then the artist's impression wouldn't be much use. Now that the article is on 0.999... itself, I would say that we need some picture of the number, and just pointing to "1" on the number line wouldn't really cut it. I actually think it's a rather neat way of showing the infinity of nines without resorting to the ellipsis notation. As for the calculator one, put me down as neutral. Confusing Manifestation 04:12, 29 September 2006 (UTC)
replies: text: Yeah, I like the artistic impression image (in fact, while this is the first time I've seen such an image, I've been thinking about how interesting it could be many years ago), and completely agree with everything ConMan said. I think it should stay. About the "Calc thingy" image, I am inclined to exclude it. -- Meni Rosenfeld (talk) 07:19, 29 September 2006 (UTC)
replies: text: Some exquisitely moronic comments here. Why is some picture the "clearest indication that the 9s repeat infinitely"?  That's what we have the definition for. Pictures lie. Why do we _need_ "a picture of the number"?  There is not even such a thing. It's at best a picture of this particular representation of 1.  Whoop.  All in all, it's at best an obfuscation.  And the syntax error is too silly for words and really indefensible in anything that takes itself seriously.  But hey, it's your Wikipedia.82.93.10.238 21:28, 30 September 2006 (UTC)
replies: text: It is an artistic representation. If it is free, it is welcomed. -- ReyBrujo 21:43, 30 September 2006 (UTC)
replies: text: There is no place for personal attacks on Wikipedia or in any intelligent discussion.  If you don't agree with someone, fine, but that does not make them a "moron".  The picture of 0.999... is not necessary; it clarifies that 0.999... recurs without end.  The calculator screenshot, though I think it should be excluded, illustrates the point that many people disagree with the assertion that 0.999... equals 1 because technology is incapable of assisting them.  Also, it's everyone's Wikipedia, and that includes you. Supadawg (talk • contribs) 23:39, 30 September 2006 (UTC)

text: Technically, he was not making a personal attack, since he was only saying that the comments (not the people who made them) are moronic. In any case, of course the image does not add anything mathematically, but this is not a mathematical textbook here. This is an encyclopedia entry, and there's no reason we shouldn't add images which illustrate the concept - the same way articles about people have pictures \ drawings of them, and articles about geometric figures have images of them. -- Meni Rosenfeld (talk) 09:30, 1 October 2006 (UTC)
replies: text: Splitting hairs over the definition of a personal attack shouldn't protect him.  Check the section on wikilawyering. Supadawg (talk • contribs) 19:33, 1 October 2006 (UTC)
replies: text: Still, I'm glad the picture of the calculator went. I do like the artist's impression of 0.999 -- but 'it's free' is not an argument for putting it in. If an article does not need pictures, leave them out! -- Cugel 07:38, 25 October 2006 (UTC)
thread_title:  Pictures 

message: "Applications of these identities have been used in patterns in decimal expansions of fractions and fractals."
I'm particularly curious as to what fractals make use of this property. Do any even exist? —Preceding unsigned comment added by 82.93.10.238 (talk • contribs) 
:I've tweaked that sentence to be more specific; the application itself is in 0.999...#Applications. Melchoir 22:31, 28 September 2006 (UTC)
thread_title:  Fractals 

message: For the FAC, I've expanded the intro, hopefully in a different way from before. Supadawg, I hope this isn't too detailed for your tastes. Melchoir 22:18, 29 September 2006 (UTC)
replies: text: Hm?  I don't remember speaking out against detailed introductions; I just remember moving parts of the old introduction to their proper place as section introductions.  I have no problem with the new version, as it does a great job of touching on each subject presented in the article.  I just think it's a little esoteric, that's all. Supadawg (talk • contribs) 22:40, 29 September 2006 (UTC)
replies: text: Thanks! A little esoteric I can live with. The details I guess I meant were the listed descriptions of the proof methods. Melchoir 22:43, 29 September 2006 (UTC)
thread_title:  Lead section, again 

message: I'm going to try re-ordering the sections (again) in response to criticism in the FAC. Here's my thought process:
*Given that the material is broken up into sections by topic, it would be impossible to order it chronologically or by difficulty.
*And ordering the material by strict implication would make it unreadable and unmotivated.
*Therefore, the sections should be ordered by prerequisites and by motivation.
*Applications does not inform any other section, and Generalizations informs only Applications and a single subsection buried deeply within Other number systems. Neither section motivates anything else. So these two should come last.
*The first two proof sections inform Skepticism, while Skepticism motivates the third proof section along with Other number systems. So Skepticism should be inserted into the break, or at least the Education part; Popular culture should stay at the end.
Advantages:
*Motivation.
*The most well-known material occurs in what are now the first three sections, while obscure stuff appears later.
*Independent of logical issues, it just makes sense to follow the section on real numbers with the section on not-real numbers. It may also be more neutral.
Disadvantages:
*The proofs that 0.999… = 1 are interrupted. (But it is now more clear why the process of finding more proofs is extended so long, whereas before the process was carried out as a monolith, without motivation or breathing room.)
*The proofs - skepticism - more proofs layout may appear to be a contrived debate-of-the-strawmen, which is usually a sign of POV and OR. (But here there is no POV, since only verifiable opinions are described. And the skepticism/education angle is apparent in the references that support the final proof section, so the establishment of motivation isn't OR either.)
*The sections following "Other number systems" are easier to understand than it is, not harder. (This is bound to happen unless one places that section at the end, which would be logically unsatisfactory and too pro-real.)
Whew! Melchoir 16:50, 2 October 2006 (UTC)
thread_title:  Ordering 

message: It's been several weeks since I've looked at this article.  The lead is SO much better.  Reading the lead as a lay person to mathematics now tells me why this article is important and that it is reported established fact (before it seemed to suggest that it was instead establishing that fact).  The general shape of the article is much improved, especially the additions of the Skepticism section and the sections about application and related questions.  This is now an article that I can access, find intersting, and use.  Well done and thank you to everyone. Chadbald 01:31, 14 October 2006 (UTC)
replies: text: Thank Melchoir, he's done most of the work. Well, there is at least one person, whose opinion I value too highly to disregard, who thinks the article is terrible in its current state - but he seems to be the only one. We're glad you like it. -- Meni Rosenfeld (talk) 21:38, 14 October 2006 (UTC)
replies: text: I realise that this might not be the place, but I wanted to let those responsible for this article know that I found it a good read. Quite good how you included information on the issue of intuition. Was wondering, is 0.9999...8 the same as 0.999.... ? Cheers. ShaiM 12:41, 22 October 2006 (UTC)
replies: text: No. 0.999...8 isn't defined, since you'd need to find the end of an infinite (i.e. endless) string of nines on which to stick an 8. And since the string of nines is endless, that end doesn't exist. Many people propose a similar number of 0.000...1 as a potential answer to the question "What is 1 - 0.999...?", but such a numeral is meaningless, at least in the real numbers (the correct answer is, of course, zero). The very fundamental concept of a recurring decimal is that its decimal expansion does not end - there is no last place which you can change. -Maelin 13:24, 22 October 2006 (UTC)
thread_title:  Impressed! 

message: "This can be simplified by saying that: given any real number over 9, the number repeats itself infinitely after the decimal point, then 9⁄9 equals 0.999... which equals 1."
Why was this deleted? any number divided by nine euqals the number reapeating itself infinitely after the decimal point. For example, 1/9 = .111..., 5/9 = .555..., 12/99 = .121212..., 123/999 = .123123123..., so what does 9/9 equal to?
:The statement is correct, but it's clumsier than what is said above, and is not really a proof. The fact that 1/9, 2/9, 3/9 etc. equal 0.111..., 0.222..., 0.333... etc. does not prove that 9/9 = 0.999.... The same way that the fact that 02 + 0 + 41, 12 + 1 + 41, 22 + 2 + 41, ..., 392 + 39 + 41 are all primes does not prove that 402 + 40 + 41 is prime (and it isn't). -- Meni Rosenfeld (talk) 21:29, 14 October 2006 (UTC)
thread_title:  Simiplification 

message: It seems that it hasn't been proposed yet, but could you move the article to 0.999... = 1? I think it's more relevant and descriptive. CG 14:37, 15 October 2006 (UTC)
replies: text: This article was recently moved to the present title. I suggest we stop moving artiles around, just because they could be called something else.--Niels Ø 15:24, 15 October 2006 (UTC)
replies: text: It's just a suggestion. CG 17:10, 15 October 2006 (UTC)

text: I don't think titles should even be descriptive. See, for example, the redirect from September 2006 Thailand military coup d'état to 2006 Thailand coup d'état, which is the simplest title that gets the job done. "0.999..." also avoids making a statement. You wouldn't move the other articles to Negative zero equals zero, Division by zero is undefined, or Zeno's paradoxes are resolved by modern calculus, would you? Melchoir 20:00, 15 October 2006 (UTC)
replies: text: If we want the simplest title then surely it should be simply 1, since 0.999... = 1 (duck). I'm generally against the move, as the current article works well under its current name, a page describing the decimal expansion 0.999... Also as its on WP:FAC at the moment it causes problems moving at this time. --Salix alba (talk) 20:22, 15 October 2006 (UTC)
thread_title:  Move request 

message: Referring to the "Generalizations" section, the article says "For example, in base 2 (the binary numeral system) 0.111… equals 1, and in base 3 (the ternary numeral system) 0.222… equals 1." Would it be easier to understand if the article said "For example, in base 2 (the binary numeral system) 0.111… equals 1 (in base 10), and in base 3 (the ternary numeral system) 0.222… equals 1 (in base 10)."? That part just seemed a bit ambiguous to me, so it's just a suggestion. Brix. 17:36, 20 October 2006 (UTC)
replies: text: Since 1 means the same thing in binary, ternary and decimal notations, I fail to see the point of your suggestion. -- Meni Rosenfeld (talk) 18:58, 20 October 2006 (UTC)
thread_title:  Better explanation of base 2 and 3? 

message: What a wonderful article.  Maths is something I have never claimed to understand but I find it fascinating.  I only got as far as the fractional proof, but to there it is well written, clear, inciteful and informative.  Thank you to all involved in making this a featured article.  It's great exercise for the brain.  It's beaut mate and a marvellous featured article! Maustrauser 00:27, 25 October 2006 (UTC)
thread_title: Congratulations

message: "...researchers of mathematics education have studied the reception of this equation among students, who often vocally reject the equality. Their reasoning is often based..." Whose reasoning: The researchers', or the students'? I'd clear up the sentence myself, but I don't which way is correct. Thanks.
Dmp348 00:45, 25 October 2006 (UTC)
replies: text: Based on the context, it looks like it's the students' reasoning.  Fixed it, thanks. Supadawg (talk • contribs) 00:49, 25 October 2006 (UTC)
thread_title: Ambiguous statement

message: Suffice to say, if such a trivial mathematical quandary as whether 0.999... equals 1 becomes irrelevant by 2100, I will consider mankind to have collectively unplugged its head from its ass, and made some actual progress at the business of living. Chris 00:56, 25 October 2006 (UTC)
replies: text: Spoken like someone who truly does not understand the applications of mathematics.  The fact that 0.999... equals 1 is a basic principle of the real number system.  How about math for math's sake?  Next time, keep your two cents to yourself, and don't ridicule the hard work the other editors have put into this article. Supadawg (talk • contribs) 01:06, 25 October 2006 (UTC)

text: We have 1,450,000 articles here at last count.  There's no requirement that a user be interested in every one of them.  But I submit it might be more useful for our critic Chris to look in on and edit one of the other 1,449,999 that's more to his liking as opposed to making a gratuitous comment like this one. Newyorkbrad 01:10, 25 October 2006 (UTC)
replies: text: Calm down Chris, I am no mathmatician & really don't understand the significance of this, but we really should respect other people's work.Cameron Nedland 02:31, 25 October 2006 (UTC)
thread_title:  What a tragedy! 

message: Oh, the little article that could. You've grown up so well. *sniff* But seriously, congrats to all the editors that brought this page up to featured article status. Awesome work. --Brad Beattie (talk) 00:59, 25 October 2006 (UTC)
thread_title:  My baby! 

message: I've seen 0.9 recurring written as 0.9999... written with a dot over, but never witha dash, although I'm not saying that notation doesn't exist, merely that I see it more frequently represented with what looks like an Umlaut. Triangl 01:11, 25 October 2006 (UTC)
replies: text: Were you by any chance educated in the UK? Melchoir 01:15, 25 October 2006 (UTC)
replies: text: Personally I have never seen the dot, but I see the dash all the time, perhaps it's a national thing (I'm American).Cameron Nedland 02:32, 25 October 2006 (UTC)

text: At least in Canada, we use the dash. It's a regional thing, I gather. --Brad Beattie (talk) 12:15, 25 October 2006 (UTC)
replies: text: Yes appears to split along Commonwealth/North American lines I'm assuming from the above. We used the dot in Malaysia IIRC Nil Einne 16:10, 25 October 2006 (UTC)

text: I'm from Sweden; and here I've mainly seen and used the dash. JoergenB 20:02, 27 October 2006 (UTC)
thread_title:  Notation 

message: An intuitive counter to the assertion that 1 = 0.999... might hinge on wether 10 * 0.999... = 9.999... . For example, 10 * 0.99 = 9.9, not 9.99, so what does that mean for an infinite series like 0.999...?
A student might intuitively think of 0.999... as representing 1 minus an infinitesimally small number, or 
0.\bar{9} = 1 - 0.\bar{0}1
Considering this intuitive assumption, the algebraic proof might go something like this:
c = 0.\bar{9} = 1 - 0.\bar{0}1
10c = 9.\bar{9} = 10 - 10*0.\bar{0}1
10c - c = 10 - 10*0.\bar{0}1 -(1 - 0.\bar{0}1)
9c = 9 - 10*0.\bar{0}1 -(-0.\bar{0}1)
9c = 9 - 10*0.\bar{0}1 + 0.\bar{0}1
9c = 9 - 9*0.\bar{0}1
c = 1 - 1*0.\bar{0}1 = 1 - 0.\bar{0}1 = 0.\bar{9} 
c = 0.\bar{9}
----
I've removed the above from the article, for a few reasons. First, there's no such thing as a counter-proof. Second, it's original research because no known source actually operates with this intuitive assumption. Third, even in its own schema it proves nothing; it's just a manipulation that begins and ends with the same statement. Melchoir 01:35, 25 October 2006 (UTC)
replies: text: I agree with both these edits as a correct application of the WP:NOR policy. --causa sui talk 01:40, 25 October 2006 (UTC)
replies: text: and has been mentioned before...there is no such thing as an infinite expansion with a ending digit. Brentt 02:15, 25 October 2006 (UTC)
thread_title:  Intuitive counter-proof 

message: If professors in math faculties have time to waste "proving" this nonsense there are too many of them and we could save the country money by firing some. Golfcam 01:43, 25 October 2006 (UTC)
replies: text: Rest assured, mathematics professors do not waste their time or money on such trivial matters. See http://arxiv.org/list/math/recent. Melchoir 01:46, 25 October 2006 (UTC)
replies: text: What's with all the trolling on this talk page? First of all, this is to talk about the article not the subject of the article. Second, this article is relevant, notable, and verifiable. There are a whole bunch of other articles on this site that do not meet those criteria, so why don't these editors go to those articles and deal with those. Gdo01 01:46, 25 October 2006 (UTC)

text: My old high school math teacher proved it in under a minute.  Don't worry. Supadawg (talk • contribs) 02:02, 25 October 2006 (UTC)
replies: text: I find these trolls amusing. Its comedic. To humor the trolls: This topic is more relavant to math education than what working mathematicians actually do. Its a topic that highlights the clash between initial intuitions about numbers and sound theory. The reason why this topic is ever discussed, usually by math educators, has little to do with what .9999... equals (its indisputably 1), its about the reluctance of students to let go of intuitive concepts which don't work in theory. It is important that students grasp what .9999... because if they can't grasp that, then they won't be able to grasp limits. And if you can't grasp limits, then your pretty much not going to be able to grasp a good portion of math and science. Brentt 02:11, 25 October 2006 (UTC)
replies: text: Word. Melchoir 02:13, 25 October 2006 (UTC)
replies: text:  Some of the trolling going on here seems to be good old fashioned anti-intellectualism, based on the idea that careful thought about esoteric matters is a waste of time. If that were true, we wouldn't be having this discussion at all, because computers, computer monitors, and computer networks (i.e., the web) would never have been invented in the first place. To the trolls: be thankful there are people in the world who like to think more than you do. - dcljr (talk) 18:22, 25 October 2006 (UTC)

text: Don't internalize trolling here as having something to do with trolls' viewpoints on math; trolling occurs on articles in every domain. My guess is, that here, trolls defensively respond to their lack of understanding of mathematical notation, concepts, and sophistication. You're perceiving an attack or ridicule of math, when all there really is, is trolling per se. Math and theoretical physics rule, together with classical music, great literature and history. 66.108.4.183 20:29, 25 October 2006 (UTC)
replies: text: And, of course, some of the real trolls, in the original sense of that word, will themselves be math graduates who are personally not in any doubt about the properties of the reals, having a go at poking other people into outrage at their carefully contrived won't-be-told brand of simulated ignorance. -- The Anome 14:33, 28 October 2006 (UTC)
thread_title: Time to trim the fat at the math faculties

message: Wouldn't it be 1-.ooo...9?Cameron Nedland 02:36, 25 October 2006 (UTC)
replies: text: What?  Do you mean that 1-0.000...1 = 0.999...?  Such a number does not exist. Supadawg (talk • contribs) 02:40, 25 October 2006 (UTC)

text: You cannot have something after infinite 0's. --Kinst 02:44, 25 October 2006 (UTC)
replies: text: Then dividing any finite number by infinity gets zero. This means a Universe that is infinite would have to have an infinite amount of intelligent life or it could not have intelligent life at all. Because if it had 800 centillion intelligent life-forms the amount of intelligent life it would have per-area would have to be zero. As zero times anything is zero it can't have any intelligent life. After that I prove black is white and get run over in a zebra crossing:)--T. Anthony 07:32, 25 October 2006 (UTC)
replies: text: Which would be true, if there was such a thing as an infinite universe. -- 86.128.253.74 09:50, 25 October 2006 (UTC)

text: Yes, what Supadawg said.  I am no mathmetician, if you can't tell.Cameron Nedland 02:45, 25 October 2006 (UTC)
replies: text: Well, 1-0.000...1 = 0.999...9, but that implies that the string of 9's ends, and it does not. --M C Y 1008 22:36, 26 October 2006 (UTC)

text: Well... I wouldn't say that these things don't exist or can't be had. It's just that they aren't decimals, and they don't represent real numbers. There isn't even a theory of what they might be or represent, and the article touches on some of the barriers to constructing such a theory. Melchoir 02:47, 25 October 2006 (UTC)
thread_title:  .999... = 1? 

message: Just wanted to say-- this is excellent work.  I never would have believed such a great article could have been constructed on this topic, or that it could be made so accessable and, honestly, fascinating.  I know a thing or two about math, but there are a lot of really creative choices made in this article that never would have occurred to me--  the page image that so perfectly illustrates the concept of string shooting off to infinity, the discussion of mathematical education, the intuitive proofs, the popular culture discussion, etc.  Before reading this page, I could have written an article talking about why .999=1, but I never would have thought to make it so... comprehensive and so fun.  Everyone involved should be extra proud of themselves.   --Alecmconroy 02:42, 25 October 2006 (UTC)
thread_title:  This is a really good article

message: You torched the article?
:Nah, a vandal torched the article and was quickly reverted. Melchoir 04:58, 25 October 2006 (UTC)
thread_title:  Woah: 

message: I ran into this issue when I was making some rules in a game where the length of certain objects put them into different classes, and I realized that it was difficult to describe a range in a way that made clear which class lengths exactly on the borderline fell.  My solution was to use .999... notation:   ClassBlue = 3 ft to 3.999... feet, ClassRed = 4 ft to 4.999... ft.  Now the article is telling me that this notation is wrong, and I haven't unambiguously defined if a pole exactly 4 ft is ClassBlue or ClassRed.  
How do I do this?  How do I describe the maximum value of X where X<1?  If .999... isn't the answer, then what is?
This also comes up with legalistic issues, like if it is EXACTLY your 21st birthday, can you buy alcohol?  After all, you aren't "over 21".  The article should address this, since it is how this issue effects people in real life. Algr 06:33, 25 October 2006 (UTC)
replies: text: There is no such "maximum value" among the real numbers. However, it is certainly possible to describe a range of numbers that includes every number between two endpoints but not the endpoints themselves. Such a range is called an open interval. See the article interval for more information. Alternatively, you could just write like this: Blue: 3 ≤ x < 4; Red: 4 ≤ x < 5, etc. Or perhaps better yet, spell out what you mean in plain English. Fredrik Johansson 06:45, 25 October 2006 (UTC)

text: Real numbers don't exist in the world we live in: there is an inherent 'graininess' to the universe. If you measure a distance, no matter how accurate you are, you can't measure to more accuracy than Planck length. If you measure time, you can't be more accurate than Planck time. Irrational numbers are purely theoretical, in the sense that no physical real world measurable quantity is irrational. Maelin 06:50, 25 October 2006 (UTC)
replies: text: I would contend that the entire concept of "infinity" which is a pre-requisite for the proof that 0.999... = 1, does not exist in our universe. Ansell 06:54, 25 October 2006 (UTC)
replies: text: I'm confused by that. If infinity is real than why would all numbers divide by infinity be 0? Because .999... strikes me as being the same as saying that 1-(1/infinity)=1. This would mean 0=-1/infinity. So does that mean that if you multiplied zero by infinity you get +/-1? I'm admittedly a layman on this, but I do read math books for pleasure. I'm confused.--T. Anthony 07:50, 25 October 2006 (UTC)

text: Anyway, I'm not sure if the article can address this particular topic. Unlike, for example, -0 (number) and its meteorologists, we don't have any evidence that 0.999… is useful as a recording convention. I encourage you to look for such evidence; it would indeed be a valuable addition to the article. Melchoir 07:13, 25 October 2006 (UTC)
replies: text:  Well, I think I just gave you some examples of .999... being useful.  Blue: 3 ≤ x < 4; Red: 4 ≤ x < 5, is just ugly as sin compared to 3.999..., and I'm guessing would be understood by few people besides math fans.  (I though of it, but rejected it for that reason.)  Algr 07:51, 25 October 2006 (UTC)
replies: text:  Blue: 3 ≤ x < 4; Red: 4 ≤ x < 5, is perfectly meaningful and standard terminology. I don't see why it should be "ugly". --Kprateek88(Talk | Contribs) 18:01, 28 October 2006 (UTC)
replies: text: No offense, but are you personally important enough that Wikipedia should be reporting on your use of mathematical notation? Melchoir 09:22, 25 October 2006 (UTC)
replies: text:  Well, if you honestly believe that I'm the first person ever to define a range as "Under four" then I must be incredibly important.  This is basic stuff, that peiple run into every day.  Another example, is 12 pm, noon or midnight? Algr 17:26, 25 October 2006 (UTC)
replies: text: I'm saying that 3.999… is not commonly used for this purpose; at the very least, we cannot assume that it is without some kind of evidence. Melchoir 00:33, 26 October 2006 (UTC)

text: I would say that to speak of there "not being one world" is itself radically constructivist, and the rest of the world believes there is only one world, to some extent. Radical constructivists have a hard time coping with the entire concept of an objective science IMO. Ansell 08:09, 25 October 2006 (UTC)
thread_title:  Practical use of .999... issue 

message: I hate to clutter up the talk page with completely nonproductive and unabashed praise, but in this rare case I really must. I'm no student of math, but I found this article completely fascinating, and after reading some of the sources I can see how accurate and well-researched it is. Cheers! SlapAyoda 06:56, 25 October 2006 (UTC)
replies: text: Awesome. This is certainly a more welcome "clutter" than the opposite reaction! Melchoir 07:02, 25 October 2006 (UTC)

text: Just tried to flick this through this article before the working day begins. Have not a clue what it all means, but I can tell just how well researched and put together this article is. Well done to all - Wiki at its best. Now, back to the Weetabix.....doktorb wordsdeeds 07:17, 25 October 2006 (UTC)
thread_title:  Wow. Thank you. 

message: I'm a confirmed non mathematician and I wanted to congratulate all concerned on an outstanding article.
My instant reaction was that this was tosh, but having read, understood and laughed out loud at the "fraction proof" and the "algebra proof", I have to hand it to you for producing an understandable article. OK, OK, you lost me completely with the "infinite series" section, but I'd understood enough by then to have the hang of the issue. Outstanding work. Deserved FA. --Dweller 08:28, 25 October 2006 (UTC)
thread_title:  Oustanding article 

message: When I first read this phrase in the introduction, I mistakely read it as 'non-zero-terminating decimal', that is, a decimal number that doesn't end with 0. It took a few moments of wondering why 10, 20, 100, and so on should behave differently from other values before I realised my mistake. I suggest that 'terminating, non-zero decimal' may be less ambiguous, or maybe just an extra comma - 'non-zero, terminating decimal' - would be sufficient to satisfy pedants like me.
I don't want to edit the page directly (a) because it's currently on the main page and (b) because my version sounds less elegant, so unless it's deemed worthwhile I'm quite happy to leave things as they are. Still, in the spirit of Wikipedia I offer my suggestion up for comments. Gholson 11:45, 25 October 2006 (UTC)
replies: text: Melchoir has made an edit similar to your suggestion. -- Meni Rosenfeld (talk) 13:56, 25 October 2006 (UTC)
replies: text: Thanks, Melchior and Meni. And well done for keeping track of the sandstorm of comments on this page, which must be exhausting. Please accept a virtual pat on the back. Gholson 12:16, 27 October 2006 (UTC)
replies: text: Just a pat on the back? I think our good friends deserve some barnstars. :) - KingRaptor 12:38, 27 October 2006 (UTC)

text: No problem, it's all in a day's work :) -- Meni Rosenfeld (talk) 14:51, 27 October 2006 (UTC)
thread_title:  Non-Zero Terminating Decimal 

message: I vividly remember at the age of 10, being quite distressed trying to understand this concept, visiting it again, I'm still not quite sure about the c=0.999... proof, although I am happier with the 0.3333... x 3 proof for some reason.  Glad this has made the front page, although I'm sure you're going to lose lots of people even before the series explanation, let alone the much further proofs, which people seem to be saying are much more robust, I certainly didn't make it that far.  Have fun with the trolls and vandals, I'm sure there will be many today. TerriG149.155.96.5 11:48, 25 October 2006 (UTC)
replies: text: Well, I've had my fair share of dealing with trolls in the context of this article - and I can say that the vast majority of the people criticizing the article right now are not trolls. They're here for a real disucssion, and we're willing to provide it. -- Meni Rosenfeld (talk) 14:10, 25 October 2006 (UTC)
thread_title: Problems with 0.999....

message: :Moved to Talk:0.999.../Arguments. --Brad Beattie (talk) 13:44, 25 October 2006 (UTC)
thread_title:  well it isnt equal but frightening near

message: Moved to /Arguments. Melchoir 20:13, 25 October 2006 (UTC)
thread_title:  Show your work 

message: :Moved to Talk:0.999.../Arguments Argyrios 15:20, 25 October 2006 (UTC)
thread_title:  0.999 ≠ 1, but whole fractions work 

message: :Moved to /Arguments →AzaToth 16:09, 25 October 2006 (UTC)
thread_title: Random question...

message: Moved to /Arguments. Melchoir 20:14, 25 October 2006 (UTC)
thread_title: Cogent objection?

message: I was always taught that two numbers are unique if and only if there is another unique number that lies between them, and since there is no possible number between .9~ and 1, they are not unique, but are equal.  I can't find any sources on this though - everything I find on the internet uses one of the examples already provided. Could this possibly merit inclusion in the article? -- FireCrotchRIO 16:49, 25 October 2006 (UTC)
thread_title: Definition of uniqueness?

message: Even though this is a featured article, there are other things could be added (once its feature day ends), e.g.:
* "Infinite series and sequences" could be stated in English prior to being stated in math, e.g.: "Two numbers are identical if and only if their (absolute) difference is not positive.  Given any positive value, the difference between 1 and 0.999... is less than this value.  Thus the difference is 0 and the numbers are identical.  This also explains why 0.333 = 1/3, etc.  In other words..."
* The problem here can be considered one of notational misunderstanding as much as mathematical misunderstanding.  In language, "..." means that some finite portion is left unstated or otherwise omitted (as in the above bullet point), whereas in math "..." means that some infinite portion is left unstated.  Some just want to "fill in the gap" between the first and last "9" that would be implied by a linguistic interpretation. 
* It could also be mentioned that, just as human beings have difficulty understanding repeating decimals and irrational numbers, computers cannot "understand" non-dyadic rationals, because none of these "end."  (Obviously, the connection would have to be put more clearly than this.)
Calbaer 20:52, 25 October 2006 (UTC)
thread_title:  A couple of suggestions for the end of the day 

message: Cute article.  I don't understand why the very simplest proof is not presented, namely that 1.0-0.9 = 0.1, 1.00-0.99 = 0.01, etc. so the difference must be smaller than 0.(0)1 for any number of (0)'s.  If you choose any number other than 0.00..., it will have to have a non-zero digit somewhere, so it must be 0.  This argument is correct in terms of the elementary understanding of arithmetic on decimal numbers (which assumes that every number has a decimal representation), and can be made rigorous (but that would be in appropriate in an introduction). --Macrakis 23:11, 25 October 2006 (UTC)
replies: text: A proof similar to the above should perhaps be added. Unfortunately, the skeptics won't be satisfied, since they believe some magical "0.000...1" is the result of the subtraction. -- Meni Rosenfeld (talk) 10:40, 26 October 2006 (UTC)
thread_title: Simple proofs

message: I just reverted the following addition by User:Yuraty:
 --ZeroOne (talk | @) 21:30, 25 October 2006 (UTC)
replies: text: Nice use of Zeno's paradox. Shame it isn't really applicable. GeeJo (t)⁄(c) • 21:59, 25 October 2006 (UTC)
replies: text: Pfft. Zeno never took into account that while you're covering less and less space, you're covering it at a greater and greater speed. Zeno needs a lesson in calculus and the converging values of infinite geometric series. Too bad he's dead. :P --Brad Beattie (talk) 02:20, 26 October 2006 (UTC)
replies: text:  I never really thought of Zeno's paradox that way, so thanks for the new insight. However, I think you meant that the time period is smaller. The speed should remain constant. As an object approaches the goal, each sub section is completed quicker and each length is proportionally smaller, therefore the speed doesn't change ( s = d/t ). Since it takes less and less time to complete each subsection, the object will eventually reach the goal. Falsedef 04:57, 26 October 2006 (UTC)
thread_title:  Not true? 

message: Moved to Talk:0.999.../Arguments#Step 2??? Supadawg (talk • contribs) 03:19, 26 October 2006 (UTC)
thread_title:  Step 2??? 

message: :Moved to Talk:0.999.../Arguments. --Brad Beattie (talk) 02:22, 26 October 2006 (UTC)
thread_title:  your loophole 

message: The section titled  Generalizations shows that any real number can be written in two ways with one way having an infinite length of 9s, like 0.24999... and .25. Would this apply to the 3s in 33.333... (to make 33.4) or any other number? Tim Q. Wells 23:30, 25 October 2006 (UTC)
replies: text: It's not any real number, just the ones that have terminating decimal representations to begin with. 33.333... doesn't have an alternate decimal representation, since it doesn't end either with repeating 0s or repeating 9s. Melchoir 23:33, 25 October 2006 (UTC)

text: Yes, 33.3 = 33.3999…; otherwise this is just wrong. Melchoir 23:41, 25 October 2006 (UTC)
replies: text: Thank you for answering (it was a bad mistake). Tim Q. Wells 01:43, 26 October 2006 (UTC)
thread_title:  Other numbers 

message: That edit summary is hilarious.  It reminds me of Wayne's World (________ says what?). Ufwuct 00:16, 26 October 2006 (UTC)
replies: text: I got this on my talk page. Actually, I was reverting unrelated vandalism at the time, and that edit got caught in the revert, but it's all good. —Ashley Y 00:58, 26 October 2006 (UTC)
thread_title: [http://en.wikipedia.org/w/index.php?title=0.999...&diff=prev&oldid=83736690 Anyone who deletes this...]

message: Moved to Talk:0.999.../Arguments#Failed Logic Supadawg (talk • contribs) 03:19, 26 October 2006 (UTC)
thread_title:  Failed Logic 

message: Moved to Talk:0.999.../Arguments#No!! Supadawg (talk • contribs) 03:19, 26 October 2006 (UTC)
thread_title:  No!! 

message: I've been helping BradBeattie move topics arguing against the article to Talk:0.999.../Arguments.  After people reply there, proving that they know where their topic went, the leftover notice on this page is deleted.  Melchoir, I don't know how you can reply to nearly every single new topic, but I commend you for it.  Sometime, I'll go through and add s to the new topics, but that will be incredibly tedious.  After about a month, I'll do another round of archives, but if the talk page keeps growing so fast, it might have to be sooner.  Hopefully this will all die down now that we're not a Featured Article anymore, so we can get on with improving the article. Supadawg (talk • contribs) 03:19, 26 October 2006 (UTC)
thread_title:  Talk Page Maintenance 

message: :Moved to Talk:0.999.../Arguments. --Brad Beattie (talk) 05:18, 26 October 2006 (UTC)
thread_title:  Wait, if the formula is true... 

message: Just want to say well done to all those who withstood the main page exposure, over 500 edits in a single day! --Salix alba (talk) 07:53, 26 October 2006 (UTC)
thread_title:  Well done 

message: In the introduction, a number of claims are made about researchers into maths education and their analyses of the reception given to this claim by students. Perhaps the relevant articles published on these points should be cited. This is one example but much of the article seems equally devoid of sources even when specific non-mathematical points are being made. Davkal 11:09, 26 October 2006 (UTC)
replies: text: Per the Manual of Style, introductory sections should act as a summary, and not give any information that isn't available further down. As such, they aren't usually cited, but the relevant bits in the article that they summarise are. Have you checked the remainder of the article for the cites you're seeking? GeeJo (t)⁄(c) • 17:52, 26 October 2006 (UTC)
thread_title: where are the sources

message: Despite all the vandalism, this article was greatly improved during its time on the main page!  See this before-and-after the main page exposure diff. —Mets501 (talk) 18:11, 26 October 2006 (UTC)
thread_title:  One day's changes 

message: or  ? →AzaToth 19:15, 26 October 2006 (UTC)
replies: text: The character spacing on the new image seems to be too tight for its font. If you loosen it up, it'll probably be easier to read. Melchoir 19:25, 26 October 2006 (UTC)
replies: text: I agree: loosen it up and I also would make the shadows a drop lighter. —Mets501 (talk) 19:26, 26 October 2006 (UTC)

text: Is the shadow supposed to be subtle? The 1 is kinda hard to notice. Falsedef 19:28, 26 October 2006 (UTC)

text: Agreed -- it would be better with larger character spacing. The variegation on the 9's is also superfluous at the size we're using here. For now I think the grayscale image is easier to read. —ptk✰fgs 20:27, 26 October 2006 (UTC)
replies: text: I don't like the new image. The first one is very charming because of its simplicity. This is an encyclopedia, and for the purposes of illustrating an infinitely recurring sequence of numbers, I find the first one to be much more concise. Less objective is the opinion of mine that the 3D and color effect on the new version are but simple effects that actually impede the image's visual integrity. Also, keep in mind that the original image prints much easier. —msikma <user_talk:msikma> 20:29, 26 October 2006 (UTC)
replies: text:  it might work better if the shadows were in front of the 9's instead of behind them.  (Backlit) It is too fussy as is.  Algr 20:48, 26 October 2006 (UTC)
replies: text: Try a backlit image so we can compare. I like the subtlety. I agree that this image has great potential. I also agree with previous comment re: spacing. Good work. Argyrios 22:00, 26 October 2006 (UTC)

text: I'd go for AzaToth's new image if the shadow were in front of the digits so they would stand out more. Maybe even make the shadow a different color, so it's not confused with the 9s. — Loadmaster 23:28, 26 October 2006 (UTC)

text: I'd say we should not change the image because the current one is much more concise and works better when printed. This is just bad design; taking an existing design and applying "cool effects" to isn't what I consider to be a suitable improvement. —msikma <user_talk:msikma> 13:34, 27 October 2006 (UTC)
replies: text: The reason I like the image is that the addition of the shadows is not merely a "cool effect," but actually adds meaning to the picture. After all, a large part of this article is devoted not just to the fact that 0.999... = 1, but to the fact that many people find this jarring and counterintuitive and seemingly impossible. The numbers casting those shadows is similarly jarring and counterintuitive and impossible-looking (yet, like the proof, right in front of your eyes and undeniable). I think the new image would do an excellent job representing both the mathematical and sociological / educational aspects of this article. Argyrios 18:10, 27 October 2006 (UTC)
replies: text: It's badly done and I don't share the idea that the shadow has deeper meaning. I find it to be a rather shallow explanation of what appears to be, like I still think it is, an image with "cool effects" thrown onto it. I've been a graphic designer for years, and even though this new image is more sophisticated, I would never choose it over the old one, which fits perfectly with the typical black on white text of the article. Plus, I think that it's a big thing that this image impedes usability in that printers might choke on it (many people have either black and white printers, do not like to needlessly spend color ink, or have a bad DPI setting for color prints so the image won't be rendered correctly anyway). —msikma <user_talk:msikma> 22:31, 27 October 2006 (UTC)

text: Oh, and that said, I should note that I don't feel like I "own" this article, or anything (especially since I've not made one non-minor edit to it), but I just personally would not choose the image. You're free to do so if you do like it. I won't edit it out (straight away)... :) —msikma <user_talk:msikma> 22:32, 27 October 2006 (UTC)
thread_title:  image 

message: As described here. 
Isn't H(1-0.999999) = 1 and H(0.999999-1) = 0, or to put it another way doesn't 1-0.999999 = 0+, and 0.999999-1 = 0-. Of course you could argue that in the limit 0- = 0+ = 0, but such reasoning isn't valid if there's a Heavyside or Dirac Delta Function in the neighbourhood. 
Sam 213.208.101.80 22:30, 26 October 2006 (UTC)
replies: text: First of all, 0.999999 is not the issue; 0.999... is. I am assuming that is what you meant. I believe that if you define H(1-0.999...) = 1 and H(0.999...-1) = 0, what you have is not any sort of function at all, because H(0) would evaluate to both 1 and 0. Argyrios 22:40, 26 October 2006 (UTC)

text: (edit conflict) I don't understand what you are arguing. You are deliberatly putting a discontinuous function at x=0. Then you are approching 0 from either side and noting that there is a step. No surprise there! vWhy can you say that in the limit at epsilon >0 H(1-(1-epsilon)) = H((1- epsilon)-1) = 1/2 as per the definition of the heaveside step function? Theresa Knott | Taste the Korn 22:47, 26 October 2006 (UTC)
thread_title:  What about the Heaviside Step function? 

message: The spoken article for this page is nuts. It's particularily loud, quality is similar to that of a telephone, and not to mention it's almost an hour long. I kind of feel sorry for whoever made it, the poor guy.
Just thought I'd point that out.
Oh, and 0.999... does not equal 1. 1=1, end of story. Any other number is different and should be regarded as such. LOL NIRVANA2764 20:45, 28 October 2006 (UTC)
replies: text: You're right, any other number is different and should be regarded as such. 0.999... is not an other number, it's the same number. -- Meni Rosenfeld (talk) 21:05, 28 October 2006 (UTC)

text: Leave it on the arguments page. Melchoir 03:30, 29 October 2006 (UTC)

text: 0.5 and 1/2 are the same number, but are written differently, spoken differently, and referred to differently. Any decimal with an infinite number of places will require infinity to understand it by definition. 0.999... does not come before 1 on the number line, as 0.999... and 1 have exactly the same value. -- Schapel 13:44, 29 October 2006 (UTC)
thread_title:  Spoken Article 

message: Moved to Talk:0.999.../Arguments#Error in logic in calculus and analysis section by Calbaer 02:39, 2 November 2006 (UTC)
thread_title:  Error in logic in calculus and analysis section 

message: In the opening: "A similar phenomenon occurs in balanced ternary, where 1/2, instead of 1, has two possible expansions." My issue with this is that 1/2 has two expansions in decimal as well. What's with this sentence? --King Bee 14:27, 31 October 2006 (UTC)
replies: text: Since this point gets only a single, short sentence in the body, I don't think it deserves a place in the opening anyway. Melchoir 17:44, 31 October 2006 (UTC)
replies: text: Agreed. --King Bee 18:17, 31 October 2006 (UTC)
thread_title: This sounds weird