# Is it time to retire the 0.999=1 question (and other historical questions)

Some questions, like the Is it true that $0.999999999\ldots = 1$? attract a lot of answers, and that's good. But after six years, a lot of these answers repeat themselves, and literally add negative value to the thread: the noise to signal ratio worsens. There are currently more than 30 answers deleted on that very thread.

Is it perhaps time to retire this thread and lock it (maybe just the question, not the answers, so they can still be voted and commented upon)? If this is supported, perhaps we can establish some guideline as to when these retirements should happen? There are other similar questions I imagine can be retired.

• Another positive side that I can see in locking these questions, is that it protects them from deletion (big problem in here...). – Surb Dec 14 '16 at 7:26
• I'm a bit surprised that there aren't more comments here. But I'm not inclined to lock or close the historical giant questions, at least not at their current rate of popping back up. They continue to receive a trickle of upvotes, and there have been good edits more than two years after initially being asked. The $0.999\ldots = 1$ seems to receive about one answer per month, which doesn't seem too bad to me. – davidlowryduda Mod Dec 14 '16 at 19:04
• @mixedmath do you expect further answers that add something relevant and will get any relevant visibility? – quid Mod Dec 14 '16 at 22:50
• @quid Generically, I'm not sure. On this question --- no, I do not expect new answers to add new insights on the problem. But I am also aware of the ideal, where some new answer might come along and provide a different point of view that helps someone else. I think that locking the question is not a good action, as I see no good reason to prevent upvotes or (generically) edits. I think that closing is not a good action as we usually close to indicate questions that are a poor fit for the site, whereas these questions evidently are appropriate for the site. – davidlowryduda Mod Dec 14 '16 at 23:07
• "I think that closing is not a good action as we usually close to indicate questions that are a poor fit for the site, whereas these questions evidently are appropriate for the site." Why is it evident? One might say it "lacks context." Incidentally, the question was closed, in the 'old days,' in 2010, which I am often told were much better and not so hostile. Plus, the question was locked from 2010 to 2014. Given this it might be a good example for a Q that should be historically locked. – quid Mod Dec 14 '16 at 23:46
• Leaving that aside and let's assume for the sake of argument it is appropriate (and I have no strong feelings about it being otherwise): the question is evidently exceptional so what we usually do is not all that counts. We usually also do not protect questions. In this case the "protect" is empirically just not strong enough. Re improvements by edits: the last edit just undid poor grammar introduce in the penultimate one, which did nothing besides that. @mixedmath – quid Mod Dec 14 '16 at 23:54
• This post seems somewhat similar: Should we close/lock old questions with many answers at some point?. Even this particular question is mentioned there in comments. – Martin Sleziak Dec 15 '16 at 4:56
• Thanks @Martin, I had a feeling I brought this up sometime in the past. – Asaf Karagila Mod Dec 15 '16 at 4:58
• @mixedmath: Looking at the mention of this question in the question Martin linked above, it shows that in one year over 17 answers were added, most of which were deleted. – Asaf Karagila Mod Dec 15 '16 at 5:00
• I, for one, like the thread and welcome its expansion. I have 6 different proofs that range purely from thought experiments to rigorour proofs that I like to use. But the arguing is what gets me. – The Count Dec 15 '16 at 15:00
• @TheCount: You make it sound as though I'm suggesting to close every question with many answers. This is certainly not the case. – Asaf Karagila Mod Dec 15 '16 at 15:41
• @TheCount: Sure, but in the last year most of the answers that were added were also deleted. And probably those that weren't deleted, are just repeating arguments from older answers. – Asaf Karagila Mod Dec 15 '16 at 15:45
• @AsafKaragila, I was only tangentially talking about the question, honestly. Just making a comment from personal experience. Carry on, carry on. – The Count Dec 15 '16 at 15:48
• @amWhy I assume it means that the question will be locked, and future users will be "banned" from asking it again in the sense that their new question will be a duplicate of the old one and closed as such (with a link to the old one as usual). – Najib Idrissi Dec 15 '16 at 20:31
• The question here has been locked. – Watson Dec 27 '16 at 11:27

TL;DR. Stack Exchange does not have any functionality to "retire" on-topic questions. The "Historical significance" lock reason is for very specific use cases where the question itself is now off-topic, and intrinsically so. The use of this lock reason to simply "retire" a question would be, IMHO, abusing that functionality. As is generally the case, continued community moderation of the question is the appropriate way forward.

Quite frankly, I don't see under what guise we can lock the question while at the same time adhering to the proper use of this tool. Of the reasons for locking questions we currently have, the closest match (here meaning not obviously inappropriate) is the Historical significance reason, which is described as follows in the post notice.

This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here. This question and its answers are frozen and cannot be changed. More info: help center.

That is, the intended use case for this is when a question is (no longer) on-topic, but is nevertheless useful to the site. And recall what happens when a question is locked for this reason (from Meta Stack Exchange).

In addition to the post notice being prominently displayed, posts which are historically locked are "frozen in time": they cannot be voted on, flagged, answered, edited or commented. Historically-locked questions are omitted from normal question lists (those on the home page, /questions, and the various per-tag lists), but can still be found by searching for words in the post or title (via either site-search or Google, etc). The visual appearance of the entire post is altered by removal of the voting arrows from the question and all answers.

So locking the question for "historical significance" will completely freeze the question (and its answers) in their current state. Forever. (Or until another moderator unlocks it, or uses special powers.) To give an example, here is a question currently locked for historical significance: Can I use my powers for good?

Other sites seem to be able to deal with questions with a high number of (deleted) answers without resorting to locks. Consider the following question on Stack Overflow:

Currently that question has 62 undeleted answers (and I am told 19 deleted answers). The undeleted answers include numerous flat out incorrect answers, and a number of duplicate answers (even a self-duplicate: someone posted essentially the same answer twice). The latest (undeleted) answer was posted on 10 Nov 2016, and the SO community seems to be moderating it just fine. (The deleted answers include your usual comments-as-answers, and several approaches using languages other than Java, the language specified in the question's tags.)

And this is just an example. There are other questions on Stack Overflow with many more deleted answers: 38, 41, 62.

Thanks to Daniel Fischer for supplying the information about the deleted answers to these Stack Overflow questions.

• To reiterate the question was closed shortly after it was asked. Plus, it lacks context, which makes it so overly broad (allowing too many answers). One can easily argue "it is not considered a good, on-topic question for this site." IMO it's at best borderline. How sure are you the question would not be closed when asked now (disregarding dupe)? Either way, it was considered as not up to the standards of the site in 2010. – quid Mod Dec 16 '16 at 10:56
• @quid: To be a bit more complete, the question was closed about 9 hours after being asked, and then reopened about 3 hours after that. Since that time it has received three close votes (all in July 2014), and went through the close votes review queue twice (resulting in 6 "leave open" votes, and 1 close vote). I think there is something to be said about the intrinsic interest of this question. This alone sets it apart from the often artificial questions copied from textbooks/assignments/exams/contests. – user642796 Dec 16 '16 at 13:07
• "...the question was closed shortly after it was asked." - The older meta thread, for reference. – J. M. ain't a mathematician Dec 16 '16 at 18:31
• I find your attempt at being more complete rather misleading given the fact, which you somehow do not consider as relevant enough to acknowledge it, that the question was locked for the larger part of its lifetime up to this day. Plus, it is a textbook exercise, for school children no less. – quid Mod Dec 16 '16 at 19:21
• @quid I honestly didn't consider that it might have been locked at some previous point. The moderator timeline for that question is rather busy, and I searched for what I thought were relevant data: reviews, close votes, and reopen votes. To be more complete, yes the question was locked (without any stated specified reason, a functionality that no longer exists) from 18 Aug 2010 until 27 Mar 2014. The three now aged-away close votes (and two close vote reviews) occurred about 2 months after the unlocking. [cont...] – user642796 Dec 16 '16 at 19:52
• [...inued] It may be a textbook exercise, but there is something more intrinsic about the question than, for example, "What is the remainder when $10^{5^{102}}$ is divided by $35$?" At any rate, I do not agree with locking this question for historical significance (or any other reason now available), so those wishing it locked will have to badger one of the other eight. – user642796 Dec 16 '16 at 19:56
• "I honestly didn't consider that it might have been locked at some previous point." I had mentioned it explicitly in a comment in this very meta thread. :-/ – quid Mod Dec 16 '16 at 20:16
• @quid: No, it is not a textbook exercise for schoolchildren, unless you accept one of the superficially convincing pseudo-answers like $1=3\cdot\frac13=3\cdot0.\overline{3}=0.\overline{9}$. Schoolchildren don’t generally get more than a hand-waving explanation of the decimal representation of irrational numbers to start with. In any case the question is a very common point of entry to a fundamental structural feature of the representation of real numbers using positional notation and as such is obviously appropriate here. – Brian M. Scott Dec 17 '16 at 2:09
• @Brian, quid, ArJaFi: I don't think anyone is arguing that asking whether or not $0.\bar 9=1$ is appropriate. If anything the argument is that this specific question (which is probably a seed question from the first days of the site?) is subpar when judged in 2016 standards. While we're not going to pretend that all old questions should be closed, this one pops up often enough to consider locking it is not necessarily a bad idea. – Asaf Karagila Mod Dec 17 '16 at 10:33
• @BrianM.Scott your comment adds to my critique of the question in its current form, namely that it suffers from not spelling out the level of rigor at which answers is desired (there is not even a clue towards it). The sane thing to do would be to close this one as too broad, and allow spin-off. That said, I maintain that summing the geometric series $aq^n$ with $a=9$ and $q = 0.1$ is a textbook exercise for school children. – quid Mod Dec 17 '16 at 11:49
• @Asaf yes. The specific problem is that the question lacks context and this lack of context makes it too broad (allowing too many answers). Several versions of this question could coexist. – quid Mod Dec 17 '16 at 11:56
• Sorry I forgot part of the argument in the penultimate comment, to @BrianM.Scott : school children do learn to convert rationals to (periodic) decimals and the other way around. They apply the thus learned technique to many examples and "everyone" is happy with the result. This particular one is not really special. The result on gets for $0.9\ldots$ using this technique is just $1$ as you of course know. This may or may not be explained with sufficient rigor, but that's true for most things in school math. In that sense I am doubly puzzled what your issue with my assertion was. – quid Mod Dec 17 '16 at 13:30
• @quid: People who ask this question are obviously not ‘happy with the result’. Whether they realize it or not, they are in effect asking how the decimal representation of numbers with no finite decimal expansion really work. Being able to perform that algorithm correctly certainly does not entail such understanding. – Brian M. Scott Dec 17 '16 at 18:06
• "Quite frankly, I don't see under what guise we can lock the question while at the same time adhering to the proper use of this tool." - as a community-run site, we can determine what we want to use the lock took for, so if we decided to use it here, I would view that as a proper use. We can't control the details of exactly what the lock tool does, of course, but we can decide which questions we'd like to apply it to. I'm not sure if it is the right tool in for the 0.999 question, but I do think the community has the prerogative to decide if we want to use it that way. – Carl Mummert Dec 17 '16 at 23:05
• I do not see how you can maintain the historical lock on math.stackexchange.com/questions/151938/… given what you say here. Maybe you want to reconsider your earlier action or this answer. – quid Mod Dec 18 '16 at 19:24
• I didn't know he had an opinion on whether or not we should keep some question on Math.SE open. That is impressive that he cares so much! – Asaf Karagila Mod Dec 17 '16 at 23:05
• @AsafKaragila He doesn't have an opinion on your proposal, but the fact that his ultrafinitistic perspective on 0.99999.... has not yet been included, implies that retiring the question would be a premature action. – Count Iblis Dec 18 '16 at 0:58
• And we should have guessed that from your link only answer? – Asaf Karagila Mod Dec 18 '16 at 5:33
• Did I read that link correctly? Why are people like that allowed to have doctorates in math? Sigh. – user307169 Dec 18 '16 at 7:41
• @tilper: I agree that Doron Zeilberger's opinions are fringe, controversial and often formulated in an antagonizing way. Ultrafinitism is not necessarily nonsense, though. It's just that many of those arguing for it (and the more vocal ones, I might add) usually argue something like "I don't like infinity, so I must be right and everyone else is dumb!" which is why ultrafinitism usually brews controversy in these discussions. I don't necessarily disagree with having an ultrafinitistic answer to "Why $0.\overline9=1$" on the site, but it would have to be well-argued. – Asaf Karagila Mod Dec 18 '16 at 9:18
• @tilper you may have read it correctly in the literal sense, but it is likely you miss a lot of relevant context in which the(se) opinion(s) need to be taken..Either way there is no doubt that Zeilberger is a first-rate mathematician, with various important contributions, especially in classical combinatorics. – quid Mod Dec 18 '16 at 12:48
• Interesting. Thanks. I guess I just can't really imagine a context in which a statement like "there are no infinite sets" can be taken seriously. But such are the joys of using this site.. – user307169 Dec 18 '16 at 23:53
• Professor Zeilberger can't imagine a context in which the statement "there exists an infinite set" can be taken seriously. – Austin Mohr Dec 20 '16 at 8:16
• Thing is that we're ultimately all just finite state machines, in principle we could just as well have been generated inside a huge but finite cellular automaton (CA) that simulates the laws of physics. Now, anything that appears inside a CA is always reducible to just discrete math. So, a mathematician may think about doing math involving uncountable sets, but at the end of the day he/she is just a neural network that can only execute finite formally describable algorithms. – Count Iblis Dec 20 '16 at 18:42
• You sound awfully certain. Do you have any actual proofs? – Asaf Karagila Mod Dec 20 '16 at 22:00
• @AsafKaragila Computer Algebra systems can do math. But I think it's not controversial to appeal to formalism, so one can always interpret math as a game played with symbols, you can only ever manipulate finite strings of symbols. If one wants to refer to some infinite string of symbols one necessarily has to invent a new symbol, or an entire formalism to represent this. – Count Iblis Dec 20 '16 at 23:06
• Nobody disputes that. But who ever said that math has to describe physical reality as we comprehend it? Math is its own thing. – Asaf Karagila Mod Dec 21 '16 at 5:09
• I don't undestand neither the discussion nor the downvotes. It seems that you discuss here about ultrafinititsm. But actually the discussion should be about @CountIblis objection that even for such a simple question there are answers to this quesions that are not yet posted and so a question should not be closed. – miracle173 Dec 22 '16 at 10:57
• @miracle173: It's funny that you say that you don't understand the downvotes, because at least some of them are explained. Mine, for example. I couldn't have guessed that the meaning was "Hey this answer is missing", and not "Well, how about this answer", until Count Iblis explicitly explained that in the comments. Much like how a badly written paper gets rejected, or at least not accepted until revised, badly written answers get downvoted. Not to mention that there are two answers about ultrafinitism there, both by Count Iblis, and both deleted. Why? Because controversial topics [...] – Asaf Karagila Mod Dec 23 '16 at 6:53
• [...] need to be carefully addressed. On the other hand, it is often the case with ultrafinitists that they flatly claim "Well, this question is meaningless". If it's so meaningless, how come so many people can find meaning in it? Are we all wrong? No. We are not. We just view mathematics differently. And as I wrote, I'd be very happy to upvote an answer which explains the ultrafinitistic approach here, rather than dismissing all of the non-ultrafinitistic mathematics. Until then, I am neither a mind-reader, nor approving of this idea. – Asaf Karagila Mod Dec 23 '16 at 6:55