# Why is “infinity minus infinity” a Community Wiki question?

I have an inquiry on the grounds of curiosity. The following question has been marked Community Wiki on August 31st:

What is the result of infinity minus infinity?

From my understanding, you have a base policy that and questions are Community Wiki as a means to discourage their proliferation. The above question, however, is not a soft question or big list, neither in tag nor apparently in essence (my understanding of what a soft question is, this isn't one to me, but I'm happy to admit I may not fully grasp your definition of a soft question).

It is a pretty direct question ("What does the equation of infinity minus infinity yield?") that even has a highly voted, and very illustrative, answer ("Indeterminate, as proven through comprehension"). The question is even amongst your top-voted questions, which is a nice place to see that it is otherwise populated primarily by normal questions. It seems like it would fit in nicely with all those normal questions.

As such it leaves me confused. Why is this question marked community wiki? I can find no discussion or indication as to why this question was marked as community wiki, or any policy discussion here on Meta which applies to this question.

• "It is a pretty direct question" in fact, it is not. Term "infinity" doesn't have one precise mathematical meaning. – Grigory M Sep 21 '11 at 12:56
• @Grace CW is used on MO as one way to discourage posts that are at the boundary of being too low-level. Unfortunately some of our members - also MO members - are trying to do the same here. But that policy does not fit here because this site is - by charter - a general level math site. Questions are welcome here at all levels. Indeed, some of the lower-level questions such as the one you cite are questions with the potential to have the most impact on layfolks. Thus it is unfortunate that such questions are being labeled with red scarlet badges that will discourage further good answers. – Bill Dubuque Sep 21 '11 at 13:18
• @Grace Ditto for MO bias against big-list and "soft" questions. Many such questions would be the most valuable questions to layfolk. Many big-list questions are valuable for pure-math students since they provide crucial background for comprehending abstractions - which is often sorely lacking in textbooks and lectures. By snubbing these questions one is short-circuiting a valuable resource - one that can not be easily be duplicated elsewhere, e.g. classrooms (time-limited) or textbooks (space limited). MO policy doesn't fit here in any shape or form. It's sad that some try to force it to. – Bill Dubuque Sep 21 '11 at 13:27
• I believe Bill's characterisation (in his first comment, not the second; of both MO and Math.SE) to be incorrect. At MO they aggressively close low level questions. CW has never been used at MO to discourage low level or poor questions. His comment also makes it sound like it is a general phenomenon that CW is used in this fashion on this website. I cannot find any evidence for this claim. Considering my response below and Mariano's general stance, I'm curious where Bill develops his misconceptions. – Willie Wong Sep 21 '11 at 13:35
• @Grace As for any general level math site there will always be tension regarding the primary focus of the site. Some will prefer it to be mainly for education of (pure) math students whereas other will warmly welcome questions at all levels - including trivial questions that would be mundane to math students. It is possible for a site to be successful at both. But this requires nontrivial conscious effort to eliminate such bias. Here that is difficult because it is firmly rooted -having been imported from MO by some early members of the site. – Bill Dubuque Sep 21 '11 at 13:46
• @Willie My remarks are based on my experience on MO, here, and many other general-level mathematics sites (a few decades worth). I believe them to be fairly accurate in general. – Bill Dubuque Sep 21 '11 at 13:48
• I'm kinda thinking that the question of the level of math is a bit tangential to the inquiry at hand here. The flag reason proposed is on "research effort" and "popularity", and it is what allegedly led to the community wiki status. – Grace Note Sep 21 '11 at 13:51
• @Grace It is not tangential. It is in fact the main driving force behind many of these decisions (whether or not folks will publicly confess to such). – Bill Dubuque Sep 21 '11 at 14:14
• @Bill Is it the driving force behind this decision? I'm not seeing the low-level/high-level camp providing any support for the conversion of the infinity question. I'm not really seeing a whole lot of enthusiastic support for the particular conversion at all, honestly, but that's yet another tangential observation, this time on my part. – Grace Note Sep 21 '11 at 14:21
• @Grace I presumed you were interested in inferring general policies in effect here. Only by correcting those can one have any hope of influencing the global site dynamics. – Bill Dubuque Sep 21 '11 at 14:25
• @Bill Be that as it may, it's not my intent to use my question here as a pedestal to launch into a discussion about the general policies or influence global dynamics. My intent here is exactly the question at hand - why was this question made community wiki, under what policies did we go towards the conversion, and the validity and practice of those policies. Discussing policies not directed toward this instance would be losing that focus, I would think. – Grace Note Sep 21 '11 at 14:32
• @Grace But "under what policies" is precisely the issue of what are the general policies, how are they being applied, what should they be, etc. – Bill Dubuque Sep 21 '11 at 14:37
• There is no reason that such a question should be community wiki --- it is a legitimate question, which has more or less a definitive answer, namely that such an expression is indeterminate without more information/precision as to what is meant. – Matt E Sep 21 '11 at 19:06
• @Willie Wrong. Would you please be more civil and stop saying things like "Bill's misconceptions" when you happen to disagree about subjective matters. While that is not as offensive as some of your earlier personal attacks, I still find it very off-putting and quite nonconstructive. If you do not stop these personal attacks I will open a meta thread on the matter. – Bill Dubuque Sep 21 '11 at 19:17
• @Bill: Not once in your initial comments I have seen the words "in my opinion", I believe that Willie's comments are more reflecting of the CW spirit on both sites. Furthermore remember that you are discussing this with an outsider diamond user, and your words sound as though they represent the entire community when in fact they do not. Please try and be more relaxed and be sure to say it is your opinion and your interpretation, and not just say things as if these are facts. This is just plain demagogy. – Asaf Karagila Sep 22 '11 at 6:09

My own view is that this question should not have been made CW. It is a legitimate question, which has more or less a definitive answer (namely that such an expression is indeterminate without more information/precision as to what is meant).

Edit by J.M.: considering the number of upvotes on this post, can there be a final decision by the mods on whether CW status should be unset for this question?

• I distinctly remember the guy who posted the highest-voted answer wondering aloud why the question was suddenly CW. I told him to open up a new meta thread, but he decided not to follow through... oh well. As a question addressed to anybody reading: if CW is undone for this question, would it be possible for the answerers to get the rep not gained in the time it was CW? – J. M. isn't a mathematician Sep 22 '11 at 0:30
• @J.M. that should probably be a new question either here or at meta.SO. – Willie Wong Sep 22 '11 at 1:06
• @J.M. Yes, if we reverse the community wiki status, it will be as if there never was community wiki on the posts. A recalculation will be necessary to refund the reputation. – Grace Note Sep 22 '11 at 11:50
• Thanks @Grace. I suppose a poll of some sort is in order... – J. M. isn't a mathematician Sep 22 '11 at 12:10
• @J.M.: I read meta.math.stackexchange.com/q/2938/11020 and the blog linked in Jeff's post and decided to just let it ride. Honestly, I consider my gold-badge answer to be, while encouraging, quite a fluke! In any case, I wouldn't mind the extra 1000 rep :) – Altar Ego Sep 22 '11 at 13:12
• @Altar You wouldn't get that much. Remember, there's a 200-rep-per-day limit, and you got at least 74 across two days cancelled out from that, nevermind what you may have lost from votes on otehr posts. – Grace Note Sep 22 '11 at 13:28
• @Grace: I see, and rep is not in the top ... well... 3(!) reasons that I disagree with the CW-ification of this (and other) questions. It could just be my misunderstanding and/or ignorance of the MSE culture, but it seems to cheapen both questions and answers. Again, I am honored to have such an answer and strive to communicate excellently with my students, so I didn't really say anything until J.M. at-alerted me. – Altar Ego Sep 22 '11 at 13:36
• @Altar Haha, sorry if I made it sound like you were greedy, was neither my interpretation nor my intent. – Grace Note Sep 22 '11 at 13:46
• @Rasmus Since it was I who stressed in the comments that the question is ill-posed in its current form, I think it is my duty to elaborate a bit. Sometimes questions on general topics like this - when posed by a layperson - are not capable of being better posed. A layperson simply does not have the math background to do so. But we do. So we should do all that we can to help such FAQs receive good answers - so that they can be definitively answered once-and-for-all. Making it CW will only discourage further answers, making it more likely that the question will frequently reappear. – Bill Dubuque Sep 22 '11 at 16:09
• @Rasmus I believe Matt's answer here states that the question here is legitimate and has a more or less definitive answer - not that the definition of a legitimate question is the presence of the latter. This is probably a bit clearer to grasp in the context of his earlier comments, which use the word "with" to join the clauses rather than "which has". – Grace Note Sep 22 '11 at 17:13
• @Rasmus: Dear Rasmus, As an indication of why this question is well-posed, let me offer the following example: if a student were to ask "why must a signed measure assume only finite values (or at least not both infinite and negative infinite values)", the answer would be "because we can't make sense of $\infty - \infty$". The student could then ask "why not", and we would explain why, using examples similar to the answer to the question under discussion. Now the question under discussion is essentially of the same nature (except without the initial movitation coming from measure theory), ... – Matt E Sep 22 '11 at 20:38
• @Rasums: Dear Rasmus, The body of the question says "Is it $\infty$ or $0$ or what"? I think this is a pretty clear indication that the questioner doesn't know the answer, recognizes that they don't know the answer, and would like advice on what the answer is. Given that they don't know in advance that the quantity they write down is indeterminate, I think it's asking a bit much to expect an explicit recognition of this to appear in the question. In short, I think that the question is phrased in as reasonable a way as possible given that the OP clearly doesn't know (or perhaps even suspect) – Matt E Sep 22 '11 at 20:51
• @Matt That is consistent with what I wrote. Namely, while technically I consider the question to be ill-posed, this is something I can forgive given that the OP might not have the background to make the question precise (or to recognize that it is imprecise). Many questions from laypersons possess analogous fuzziness. This isn't necessarily bad, because such fuzzy questions open up opportunities for those more knowledgeable to have some leeway on how to interpret the query - often leading to very interesting expositions that would otherwise not occur in reply to a much more focused query. – Bill Dubuque Sep 22 '11 at 21:36
• @Rasmus I am not sure I agree. Since someone who doesn't already know the answer is most likely a layperson, I think that for the benefit of those who would find such a question useful, it is best not to introduce a bunch of technical corrections in the question. Rather, those technicalities should be addressed in an answer. – Willie Wong Sep 23 '11 at 17:27
• I'm technically for the reversal of the community wiki (on the grounds that there hasn't been strong support for the current status, and lots more support opposing that status), and recommend it as the course of action. – Grace Note Sep 26 '11 at 15:24

It appears that Qiaochu converted it to CW after a user flagged it with the following comment:

I'd suggest CW ("Sometimes you have content which is valuable and on-topic, but is perhaps a bit too popular." — it's popular question, but does it show enough "research effort" to give +40 score? and the same question about most popular answer)

The quoted sentence is from this blog post, so may read somewhat familiar. :-)

With that said, I am personally not entirely convinced that that is a good reason to make the question CW. (To be honest I am somewhat surprised that the question isn't a dupe: it seems like such an obvious question to be asked on a Maths website.)

Furthermore, I think the Maths site's habit of using CW for and (which I fully support) already makes it unsuitable to use CW also to discourage content. I quote the next few sentences from the same blog post

... It runs the risk of overwhelming the rest of your site if it grows untamed. In these circumstances, community wiki can be a way to preserve the value of these posts while stifling their growth. Keep in mind, though, that in using community wiki to stifle growth, you should actually follow through with it — a site should never have more than one community wiki question for every hundred questions. Having too many community wiki questions defeats the entire purpose.

(What actually is our community wiki percentage? I am not quite sure how to find out an answer to that question myself.)

• I meant "popular" on the scale of "question volume", not "question votes" in that particular quote - what plagues some sites is the sheer volume of these questions, not so much how popular an individual question is. As for the size of Community Wiki, let me crunch some numbers for you. I'll be right back. ♪ – Grace Note Sep 21 '11 at 12:38
• You have 350 open Community Wiki questions, out of 21351 open questions in total. Which is about 1.6% - high-ish but not too condemning. Note that there are 410 open soft questions and 132 open big lists, so they're not all Community Wiki by volume alone. Currently, Mathematics also has the highest SE2.0 question volume, by the way. – Grace Note Sep 21 '11 at 12:44
• Thanks, I didn't know about the wiki: and closed: keywords in the search. – Willie Wong Sep 21 '11 at 12:55
• (In the interest of full disclosure: I am the user that flagged that post.) – Grigory M Sep 21 '11 at 12:57
• @Grigory A fair disclosure but I'm not personally invested in learning who was flagging as much as the reasoning behind it (which, well, the flag reason Willie posts illustrates that anyway). I take it by being just a comment, you're simply supplementing this answer, or do you have a response of your own to craft? – Grace Note Sep 21 '11 at 13:03
• Just another link - you have 164 questions that have neither tag, but are community wiki and open: math.stackexchange.com/…. It may be wise to review the lot of them to try and figure what should stay, what should go, or what may simply just be missing the requisite tag. – Grace Note Sep 21 '11 at 15:47
• @Grace: most are just missing the (soft-question) tag; a few are (big-list) style (reference-request)s. I actually looked at it immediately after you showed me the syntax for the search. I'd rather not bump those questions to the front page if I don't have to. – Willie Wong Sep 21 '11 at 15:51
• @Grace The search you did above returns 0 results, not 164 when I run it. – Bill Dubuque Sep 21 '11 at 16:19
• @Bill Ah, the square brackets in the parentheses broke it. I've revised the comment, it should work now. – Grace Note Sep 21 '11 at 17:13
• Dear Willie, With regard to the sentence beginning "With that said", I don't think that this question should have been made CW. It is a reasonable question, with a more-or-less definitive answer. Regards, – Matt E Sep 21 '11 at 19:07
• @Matt Could I convince you to post that viewpoint, and its reasoning, as an answer rather than having it tucked and hidden here in comments? – Grace Note Sep 21 '11 at 19:21
• @Matt Yes, please do post an answer. It is important that those with crucial experience do speak up on such matters. – Bill Dubuque Sep 21 '11 at 19:38
• It's obvious, at least in retrospect, that this question should not have been made CW. However, as they say in chess, even a master makes a blunder now and then. (Or, as they say in the classics, even the great Homer nodded now and then.) – Mike Jones Sep 24 '11 at 21:55