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Why was this question actually closed? Those who closed it chose not a real question from the admittedly rather limited menu, but in fact the question is perfectly clear:

Let $G$ be a group, and consider $H=\{g\in G:|g|<\infty\}$. Prove that $H$ is a subgroup.

That $|g|$ means the order of $g$ here is obvious, and the notation is certainly not the querent’s invention: I’ve seen it in a number of places.

The fact that the assertion is false does not make the question hard to understand, and indeed a perfectly good answer was given. The fact that the question was phrased as a command, in a manner that some find displeasing, also does not make it hard to understand. So why was it closed?

Added: Here is a direct link to the question. It is possible that the querent miscopied the question, omitting a hypothesis, but it’s by no means certain, even if the question is homework: it could be a mistake on the instructor’s part, or it could be a deliberately misleading question. In any case, allowing a new user only two hours to clear things up seems more than a bit unfriendly.

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  • $\begingroup$ @Martin: Thanks, Martin; I’m not very familiar with the meta tags. $\endgroup$ – Brian M. Scott Oct 22 '12 at 12:22
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    $\begingroup$ Further, I think that the 5 downvotes are uncalled for. Probably the OP simply omitted an abelian hypothesis (which may have been implicit in their context). But, perhaps before they noticed this, their post was closed and heavily downvoted. That's not very friendly behavior, esp. towards a new user (who joined 6 days ago). $\endgroup$ – Bill Dubuque Oct 22 '12 at 17:15
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For what it is worth: probably due in large part to the posting of this very meta question, the original question under discussion has since been re-opened by the votes of five community members.


(I am writing this as there is no real correct answer to the question posted here on meta; and accepting this answer could be a way to indicate that the issue is "resolved".)

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    $\begingroup$ Thanks, Willie; I was trying to figure out a way to do that. $\endgroup$ – Brian M. Scott Oct 23 '12 at 8:11
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Before the "close" button comes the "edit" button.

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    $\begingroup$ Actually, before the close button comes the flag button. $\endgroup$ – Asaf Karagila Oct 23 '12 at 2:47
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    $\begingroup$ @Asaf: Interesting, are we seeing a different interface? Mine says "share edit close flag". Or were you not being so literal? Or reading from the other direction? $\endgroup$ – Ilmari Karonen Oct 26 '12 at 14:32
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    $\begingroup$ @Ilmari: Hebrew is a right-to-left language, and as a native speaker I am always inclined to read from both direction. I was also pointing out the relativism of this post, which was my main point. $\endgroup$ – Asaf Karagila Oct 26 '12 at 14:36
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    $\begingroup$ @AsafKaragila This is cultural trolling! $\endgroup$ – Billy Rubina Nov 3 '12 at 20:30
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I voted to close because the question as written is unanswerable: you can't prove that statement because it's false. I'd be happy to vote to re-open if the OP rewrote the question in a way that's answerable. "How do you prove this false statement" is not a real question. "Is this statement true or false" is a real question, but more likely the OP just mis-stated the question.

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    $\begingroup$ The question is manifestly not unanswerable: a correct answer was given. The statement that you want to prove is false without some additional hypothesis, e.g., that $G$ is Abelian, and here’s a counterexample in the general case is a perfectly good answer. $\endgroup$ – Brian M. Scott Oct 22 '12 at 11:31
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    $\begingroup$ @BrianM.Scott: Fair enough. I was just explaining my reasoning since you'd ask what the "real reason" was. I didn't actually expect this to be a controversial close because it seemed to me that it was clearly not a real question. $\endgroup$ – Noah Snyder Oct 22 '12 at 11:41
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    $\begingroup$ I can't say I am too happy about "Prove this false statement", but sometimes, having the erroneous statement is the main obstruction, and by definition, people are not aware that they have an erroneous statement, so it seems extremely unhelpful and unuseful to close these questions as long as they are easily answerable. $\endgroup$ – Phira Oct 22 '12 at 11:41
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    $\begingroup$ And I’m happy to get the explanation even if I don’t agree with the reasoning. I’m just completely gob-smacked that anyone wouldn’t consider it a real question! $\endgroup$ – Brian M. Scott Oct 22 '12 at 11:45
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    $\begingroup$ @Phira: There were already comments and an answer explaining that the statement was incorrect. To my mind this means close, wait for the OP to correct their statement, and then answer the question they actually meant to ask. There's no point gathering more answers when the (non-)question stated is not the question the OP actually meant to ask. $\endgroup$ – Noah Snyder Oct 22 '12 at 11:46
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    $\begingroup$ Since 4 other people had came to the same conclusion with no clear disagreement in comments, I didn't see a reason to guess that my reasoning was unusual. $\endgroup$ – Noah Snyder Oct 22 '12 at 11:49
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    $\begingroup$ @NoahSnyder I understand your reasons for closing, I just disagree that the question the OP meant to ask is the corrected statement. The question the OP meant to ask is more like "Why can't I prove this statement?" and the answer "Possibly, you forgot that the group is abelian." might be exactly the answer to the real question for them. $\endgroup$ – Phira Oct 22 '12 at 11:50
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    $\begingroup$ Noah, I think one of the many differences between this site and MathOverflow is that on MO questioners (querents?) are expected to give well-formed questions and if they don't they are sent packing with orders not to come back until they can do better. Here we tend to encourage people to improve their questions and try to give them the time to do it, and close questions only if, over a period of days, they refuse to or demonstrate inability to make improvements. Tell the person what's wrong with the question, then give the person a decent chance to act on the advice. $\endgroup$ – Gerry Myerson Oct 22 '12 at 12:21
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    $\begingroup$ I'll admit I failed to check how recently the question had been asked, which I usually do and should have done. $\endgroup$ – Noah Snyder Oct 22 '12 at 12:38
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    $\begingroup$ Here is an example of an unanswerable question with an answer explaining why it can't be answered: math.stackexchange.com/questions/217275/… $\endgroup$ – Michael Greinecker Oct 22 '12 at 13:22
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    $\begingroup$ By the way, Brian asked why the question was closed, and this answer tells us why Noah voted to close. I consider that to be a useful answer, so I voted it up. I've already indicated that I disapprove of what Noah did on the main site, but I approve of what Noah has done here. I wonder whether those who have voted down are not confusing the two matters. $\endgroup$ – Gerry Myerson Oct 22 '12 at 22:40
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    $\begingroup$ @Gerry Imo the most important use of votes on meta is to convey opinion on issues affecting the main site (vs. "usefulness of an answer"). This is best measured by votes on answers, not on comments, since comments cannot be downvoted. So I don't agree that one should vote as you propose. Originally this answer had a vote total of -3 or -4, which probably indicated disagreement with the expressed viewpoint and closing action. Then it shot up to +1, probably due to votes like yours (and perhaps sympathy upvotes). Due to that, the votes are now useless for measuring anything. $\endgroup$ – Bill Dubuque Oct 23 '12 at 3:36
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    $\begingroup$ Part of the confusion with voting here is the phrasing of the question. If the question had been "should this be opened or closed" then certainly the correct behavior is to downvote an answer arguing that it be closed if you disagree with the reasoning. But the phrasing of this question was "what's the real reason" and it's hard to disagree that this was at least one of the five real reasons that someone voted to close. $\endgroup$ – Noah Snyder Oct 23 '12 at 8:47
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    $\begingroup$ At any rate, it's clear to me from the comments and votes on comments that the vast majority disagreed with this vote, and a few upvotes on the answer isn't going to suddenly make me think I got this one right. $\endgroup$ – Noah Snyder Oct 23 '12 at 8:48
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    $\begingroup$ @Noah Kudos to you for explaining your thoughts. I wish the other voters did likewise. I think that much of the friction on meta is due to misunderstanding of others positions. The more folks are willing to explain themselves, the more we can understand each other and hope to reach compromises that will keep the main site running smoothly. $\endgroup$ – Bill Dubuque Oct 24 '12 at 20:52

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