Bill Dubuque raised an excellent point here: Coping with *abstract* duplicate questions.

I suggest we use this question as a list of the generalized questions we create.

I suggest we categorize these abstract duplicates based on topic (please edit the question). Also please feel free to suggest a better way to list these.

Also, as per Jeff's recommendation, please tag these questions as .






Solving $x^x=y$ for $x$: Is $x^x=y$ solvable for $x$?

What is the value of $0^0$? Zero to the zero power – is $0^0=1$?

Functional equations

$f(x+y)=f(x)f(y)$: Is there a name for function with the exponential property $f(x+y)=f(x) \cdot f(y)$?

Graph theory

How to tell whether two graphs are isomorphic?

Group theory

For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?

Linear algebra


Number Theory


Sequences/Series (also summation )

Elementary set theory

Set theory




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    Shouldn't the questions be "answers" rather than edits to the question? – Arturo Magidin Mar 31 '11 at 18:27
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    @Arturo: Yes, we could have one answer per category. Having one question per answer might not be that good. The intent was to keep the list in one place so that we can browse through easily. – Aryabhata Mar 31 '11 at 18:30
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    @Moron: Yes, I understand; but (i) we probably don't want this question to keep popping up as "unanswered". And (ii) I think if we had one answer per category (or per tag) and have people "add it to the list" there it would make more sense. Right now the question is fine, but if this keeps up, the question itself will grow too lengthy to be manageable, I think. – Arturo Magidin Mar 31 '11 at 18:32
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    @Arturo: I think having this question pop up periodically is probably a good thing :-) I do agree with one tag answer thing. If enough people upvote your comment, I will make the edits :-) – Aryabhata Mar 31 '11 at 18:37
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    @Arturo: I think that questions from the unanswered list only get bumped if they have an answer (necessarily none accepted or with positive vote count). (If I'm wrong, will someone please inform me?) But I agree with (ii). – Jonas Meyer Mar 31 '11 at 18:44
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    @Isaac: But that might lengthen the list by a large amount. I mean both the questions in the calculus tag have other tags, namely "Integral" and "Limit," but I don't think it is a good idea to create separate categories and put them in those categories. That wouldn't be a useful addition. The geometric series is definitely in the series category, why does it need to be in algebra/pre-calculus as well? Tagging the question as such is of course a good idea. Then searching the FAQ tag on the main site is very easy. But in this list? I don't understand the need. – Eric Naslund Mar 31 '11 at 20:04
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    Question: Should questions such as "Why is $0.999..=1?$" "Why is $0^0=1$? and "Why does $0!=1$" be added to this list? Should we make one question dealing with all of them at once? I mean they are asked frequently enough, occasionally with slight variations, but are definitely not "abstract generalizations." Thoughts? How could one question be added that deals with all of these type of things at once? – Eric Naslund Mar 31 '11 at 20:35
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    @Jeff Atwood: I think it'd be better for each tagged subject to have a corresponding meta thread of faqs, abstract duplicates, etc. These could be displayed to low-rep users when they add a tag to a question. Better we could force them to choose a subject/tag before composing a question, so they see the subject-specific faqs first. This would go a long way towards removing the noise/overhead generated by duplicate questions (a big problem for a general-level math forum since exercises are often tweaked year-after-year to eliminate copying - yielding abstract, not exact, duplicates). – Number Apr 8 '11 at 20:19
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    @Arturo: I am waiting for 2 more upvotes to your comment :-) – Aryabhata Apr 8 '11 at 20:49
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    I don't understand why geometric series are under two categories. – Glen Wheeler Apr 17 '11 at 19:25
  • 3… should be added, as questions about $\zeta(2)$ arise frequently. – Asaf Karagila Apr 20 '11 at 16:02
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    Maybe we should add this to the list (at least until this silliness dies down and people move on to other things)? – J. M. is not a mathematician Apr 29 '11 at 17:52
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    May be this and this should be brought under the common umbrella of obvious consequences of the binomial formula? – Jyrki Lahtonen Sep 27 '11 at 10:23
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    Hmm, I actually think it's a good thing that this "question" has no upvoted answers (and to that effect, please don't upvote any!). The bot will bump it up periodically, and we always get a reminder of these dupes. – J. M. is not a mathematician Dec 19 '11 at 0:28
  • 2 Please don't forget to edit the question 1) to include the full general problem. 2) state that it is being repurposed (see other such questions from list above for a template which you can cut and paste) 3) and tag it as (faq). – Aryabhata Apr 20 '12 at 1:22

Burnside lemma and Pólya enumeration theorem examples

Observe that the convention at the OEIS is that the term necklace refers to the slots being arranged around a circle with rotational symmetry acting on them. Similarly the term bracelet indicates reflections acting on the slots in addition to rotations. This is the difference between the cyclic group $C_n$ acting on $n$ elements (necklace) and the dihedral group $D_n$ on $n$ elements (bracelet).

symmetries of polyhedra

enumerating types of graphs

number theory and algebra

power group enumeration

necklaces and bracelets


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    Let's try to keep these in order by post ID number so that it is easy to avoid duplicates. – MJD Apr 8 '14 at 2:39
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    How would I create a tag "Polya/Burnside" on MSE and if possible re-tag these questions automatically? – Marko Riedel Apr 28 '14 at 23:26
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    @MarkoRiedel Tags are created simply by adding the new tag to a question. When creating tag, it is good to write also a tag-wiki/tag-excerpt for the new tag. It's up to you whether you discuss creating the new tag on meta first, or whether you create tag without such a discussion. But I think that it is a good thing that those questions will be bumped when retagged - other users will be alerted about the new tag by this and if they disagree, they can react on meta. – Martin Sleziak May 6 '14 at 8:07
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    This is one topic (Polya-Burnside) rather than several. The questions on coloring cubes and counting necklaces get asked all the time over and over again. That's why MJD suggested we make this list. – Marko Riedel Jun 28 '14 at 13:53

More for my own sake than anything else. Integration duplicates tend to be quite hard to find due to the large amount of symbols in titles. Here is a short list of some famous integrals that pop up periodically


There ought to be an entry for the / classic:

$$\lim_{n\to\infty} \left(1+\frac xn\right)^n = \exp x$$

I found these posts on it so far:

which I've ordered from most to least suited for status (after a suitable amount of editing). There are probably more, but I couldn't find them by searching the site.

(I've posted this answer because it is not obvious which one of the above should get status.)

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    You can add it yourself. Please feel free to do so. Pick one as the representative, and tag that as FAQ. I also downvoted this answer so that this question is periodically bumped up (no answer with > 0 votes). – Aryabhata Jan 7 '14 at 23:07

The identity $$ \sum_{k=0}^{K}\binom{n+k}{n}=\binom{n+K+1}{n+1} $$ is popping out in many, too many, recent questions. I think it is better to add this question (or this one, a little better received, even if it doesn't have an accepted answer) as a reference for future questions on the same topic.

As a reference for the convolution of central binomial coefficients: $$ \sum_{k=0}^{n}\binom{2k}{k}\binom{2n-2k}{n-k}=4^n $$ I would point at Phira's answer to this question.

The following special case of Vandermonde's convolution: $$\sum_{k=0}^{n}\binom{n}{k}^2 = \binom{2n}{n}$$ also appears very often. I'd redirect to this question.

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