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On browsing a little through MSE, I saw that the rationality or irrationality of some numbers are scattered through a lot of differently phrased questions. In the internet, some numbers are not easy to find to being rational/irrational. For instance, a simple search on the state of rationality/irrationality of $2^{\pi}$ is not an easy task.

I thought of opening a community-wiki question asking for a list of numbers which we know or don't know to be rational/irrational/transcendental.

What do you think?

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    $\begingroup$ (Maybe) related: Would “organizer posts” be useful/welcome here? $\endgroup$ – Martin Sleziak Dec 28 '15 at 7:11
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    $\begingroup$ @MartinSleziak I think that is entirely related. Considering the positive response that received, I think I'll open the CW tomorrow and see what happens. $\endgroup$ – Aloizio Macedo Dec 29 '15 at 6:50
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    $\begingroup$ This seems like a job for wikipedia, not us. $\endgroup$ – PyRulez Dec 31 '15 at 23:11
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    $\begingroup$ In fact, if you want to help, see List of numbers. $\endgroup$ – PyRulez Dec 31 '15 at 23:12
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Tags serve the purpose of grouping things like this. In particular, we have the rationality-testing tag for this very purpose. A question like "which numbers are known to be irrational/rational?" would certainly be too broad, since there are uncountably many answers to the question, but most of them would be uninteresting (either as part of a general theory that can't be explained in a short post or as unmotivated examples).

If one wishes to ask about the rationality of given numbers, one should ask a question about it. It is worthy of note that the answer to such questions is usually "we don't know, but probably irrational."

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    $\begingroup$ The existence of such a tag is a good argument against my proposal, but I have to say that your justification of it being "too broad" is a little... rhetorical. Nevertheless, your last phrase is the exact reason why I thought the idea would be helpful. Do we really want a scattered, convoluted collection of questions which are "Is it rational? - We don't know", or would gathering those in a single question be far more organized? It also seems to me that this is one of the purposes of a community-wiki. $\endgroup$ – Aloizio Macedo Dec 28 '15 at 3:43
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    $\begingroup$ From this post: meta.stackexchange.com/questions/11740/… "Why have Community Wiki posts? One of the goals of the website is to be a continually evolving source of good information. Community wiki posts help enhance the wiki aspect of the site." $\endgroup$ – Aloizio Macedo Dec 28 '15 at 3:43
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    $\begingroup$ @AloizioMacedo The questions wouldn't really be scattered if they're under a common tag, and I don't see the harm in having many questions on rationality (recalling that context is required of questions - so some motivation would be desired) - and in any case, "post the questions as answers on a single thread" is not a solution to "the questions usually don't have answers." If our site is to entertain a question at all, the machinery of the site is set up to have it exist as a question, not an answer. $\endgroup$ – Milo Brandt Dec 28 '15 at 4:21
  • $\begingroup$ Your last point is a good one, and I'll retract that part of the suggestion. Thanks for the insight. But I still disagree with the rest. For example, you didn't address my argument of "This is the point of Community Wiki posts". Also, note I'm not referring to problems about proving something is rational/irrational. I'm referring to actual curiosity/reference-like questions. For such, motivations usually are along the lines of "I was thinking... is it?". They don't come from a problem, or research, they (usually) spring to mind. Is that a proper content for a question, or a wiki? $\endgroup$ – Aloizio Macedo Dec 28 '15 at 4:57
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Admittedly, searching for "$2^\pi$" is next to impossible here. So go ahead and ask the question. If it is closed as a duplicate, you gain the link to the original question.

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    $\begingroup$ The meta-question asks if a list-question for a (comprehensive) list of such results is appropriate; the constant $2^{\pi}$ seems merely mentioned as example. It is not quite clear to me how, if at all, your post answers the question asked. Could you please clarify this. $\endgroup$ – quid Dec 28 '15 at 14:08
  • $\begingroup$ @quid Right, but we can't possibly have a comprehensive list of the irrationality or rationality of every real number that a person is likely to take an interest in. Any organizer post would only be able to cover a handful of basic constants and general forms (eg. $e^{1/n}$) which would be much easier to search for than the example $2^\pi$ seems to suggest. $\endgroup$ – Jack M Jan 4 '16 at 10:18
  • $\begingroup$ @JackM It is still not clear to me what the intent of this meta-answer is. Given the formulation "the original question" it seems to answer the question if one can ask the question if $2^{\pi}$ is irrational. This however is not what is asked for, whence my confusion. $\endgroup$ – quid Jan 4 '16 at 18:50
  • $\begingroup$ @quid The answer is also using $2^\pi$ as an example. The same advice would apply to any other constant. $\endgroup$ – Jack M Jan 4 '16 at 19:08
  • $\begingroup$ @JackM so you think the intent of this answer is to say: "Do not ask the general question you propose to ask. But feel free to ask a specific question about the constant you care about." $\endgroup$ – quid Jan 4 '16 at 19:18

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