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Many questions are about both and , e.g. determining whether a number is rational or irrational. Some of them are tagged , some and some have both:

Simply merging them into something like would be a bit crude, but also incorrect as there are questions focussing on only one of them; e.g.:

  • this one asks to find rational solutions to an equation and thus has hardly anything to do with irrational numbers.
  • this typical question is best tagged with only.
    If the OP would have asked if anything changes when $\alpha$ is rational, this would have been an example of a question to be tagged with both.

We have to do something about this issue, but what?

Proposal: Introduce a tag for questions about determining whether a number is rational, and related problems such as determining whether $(\sqrt2+\sqrt3)^{200}$ is integer or e.g. this question.
Why? Most or questions seem to be about determining whether a certain number is rational. It would be great to have them separated from other and questions. Filtering these with a new tag copes with the major part of the questions having both tags.

I think by doing this the two tags become almost separated (i.e. few questions in their intersection).

What do you think?


Some practical issues with the proposed solution

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    $\begingroup$ If you take the union of the tags, wouldn't it be more appropriate to call it real-numbers? :-P $\endgroup$ – Asaf Karagila Apr 6 '15 at 10:42
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    $\begingroup$ Given the edit, I'm in support of the request, I think, but before it can be put into action we need a better (read: less ambiguous) name to replace rationals-irrationals. $\endgroup$ – Lord_Farin Apr 6 '15 at 21:10
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    $\begingroup$ Perhaps (rationality)? $\endgroup$ – Regret Apr 7 '15 at 0:26
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    $\begingroup$ Removing the word "numbers" introduces ambiguity, IMO. The adjective "rational" is used for a lot of things... $\endgroup$ – Najib Idrissi Apr 7 '15 at 11:54
  • $\begingroup$ Perhaps rationality-test would be clearer? $\endgroup$ – punctured dusk Apr 7 '15 at 12:51
  • $\begingroup$ I went trough the 150 most recent irrational-numbers questions. 87 of them would fall under the new tag. I can make a list of them somewhere if that would be useful (I guess so). I did the same for rational-numbers (but I didn't go that far yet) and at first sight it seems only a few of them fall under the new tag. $\endgroup$ – punctured dusk Apr 7 '15 at 12:56
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    $\begingroup$ @barto rationality-test seems reasonable; perhaps rationality-testing would be more in line with existing tags. Naturally, a synonym irrationality-testing would be in order. $\endgroup$ – Lord_Farin Apr 7 '15 at 15:41
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    $\begingroup$ If we really want 'number' in it, we could make it rational-number-testing (23 characters, so there's room to add 'ir'). I don't find that necessary but it will make the tag easier to find among tag suggestions. $\endgroup$ – punctured dusk Apr 7 '15 at 16:18
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    $\begingroup$ Not sure if we want transcendence-testing too. $\endgroup$ – punctured dusk Apr 9 '15 at 6:53
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    $\begingroup$ So basically you seek a rational way to tag these questions? :) Sorry, just had to get that out of my system. $\endgroup$ – Deepak Apr 10 '15 at 13:02
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As there seems to be support for the new tag, let's try to write and rewrite the tag excerpts:

excerpt
For questions on determining whether a number is rational, and related problems. If applicable, use this tag instead of (rational-numbers) and (irrational-numbers). Consider adding a tag (radicals) or (logarithms), depending on what the question is about.

excerpt
Old excerpt: For questions on rational numbers, numbers that can be expressed as the quotient or fraction $\frac pq$ of two integers.
New: Questions about numbers expressible as the quotient of two integers. For questions on determining whether a number is rational, use the (rationality-testing) tag instead.

excerpt
Old: Numbers not expressible as a ratio of two integers. Examples: $\sqrt{2},\phi,e,\pi,\zeta(3)$. Some of them are algebraic ($\sqrt{2},\phi$) and some transcendental ($e,\pi$).
New: Questions about numbers not expressible as the quotient of two integers. For questions on determining whether a number is irrational, use the (rationality-testing) tag instead.

Feel free to discuss and edit.

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    $\begingroup$ I propose to drop the examples in the irrational-numbers wiki. Maybe we could just add "Some of them are algebraic and some are transcendental." $\endgroup$ – punctured dusk Apr 9 '15 at 6:44
  • $\begingroup$ I was not sure where to put "Some of them are algebraic and some are transcendental." so I have (temporarily) removed it. $\endgroup$ – punctured dusk Apr 10 '15 at 12:09
  • $\begingroup$ User Jean-Claude Arbaut had some remarks, see here and here. $\endgroup$ – punctured dusk Apr 11 '15 at 8:57

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