Many questions are about both rational-numbers and irrational-numbers, e.g. determining whether a number is rational or irrational. Some of them are tagged rational-numbers, some irrational-numbers and some have both:
- Both tags (104)
- Only (rational-numbers) but contain 'irrational' (32)
- Only (irrational-numbers) but contain 'rational' (211)
Simply merging them into something like rationals-irrationals 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 irrational-numbers 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 rationality-testing 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 rational-numbers or irrational-numbers questions seem to be about determining whether a certain number is rational. It would be great to have them separated from other rational-numbers and irrational-numbers 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
Executing this plan would involve adding 'For questions about determining whether a certain number is rational, use the (rationality-testing) tag instead.' to the tag descriptions.
Any better names for the new tag? rationals-irrationals has been replaced by rationality-testing in this post.
It would involve much re-tagging, unless we can work around it in a clever way: as most questions would fit in rationality-testing, we might: (I'm not sure if this is possible)
- (Temporarily) merge rational-numbers and irrational-numbers into rationality-testing
- Re-tag the questions that do not fit in rationality-testing (which I think aren't many) with rational-numbers and irrational-numbers