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I would like to get some reactions to the idea of merging several tags under an umbrella "infinitesimal". The motivation is that the individual tags each have few questions, and the existence of separate tags makes it more difficult for a user to become aware of other related questions. The tags involved are , , , and . Any comments?

Note 1. Following suggestion by @quid, I propose "to make it the master tag in tag synonym pairs without merging. Then all current tagging would stay as is, and only all future instances of the minor tag would be auto-re-tagged to the master." Actually I don't fully understand the technicalities of this proposal but I think it would be better than deleting the tag.

Note 2. The tag "non-archimedean fields" actually includes two distinct topics itself, namely ordered nonarchimedean fields such as Levi-Civita fields, on the one hand, and ultrametrics (e.g. p-adics), on the other.

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    $\begingroup$ I think at least the two "surreal" ones should likely become one. For the rest, I am generally in favor of having larger tags, but feel not well-placed to comment in detail on this particular case. $\endgroup$
    – user9072
    Commented Dec 17, 2015 at 10:03
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    $\begingroup$ Let me remind that there is a central page devoted to such matters: meta.mathoverflow.net/questions/862/help-cleanup-tags $\endgroup$
    – Emil Jeřábek
    Commented Dec 17, 2015 at 12:51
  • $\begingroup$ @EmilJeřábek, thanks, I didn't know. Should I copy my question there? $\endgroup$
    – Mikhail Katz
    Commented Dec 17, 2015 at 12:58
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    $\begingroup$ I oppose combining nonstandard-analysis, surreal-numbers. $\endgroup$
    – Gerald Edgar
    Commented Dec 17, 2015 at 14:00
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    $\begingroup$ I agree with the merge of the surreal ones. I do not favor merging any others listed. Bear in mind that infinitesimals cover a very wide range which overlaps among other things NSA, synthetic differential geometry, and valuation rings. But it would be wrong I think to merge any of these into 'infinitesimals', and of course wrong to merge infinitesimals into any of these three. $\endgroup$
    – Todd Trimble
    Commented Dec 17, 2015 at 14:56
  • $\begingroup$ @GeraldEdgar why? $\endgroup$
    – user9072
    Commented Dec 17, 2015 at 15:56
  • $\begingroup$ @ToddTrimble perhaps the tag "infinitesimals" is too unspecific then (and maybe should be dismantled)? This might explain why it is hardly used (seven questions over close to three years). $\endgroup$
    – user9072
    Commented Dec 17, 2015 at 15:58
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    $\begingroup$ @quid Yes, I was beginning to think that as well. $\endgroup$
    – Todd Trimble
    Commented Dec 17, 2015 at 16:04
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    $\begingroup$ @quid ... nonstandard-analysis, surreal-numbers are different topics. Another relative is non-archimedean-fields, which perhaps includes both of those. But I do not favor merging it either. $\endgroup$
    – Gerald Edgar
    Commented Dec 17, 2015 at 16:12
  • $\begingroup$ Is there a possibility of making "infinitesimal" an umbrella tag for these others instead of merging? $\endgroup$
    – Mikhail Katz
    Commented Dec 17, 2015 at 18:35
  • $\begingroup$ There is no technical notion of an umbrella tag. The closest one could achieve on a technical/automatic level is to make it the master tag in tag synonym pairs without merging. Then all current tagging would stay as is, and only all future instances of the minor tag would be auto-re-tagged to the master. On a non-technical level one can of course add the tag manually in addition and can write in the respective tag-wikis that this should be done. $\endgroup$
    – user9072
    Commented Dec 17, 2015 at 18:44
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    $\begingroup$ @GeraldEdgar well, non-commutative rings and lattice theory are also different topics, still they fall both under ra.rings-and-algebras. Now they also have separate tags, but just to highlight that being "different topics" is not a reason for there not being a common tag. There is an abundance of tags that group together "different topics" that may or may not have individual tags too. But, I understand it is sometimes difficult to pin down why one holds one or another opinion on such matters. So, thanks for the attempt at an explication. $\endgroup$
    – user9072
    Commented Dec 17, 2015 at 18:50

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I think of surreal numbers, infinitesimals and nonstandard analysis and three separate, distinct (although sometimes overlapping) areas, and I don't think they should be merged. They are of course often related, but it is easy to imagine questions in each one that do not involve the others.

Meanwhile, I don't mind merging the two surreals tags. I guess "surreal analysis" refers to analysis on the surreal numbers, and in this case, I'm not so sure that we need it as a separate tag. So it would be fine with me for "surreal-analysis" to be absorbed by "surreal-numbers". But I am willing to be over-ruled on that if the experts on surreal analysis think that this subspeciality really needs a separate tag for this.

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    $\begingroup$ I actually don't think of infinitesimals as an "area" at all, but rather a catch-all idea with variegated precisifications. (It often has something to do with ordered algebraic structures, but I think order might be optional, e.g., in algebraic geometry one often thinks of nilpotent elements as being infinitesimal.) Not being a precise term, I'm coming to think its use as a tag should be deprecated. $\endgroup$
    – Todd Trimble
    Commented Dec 18, 2015 at 2:48
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    $\begingroup$ Yes, I'm inclined to agree with you. My main point is that that tag should not be merged or absorbed by any of the others. I don't see it as harmful to keep it, even though I don't think it is a very useful tag. My broader opinion is that extremely specific tags are not actually useful. $\endgroup$
    – Joel David Hamkins
    Commented Dec 18, 2015 at 2:53

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