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At the moment, there are two tags which are related to the number $e$.

The has been synonym of exponential function for a long time.1 A newer tag called was created in January 2019.

Question. Should there be a separate tag for Euler's number $e$? Or is it better to have both and as synonyms of ?

A few comments about this.

  • I think that the situation where and are handled differently is not ideal. Maybe I am missing a reason why these two tags should be treated differently, but my natural instinct is that the two tags that denote the same thing should behave consistently (and one of them should be a synonym of the other one).
  • If the consensus is that the tag (or tags) for Euler's number should not be synonym of , there might be situations when it is unclear which of these tag to use. (Whether to use only or only . Or whether both of them should be used. To give at least one example, there are many questions about limits of the form similar $\lim\limits_{n\to\infty} \left(\frac{2n-5}{3n+1}\right)^n$, where the result is typically $e^C$ for some constant $C$ which has to be determined. Such question is clearly related at least a bit both to Euler's number and to exponential function. What tags would be used in such questions. Certainly there are also other examples where it would be unclear which of the tags is preferable.)
  • In the past there was only the tag which was automatically remapped to . This means that some users used the tag since the question was related to Euler's number, and the software changed it to . If the tags should be kept separate, then we should have a look at older questions and retag some questions where or is more suitable than .

EDIT: Looking at the comments, maybe I should clarify that I do not advocate for either of the two possibilities - this is more a call for a discussion and an attempt to find out how the users feel about this. However, as I said above, I do think that the tags and should be treated in the same way; the current situation seems inconsistent to me.

I will explicitly say that I am aware that there exists a tag management thread. I have posted this as a separate question, since I expect that there might be a longer discussion around these tags - and it would be difficult to have such discussion in comments under an answer in the tag management thread.

1There are several things which are called Euler's number. However, using this name for the constant $e\approx 2.71828$ is the most frequent and this is also what is indicated in the tag-info for (eulers-number).

2Being a synonym means in practice that if somebody enter as one of the tags, it is changed by the software to when the question is submitted. Both based on this SEDE query and the list of tag synonyms, I get that the synonym was created in January 2013.

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  • $\begingroup$ I was reminded of the problem with the tags for $e$ because at the moment there are two tags for Eulers' constant $\gamma$, one of them created today. Of course, this is a completely separate issue, since $e$ and $\gamma$ are two different constant. (And it is much easier to solve - either by creating the synonym or by removal of one of the tags.) $\endgroup$ – Martin Sleziak Feb 4 '20 at 8:49
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    $\begingroup$ I upvoted this post because of its quality, but I don't feel like there should necessarily be two separate tags. Not saying that the number $e$ isn't important in itself, but it's not likely to generate many questions apart from a few philosophical ones and a few ways to compute/approximate it. $\endgroup$ – Arnaud Mortier Feb 4 '20 at 9:06
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    $\begingroup$ Also, instead of $e\approx 2.71828$ I would write $e\approx 2.718281828$ just for the sake of it :-) $\endgroup$ – Arnaud Mortier Feb 4 '20 at 9:08
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I have no strong feelings about whether there should be a separate tag about the number 'e'. (It was convenient way back when, when most of the questions tagged 'e' is about the function $e^x$.)

I do think that the names can be confusing, whenever something has to do with Euler.

Maybe, if we want to rename:

  • For the number '$e$', name the tag 'eulers-number-e', and make 'base-of-natural-log' and 'base-of-natural-exp' synonyms to it.
  • For the number '$\gamma$', name the tag 'euler-mascheroni-constant-gamma' (still fits under the 35 character limit.)
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There is an obvious connection between $e$ and the exponential function $e^x$ (in the strict sense - could also be $a^x$). But the one is a number, important enough to deserve specific study, and the other a function. There must be a substantial corpus on both topics.

I would vote for a tag "$e$", separate from "exponential-function", having the synonym "Euler's-number", as the latter is a little less popular.

As for the possible confusion between $e$ and $\gamma$, it seems that usage differentiates Euler's number and Euler's constant, or better, Euler-Mascheroni's constant.

On second thoughts, the description of the "exponential-function" makes no reference to the constant $e$ at all ! We are in the case of $a^x$.

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