Should there be a separate tag for Euler's number $e$?

Question

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

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

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

A few comments about this.

• I think that the situation where e and eulers-number 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 exponential-function, there might be situations when it is unclear which of these tag to use. (Whether to use only eulers-number or only exponential-function. 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 e which was automatically remapped to exponential-function. This means that some users used the tag e since the question was related to Euler's number, and the software changed it to exponential-function. If the tags should be kept separate, then we should have a look at older questions and retag some questions where eulers-number or e is more suitable than exponential-function.

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 e and eulers-number 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 e as one of the tags, it is changed by the software to exponential-function 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.

Answer 1

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.)

Answer 2

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.

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