The epsilon-delta tag is used for questions about limits and continuity which use the $\varepsilon$-$\delta$ definition of such concepts. However, it is sometimes also used for a slightly different subject, namely the $\varepsilon$-$N$ definition of limit of a sequence, as it happened with this question. In my opinion, this is a reasonable option and I propose that the information concerning that tag asserts that it can be used for that purpose. I would like to know what the other members of this community think about that.
I hope I’m doing this correctly; I don’t respond on Meta very often other than voting.
I think this is a great extension of the tag. I also would like to say that if the description of the tag has been edited to encompass “limits . . . of sequences,” then the tag itself should reflect this. I propose it be changed to
epsilon-delta/epsilon-N or something similar. This would also encourage people to use the tag for sequences more. For example, I just asked a question to which this new tag is highly relevant.