> To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots
What's so pernicious about them? I don't see it. It seems like a clear and intuitive way to communicate a sequence to me. I even wrote a little range generator in JS to explore parsing declarations like that. https://github.com/chrisbroski/iterize It seems to work fine.
2,3,4,12 is also a "subsequence of natural numbers", but probably not what was meant by 2,3,...,12. You might counter that ... means the complete subsequence, but what do you mean by "complete"?
If I write 2,4,6,8,...,24, you probably want the ... to mean 10,12,14,...[1], not 9,10,11,12,...
Basically by the time you make ... precise, you are better off just writing the mathematical notation.
[1] See what I did there? ;)
For example, does 3, 5, ... 11 mean the odd numbers between 3 and 11 inclusive, or the primes between 3 and 11 inclusive?
Just decide on some rule for how decide and let people make their own standard if they don't like it.