Definition talk:Summation

I sense some trouble here. I have added a handwavery template on a proof yesterday because it used ellipsis for summation. Now, I find that our very definition of summation has the same problem. We really ought to give an inductive definition (perhaps by well-founded recursion on the finite subsets of $\N$) as a precise definition to fall back on.

There are some nasty theorems waiting out there once we're done defining (for example that the sum over a finite set $I$ is well-defined, as in independent of the bijection $I \to n$ chosen). I'll put it on my to-do list for when I get back from my vacation (which should be around July 22). &mdash; Lord_Farin (talk) 13:57, 3 July 2013 (UTC)


 * I have started the nasty work. I'm currently using elements of an abelian group as values, but this can easily be replaced by a more general thing, if needed. That's not my main concern at this point. --barto (talk) 05:49, 19 October 2017 (EDT)


 * Can we keep the specific-to-numbers stuff? --prime mover (talk) 06:54, 19 October 2017 (EDT)


 * Seconded. Tasty genericity should not alienate the high school student looking a bit beyond their textbook. &mdash; Lord_Farin (talk) 12:27, 19 October 2017 (EDT)


 * You mean for example using $\R$ instead of any abelian group? Fine for me, but it will imply that we will have to duplicate all those proofs for abelian groups. But okay, it is probably worth the effort making a distinction. --barto (talk) 12:57, 19 October 2017 (EDT)