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)