Talk:Iterated binary operation

I removed the use of interval notation for indices, since they are varying over integers and not reals. Additionally, I moved the mention of index ranges out of the definitions of the functions and into the notation to make the function definitions more clearly about sequences.NoJoy (talk) 15:36, 30 April 2008 (UTC)

Infinite iterations
Delaszk removed the restriction that the iterations be finite, with the edit comment "no need for iteration to be finite"; and added some references to infinite iteration. I do not quite agree. The article treats general binary poerations (magma operations, if you wish); and in general, the results of infinite operations are not defined. Now, the iterations here are expressed in terms of actual function valuess (with the exception of someone mentioning binary trees, which however still should be labelled with actual elements). You may always define an infinite iterative expression formally, and you might perform some operations on the expressions formally; but this is very far from both the iterated operations as covered by this article, and also from those actual examples of limiting infinite iterations to which Delaszk added references.

I think the infinite iterations should be treated on the same level as the empty ones are: Under some conditions, it is possible to put a meaningful definition to them. I'll make a try in this direction, which includes reverting one of Delaszk's edit. Change back, i fyou don't like it! JoergenB (talk) 20:21, 21 August 2008 (UTC)

Substack
For the last equation in the article, $$\sum_{\begin{array}{c} i \in 2\mathbb{N} \\ i \leq n \end{array}}$$, I tried to get the two subscripts closer together, but I'm not sure if it's possible. Wikipedia doesn't accept the "\substack" command in mode, so I had to use an array instead ("\sum_{\begin{array}..\end{array}}"), which is why the subscripts are so far apart. I couldn't find any way to modify row spacing in arrays, and wikipedia also doesn't accept "\vspace{-0.1cm}" etc., so that won't work. If anybody happens to know how to emulate "\substack" with wikipedia formatting, I'd be grateful if you could edit the article.

MacLane reference
The article references the first edition of MacLane. Could someone update the reference for the second edition? (I have the second edition, but page 142 there does not talk about iterated binary operations.) Thatsme314 (talk) 02:29, 2 May 2022 (UTC)

Names of iterated "and" and "or"
Is it worth mentioning (and showing) that these operations are often referred to as "all" and "any" in programming language and everyday speech? Even though the names don't exactly match the form of "sum" and "product". Elias (talk) 06:46, 5 October 2022 (UTC)