# Talk:Addition

One of the basic principles of good illustration is to label things where appropriate.  But this article has two illustrations with the same unlabeled three colors. "Adding π2/6 and e using Dedekind cuts of rationals" --What is red, what is blue, and what is green?  I don't know how this article got nominated to be a good article, with problems like this. 37.99.82.253 (talk) 09:57, 25 April 2021 (UTC)

Three years on, and the illustrations are still mystifying.  Kdammers (talk) 18:28, 14 June 2024 (UTC)
@Kdammers: I have looked at the Dedekind cuts version of the diagram, and thought about it fot some time, and I absolutely cannot understand it at all, so, adding to that the two comments above from you and someone else, I have removed it. The Cauchy sequence version I can understand, so I've given it the benefit of the doubt and left it in place. However, I doubt that it would actually help anyone to understand the concept if they didn't already understand it, and I wouldn't quarrel with anyone who decided to remove that one too. JBW (talk) 21:02, 15 June 2024 (UTC)

Additional adding animals apparently include ocean-dwellers (https://www.uni-bonn.de/en/news/060-2022), but, behold, bees belong by other adders as well (according to https://theconversation.com/can-bees-do-maths-yes-new-research-shows-they-can-add-and-subtract-108074). Should these be added to animals adding section? Kdammers (talk) 16:58, 16 June 2024 (UTC)

This experiment showed that if you do many many training runs with bees where you show 2–3 colored shapes next to an entrance to a Y-shaped room with two further examples of several shapes, one side of which leads to sugar water, where the "correct" choice had 1 shape more than the original collection if the shapes were blue or 1 shape less than the original collection if the shapes were blue yellow, then the bees can eventually learn to get the answer "correct" about 2/3 of the time.
Concluding from this that bees can "perform basic maths" seems.... very liberal with definitions. To me personally this seems much closer to "rat memorizing a maze" than to a person or animal learning to add and subtract. I would skip mentioning this study here, but it might belong in some kind of article about bees' cognition and memory. –jacobolus (t) 19:35, 16 June 2024 (UTC)
@Jacobolus: One of the blues in your post should be a yellow. Also, unless I have misunderstood, your "2-3" shapes should be "1-5".
An interesting experiment. However, I agree that interpreting this experiment as showing that bees "can add and subtract" is being, as  Jacobolus pits it, "very liberal" in use of terms. I think the experiment could be taken as indicating that the bees have a rudimentary and very imperfect ability to distinguish between "greater" and "less", which I suppose could be described as performing very basic maths, but I think that's the absolute limit. JBW (talk) 22:42, 12 January 2025 (UTC)

This does not sound right. Should it rather be something like: "The real number 0 is defined as the Dedekind cut that separates the rational numbers into two parts: the negative rationals and the non-negative rationals" Merlin.anthwares (talk) 21:06, 12 January 2025 (UTC)

@Merlin.anthwares: Separating the rational numbers into two parts is an intuitive description of the idea behind what a Dedekind cut does, but the formal definition of a Dedekind cut is, as stated in the article, "a non-empty set of rationals that is closed downward and has no greatest element". Therefore the definition of the real number 0 as the set of negative rationals is correct, albeit unintuitive. JBW (talk) 21:31, 12 January 2025 (UTC)
Thank you for your explanation! Merlin.anthwares (talk) 23:21, 12 January 2025 (UTC)

@D.Lazard, can you explain what you mean by "I the line is broken, the resulting indentation would be incorrect"? On my phone it appears just fine. 
On the mobile app, if a formula is too long, it forces the whole article to scroll side-to-side rather than just the formula, making a very annoying reading experience. And on the mobile web interface, there is no way to scroll at all, so the formula just gets cut off with no way to see the rest. – Farkle Griffen (talk) 18:28, 30 March 2025 (UTC)

Normally, displayed formulas must be indented, and, if a formula is broken over two lines, the second line must be more indented. With your edit, the first line remains indented, but there is no indentation at all for the second line. So, your edit make things worse on many devices.
I tryed to limit the length of the lines by using the "align" latex environment, but one of the matrices alone has a width that exceeds the line length on mobiles in portrait mode (landscape mode is possibly a partial answer to your problem).
In view of the multiplicity of reading devices, the only reasonable solution seems a request to WP:Phabricator.
You may also ask to WT:WPM whether somebody has a better solution. D.Lazard (talk) 20:51, 30 March 2025 (UTC)
"With your edit, the first line remains indented, but there is no indentation at all for the second line". I don't know what you mean here... On my phone, after the break they appear on the same indent. I tried this on my computer too by limiting the width of my window and they also appear to be on the same indent. On larger screens there is no break displayed at all, so this only affects users who already have issues due to the length. If your issue is "if a formula is broken over two lines, the second line must be more indented", this seems extremely minor compared to the formula being cut off entirely. Slightly inconvenient indentation is certainly better than that.
"but one of the matrices alone has a width that exceeds the line length". They all seem to fit on my screen when breaks are put between each (though the largest one just barely). In any case, that's no reason to make the problem worse by lining up the equals signs, forcing them off the screen further. The breaking I used for the matricies looks fine on large screens and is more visible on smaller ones. What's the objection? – Farkle Griffen (talk) 21:16, 30 March 2025 (UTC)
@D.Lazard, please self-revert to allow users with smaller screens to read the article. – Farkle Griffen (talk) 21:20, 30 March 2025 (UTC)
Sorry, I misunderstood your above comment: it referred to section § Scientific notation and I answered about section § Matrices. For § Scientific notation, my edit summary said "Not a good way for allowing line breaks". This meant that there were better ways, and that I was not willing to spent time to apply them. Thanks to Jacobolus to have correctly fixed the format of this formula. D.Lazard (talk) 08:18, 31 March 2025 (UTC)
I'd like you to respond to my question about the matricies too: you say "So, your edit make things worse on many devices"; if my version only affects cases where the formula is already off the screen, how could it make it worse? It would only add visibility, no? I'd like to re-add my version of the formula for matrix addition since the current version is cut off on most small screens.
I agree Jacobolus' version is better, but my version was an improvment from the original. In the future "This is an improvment, but it could be done better, but I'm not willing to spent time to apply it" is not a reason for a revert. – Farkle Griffen (talk) 15:24, 31 March 2025 (UTC)
Adding line breaks between matrices here doesn't seem practical. Mediawiki should do a better job of allowing scrolling or resizing of formulas on phone displays, but that's a missing software feature, not something we can very easily accomplish as authors. Trying too hard to work around the severe constraints of tiny phone screens under our current constraints ends up causing more harm than benefit in my opinion, and doesn't even necessarily help that much on phones. If the content is outright inaccessible to you (impossible to scroll to see) then that's a software bug, and should be reported in the mediawiki bug tracker.
It's generally problematic to make mathematical content targeted to multiple devices, and there's no easy universal fix. The best output for a mobile device is never going to be great on a desktop browser, and vice versa. One helpful approach is to just make separate versions targeted at each type of reader device, but that's not really possible in current Mediawiki, or practical for Wikipedia authors. –jacobolus (t) 17:36, 31 March 2025 (UTC)
I completely agree that Mediawiki should do something about this. But apart from making a report, I don't see much point in talking about it. And I'm not trying to implement a policy or find a universal solution, I'd just like to not be reverted for relatively minor changes that make formulas readable. What's the issue with my prefered version of the matrix formula? It seems fine on my computer, but colapses down on my phone. I honestly don't understand why it was reverted. – Farkle Griffen (talk) 05:55, 2 April 2025 (UTC)
Your preferred version violates basic conventions about how alignment should work across line breaks in mathematical typography which have been fairly stable and consistent for centuries. –jacobolus (t) 06:51, 2 April 2025 (UTC)
If this is just a dramatic way of saying "The equals signs should line up and/or subsequent lines should be indented", then sure. But surely you agree that it's better than the alternative, no?
That said, I'd like re-add my preferred version. Do you oppose? – Farkle Griffen (talk) 07:06, 2 April 2025 (UTC)
This would be WP:edit warring, since two editors are aginst your preferred version. D.Lazard (talk) 08:28, 2 April 2025 (UTC)
I'm currently discussing what to do about this with Jacobolus now over on User:Farkle Griffen/Sandbox. Maybe instead of accusing me of edit warring for having a discussion on the talk page, you could add to the discussion over there. – Farkle Griffen (talk) 09:18, 2 April 2025 (UTC)
I do not accuse you of anything. I just qualify your putative action of re-adding your preferred version. This was an answer to your question "Do you oppose?". For being clear, I strongly oppose. Also, Jacobolus's sentence "Your preferred version violates basic conventions ..." is also a clear opposition. D.Lazard (talk) 09:54, 2 April 2025 (UTC)
Yes, I am opposed. Your preferred version is not good typography in my opinion. –jacobolus (t) 11:50, 2 April 2025 (UTC)
A few comments which don't actually address the issues raised, but which are certainly related, and I mention them in case anyone is interested. The problems mentioned above relating to phones are not caused by using a phone; like most problems in using Wikipedia on a phone they are caused by serious design faults in the so-called "mobile interface", and apparently also the "mobile app". Neither of those is necessary, nor, in my opinion, desirable, for using Wikipedia on a phone. Using the proper interface (the so-called "desktop" interface) scrolling and resizing are perfectly straightforward. It is appalling that Wikipedia not only presents the very badly designed "mobile interface" as the default, but also does not make it clear to users that at a single click they can get rid of it and instead have an interface which is perfectly usable.
If anyone reading this doesn't know how to get rid of the "mobile interface" and would like to know, just find the link near the bottom of the page labelled "Desktop". It's about 50 times as convenient for reading Wikipedia, and about 1000 times as convenient for editing. At least I think so, and in my experience most people who have tried it think so, but of course there are exceptions.
As I said above, these comments don't actually address the issues raised, because our editing of articles has to cater for how most people actually use Wikipedia, not for how I think, or anyone else thinks, they would be better advised to use it; however, as I also said above, the comments are related to points raised above, and I mention them in case they may be of interest to someone. JBW (talk) 21:46, 1 April 2025 (UTC)
For the point of closing this discussion, it looks like the scrolling issue with formulas has been resolved on the mobile app and web. – Farkle Griffen (talk) 04:56, 8 July 2025 (UTC)

It has been a little while since this article has been reviewed, so I took a look and noticed lots of uncited statements. While some of these might be covered under WP:CALC, other statements such as "Likewise from augere "to increase", one gets "augend", "thing to be increased"" and "Pascal's calculator was limited by its carry mechanism, which forced its wheels to only turn one way so it could add" do need citations, in my opinion. I am happy to add citation needed templates to the article if an editor pings me. Z1720 (talk) 04:12, 7 June 2025 (UTC)


### Addition
In the lead, abstract objects such as vectors, matrices, subspaces, and subgroups really ought to be elements of abstract objects such as vectors, matrices, subspaces, and subgroups; although it is possible to refer to the direct sum of two subgroups of a commutative group, there is not an additive inverse. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:43, 17 June 2025 (UTC)

I don't understand either of your points. If A and B are, for example, both n by m matrices over a field, then there exists a matrix A + B; that is to say that one can add them. I don't see any reason to change that statement in the article, and the same applies to the other cases you mention. As for direct sums of groups (additively written,  which almost always means Abelian) agreed that there is no additive inverse, but why is that relevant? The article doesn't suggest that there is. JBW (talk) 19:14, 17 June 2025 (UTC)
Incidentally, I am not keen on the wording "abstract objects". I see matrices over the rational numbers as a good deal less abstract than real numbers, for example. JBW (talk) 19:18, 17 June 2025 (UTC)
The point is that the sentence doesn't distinguish between algebraic structure and elements of those structures, e.g., you can add two elements of a group but you cannot add two groups, unless you define addition to include direct product. However, my suggested wording was still not quite right; how about addition can also be performed on, e.g., vectors, matrices and elements of abstract objects such as  vector spaces and groups.? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 20:17, 17 June 2025 (UTC)
"Abstract object" does not mean "set of objects", so this seems like a very confusing proposal. I am opposed. –jacobolus (t) 03:31, 18 June 2025 (UTC)
We could get rid of the name "abstract objects" though, feel free to propose alternative terminology / phrasing. –jacobolus (t) 05:00, 18 June 2025 (UTC)
OK, I can see three types of uses of "addition" here. (1) There are additions of vectors and of matrices. (2) There are, of course, additions of elements of vector spaces and of groups. (3) Contrary to what Chatul says, there are indeed additions of (additive) subgroups and of vector subspaces. In the case of groups the special case of direct sums is referred to far more commonly than either the general case or other special cases, but it is by no means the only case.
Leaving aside any opinions about the expression "abstract objects", the present wording covers cases (1) and (2), and is perfectly correct. The suggested rewording to refer to adding "elements of" vectors and matrices would be very unhelpful.
Case (2) is not mentioned here, though it is covered elsewhere in the article.
I can see a case for adding brief mentions of elements of groups and of vector spaces at this point in the article. There may also be a case for removing the mentions of subspaces and subsets, since those are less basic concepts in their respective fields, and this is a general article on addition, aimed at the general reader.
I can't see any case at all for the suggested change to "elements of abstract objects", which as far as I can see would just make the whole thing confusing. What on earth does "element of an abstract object" even mean? JBW (talk) 10:24, 18 June 2025 (UTC)

In Special:Diff/1299347865, User:jacobolus disputed my recent addition of a book by Gagniuc as a reference for two claims, instead replacing them by a reference to Kernighan and Ritchie. However, K&R is only about the C programming language, while the claims sourced to it are about what happens in a "high-level programming language" in general (a lot of people would dispute that C is high level), or about operators in "Some languages like C or C++" (K&R is only about C). The Gagniuc reference has the advantage of taking a broad view of programming languages overall, unlike most available references that concern only a single programming language and cannot be used to source broad statements about programming languages in general.
Obviously we could provide individual references for this operator in C, C++, Java, Javascript, Python, Jython, and I don't know how many other separate languages. I don't think this is a helpful way to source this material and doing so to source a broad statement about programming languages in general by sourcing only individual examples raises questions of WP:SYN.
I think this change warrants a discussion here. Jacobolus: can you maybe discuss your reasons for replacing a big-picture reference with an overly specific reference, and if you have a good reason to reject Gagniuc can you maybe work harder to find a reference that is actually valid for the big-picture statements that are claimed to be sourced by your replacement? —David Eppstein (talk) 23:49, 7 July 2025 (UTC)

@David Eppstein If you will remember, Gagniuc is the guy who repeatedly created sockpuppets to spam references to his book(s) around random Wikipedia articles, even in contexts where they weren't really appropriate. I'd rather use just about whatever other source, especially since the book you referenced isn't really particularly helpful or relevant for anticipated readers of this article, and is making a claim that is frankly trivial and entirely uncontroversial. –jacobolus (t) 02:24, 8 July 2025 (UTC)
@Jacobolus. For real? Can you show Special:Diffs for the proof? Dedhert.Jr (talk) 02:50, 8 July 2025 (UTC)
Wikipedia:Sockpuppet investigations/MegGutman/Archive –jacobolus (t) 03:16, 8 July 2025 (UTC)
Aside: if you are concerned about "high-level programming languages", our article wikilinked from the relevant sentence describes that term referring to Fortran, Algol-60, and Cobol. –jacobolus (t) 02:56, 8 July 2025 (UTC)
While we are here, this whole section is a confused and confusing muddle; the references are really the least of the problem.
We skip from analog computers to "digital computers" to abacuses to a brief few mentions of pre-commercial mechanical adding machines, then electronic adders.
Next we jump to one of the least focused paragraphs I have ever seen on Wikipedia. It leads with "computational addition may be achieved via XOR and AND bitwise logical operations in conjunction with bitshift operations as shown in the pseudocode below" (but the pseudocode has been removed). Then we go back to adders, then abacuses, something about how numbers would vanish in Ancient Rome, and then a weird aside about the += operator which is a complete non sequitur.
After that we get a paragraph about overflow, and a paragraph about floating point numbers that is inscrutable who anyone who doesn't know what they are and uselessly vague to anyone who does.
I think the whole section should be substantially rewritten and reorganized before anyone wastes time trying to source each half-sentence. –jacobolus (t) 04:04, 8 July 2025 (UTC)
It does seem rather muddled: the message appears to be "addition on a computer often changes the addends" except in anything higher-level than assembly language, when it doesn't. That section needs de-crufting before sourcing. Stepwise Continuous Dysfunction (talk) 16:30, 8 July 2025 (UTC)
Whether particular CPU instructions store the result in place over the register containing one of the arguments frankly seems like an unnecessary thing to belabor in the context of this article. Save it for a dedicated article like Adder (electronics) or Arithmetic logic unit. It would be more useful here to e.g. talk about programming languages overloading the "+" operator to act on higher-level objects. –jacobolus (t) 17:21, 8 July 2025 (UTC)
I think the last chunk of that paragraph, beginning "Unlike addition on paper...", could be removed. Stepwise Continuous Dysfunction (talk) 18:03, 8 July 2025 (UTC)
Also, shoving a book from 1925 together with discussions of CPU instruction sets seems rather like synthesis. It reads like somebody had a pet theory about how "addition on a computer often changes the addends", and then citations got sprinkled on top as post-facto justification. (I haven't checked the history to see if that's what happened, but it's how it reads.) Stepwise Continuous Dysfunction (talk) 20:46, 8 July 2025 (UTC)
I'm ok with the removal of this passage. The part of the "Computers" section that I think is most important is not that part, but the following two paragraphs, on overflow and non-associativity of floating point, which discuss how computer addition differs from its mathematical ideal. —David Eppstein (talk) 21:05, 8 July 2025 (UTC)
I have added a summary sentence leading into that passage to try and tie them together and explain their importance. Stepwise Continuous Dysfunction (talk) 21:58, 8 July 2025 (UTC)

The redirect Addition tableAddition table, and pipes in other articles redirect here, where the concept is not defined. Instead, we have, in section § Decimal system, a mention of 'the 100 single-digit "addition facts"', which seem to be the entries of the standard addition table. IMO, this pedagogical pedantry and the teaching instructions that follow must be completely rewritten for allowing a target for the redirect. (For the moment, the only possible target that I have found is Cayley table.) D.Lazard (talk) 09:00, 9 July 2025 (UTC)

The addition table was defined in a section removed in April 2025 by Dedhert.Jr. I have restored the section. D.Lazard (talk) 09:22, 9 July 2025 (UTC)
I changed the section title to § Single-digit addition but left an anchor § Table. –jacobolus (t) 14:30, 9 July 2025 (UTC)
This is mostly a complaint about a matter of taste, but the term "addition fact" sounds hokey. It strikes me as the kind of term that is invented so that the people who sell schoolbooks have something to fill them with. ("Quiz: How many addition facts are there?" "List all the addition facts that use the number 7.") Is it really a standardized bit of pedagogy, as the current article text seems to portray it? Stepwise Continuous Dysfunction (talk) 21:45, 9 July 2025 (UTC)
Hence the scare quotes, and a better name would be fine ("single-digit sums"?). On the other hand this is actually a term commonly used in literature about math education, and has almost 2000 results on Google scholar. –jacobolus (t) 02:06, 10 July 2025 (UTC)
If it really is an established bit of math-education jargon, then our using it is not so bad, but it is still a curtailed notion of what an "addition fact" might be. Is satisfying the commutative property not a fact about addition? Etc. If I were writing the paragraph from scratch, I might say "single-digit sums" or "basic sums", perhaps. Stepwise Continuous Dysfunction (talk) 22:34, 10 July 2025 (UTC)

@David Eppstein: The notion of addition applies to both group elements and to subgroups of an Abelian group; similarly for submodules of modules, subspaces of vector spaces. There's also the direct sum. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:32, 17 July 2025 (UTC)

Sure, but at this level of article I think it's a mistake to introduce addition of subgroups at a point where we haven't even yet talked about addition of elements. —David Eppstein (talk) 17:03, 17 July 2025 (UTC)
I agree with David, although I have replaced (in the article), "group" with additive group. Note that the sum of two linear subspaces and the Minkowski sum of two subsets are sets of sums of elements. So they are implicitely covered by the current formulation. D.Lazard (talk) 17:59, 17 July 2025 (UTC)
Thanks; "additive group" is better. —David Eppstein (talk) 18:03, 17 July 2025 (UTC)
Maybe split § Algebra into subsections and add subsections for, e.g., additive groups, rings, Modules, fields, Direct sum of groups. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:47, 17 July 2025 (UTC)
Note that rings, modules and fields are special cases of additive groups. D.Lazard (talk) 20:02, 17 July 2025 (UTC)
Yes, as are vector spaces. However, sums of subrings, sums of subfields and sums of subalgebras are a bit more complicated. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 20:54, 17 July 2025 (UTC)
Yes, some people call "sum" the structure generated by two substructures of a given structure, but these sum are generally not specifically related to any addition (they generally involve also the multiplication). This does not belong to this article, called Addition. D.Lazard (talk) 21:09, 17 July 2025 (UTC)