Talk:Addition

The good article status of this article is being reassessed to determine whether the article meets the good article criteria. Please add comments to the reassessment page.

^{Date: 14:50, 14 June 2025 (UTC)}

Addition has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.

Article milestones
Date	Process	Result
December 27, 2014	Good article nominee	Listed
April 24, 2015	Featured article candidate	Not promoted
Current status: Good article

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2+3 = 5 apples

I read from left to right and then go down to the next line -- unless there is some spacing or other indication to do otherwise. So, when I read the picture of three plus two apples, I saw

A

AA

AA,

which is 1+2+2. I think the image should be replaced with one like

A

A.. A

A ..A

if not
AAA

AA . (where .. should be a blank space or two)

Kdammers (talk) 14:37, 26 May 2018 (UTC)[reply]

I agree with this. Unfortunately it's not too easy to edit images. Can anyone make a new image like this (3 apples on the first row; 2 on the second)? — Bilorv_(c)(talk) 16:09, 26 May 2018 (UTC)[reply]

Two years on, and the same image is still there. Kdammers (talk) 02:18, 27 July 2020 (UTC)[reply]

translation

One of the images (2+4=6) uses the word 'translation' to explain it; how-ever, "translation" is not used any-where else in the article. What does it mean? Kdammers (talk) 14:40, 7 September 2020 (UTC)[reply]

A translation is a rigid motion; i.e., moving without rotating, although in one dimension, this is a meaningless distinction (see Translation (geometry) for more, possibly technical as well). This introduction of terminology probably isn't great. If anyone wants to tweak it, please go ahead; I don't have any great ideas at the moment. –Deacon Vorbis (carbon • videos) 14:47, 7 September 2020 (UTC)[reply]

labeling

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)[reply]

Three years on, and the illustrations are still mystifying. Kdammers (talk) 18:28, 14 June 2024 (UTC)[reply]

@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)[reply]

Innate ability

Should the strange case of the Pirahãs' alleged lack of adding be brought up? Kdammers (talk) 10:11, 25 April 2021 (UTC)[reply]

Do you have the sources? - S L A Y T H E - (talk) 08:02, 20 February 2023 (UTC)[reply]

https://en.wikipedia.org/wiki/Pirah%C3%A3_language, references at footnote 6. Kdammers (talk) 18:20, 14 June 2024 (UTC)[reply]

adding adding animals

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)[reply]

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)[reply]

@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)[reply]

"defining the real number 0 to be the set of negative rationals"

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)[reply]

@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)[reply]

Thank you for your explanation! Merlin.anthwares (talk) 23:21, 12 January 2025 (UTC)[reply]

Breaks in formulas

@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)[reply]

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)[reply]

"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)[reply]

@D.Lazard, please self-revert to allow users with smaller screens to read the article. – Farkle Griffen (talk) 21:20, 30 March 2025 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

This would be WP:edit warring, since two editors are aginst your preferred version. D.Lazard (talk) 08:28, 2 April 2025 (UTC)[reply]

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)[reply]

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)[reply]

Yes, I am opposed. Your preferred version is not good typography in my opinion. –jacobolus (t) 11:50, 2 April 2025 (UTC)[reply]

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)[reply]

Article review

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)[reply]

GA Reassessment

Addition

Article (edit | visual edit | history) · Article talk (edit | history) · Watch • Watch article reassessment page • Most recent review

Result pending

Uncited statements throughout the article. While some 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) 14:50, 14 June 2025 (UTC)[reply]

Wouldn't it be just as easy to fix these issues without a threatening formal process? Did you try looking for sources for the claims you were skeptical about? –jacobolus (t) 18:28, 14 June 2025 (UTC)[reply]

@Jacobolus: Please see WP:GAR, where it says "Wikipedia is not compulsory and editors should not insist that commentators, interested editors, or past GAN nominators make the suggested changes, nor should they state that edits should have been completed before the GAR was opened." A GAR is not a threat, it is an article review process. Z1720 (talk) 18:46, 14 June 2025 (UTC)[reply]

I have read that before, and I'm not insisting anything. I just generally feel that leading with formal process is usually significantly less productive than other alternatives. The most useful is doing concrete work to fix specific problems you find. The second most useful is making a careful and detailed review (like a peer review), noting down specific problems and possible types of fixes. Starting an adversarial formal process with vague / nonspecific feedback is of very limited usefulness, and typically wastes about 3x as much attention as more collaborative efforts, and even when it manages to make improvements often leaves everyone feeling grumpy. I would recommend always trying something else first, leaving the "do this or I'll take the green badge away" threats until after you run into page where other editors are either (a) completely disengaged and unwilling to discuss concrete and specific concerns, or (b) outright refuse to make changes that seem clearly required by good article criteria. –jacobolus (t) 23:31, 14 June 2025 (UTC)[reply]

@Jacobolus: This GAR is for reassessing the article's GA status and making improvements. It is not a place to comment on the GAR process or my conduct. If you would like to continue that discussion, please post at WT:GA or an appropriate noticeboard. Would you like me to add citation needed templates to the article? Z1720 (talk) 23:42, 14 June 2025 (UTC)[reply]

If you could make a detailed and specific list of everything you think is an issue, that would be helpful – and even better if you take a crack at fixing some of those yourself. Editing the article to put little "citation needed" templates is not necessary, though you can do that if you really feel like it. (It would be significantly better still if you started with that before kicking off a formal process – something to consider for next time.) I already provided references for the two specific statements you disputed; it took about 10 minutes. –jacobolus (t) 23:54, 14 June 2025 (UTC)[reply]

Also, I think it is the place to comment, every time someone starts such a process without trying anything else first. Judging from their behavior, people starting these processes generally seem not to realize that they have more collegial alternatives available, not involving a short time limit or an implicit threat, so it's valuable to clearly explain it to make sure they get the message. –jacobolus (t) 23:57, 14 June 2025 (UTC)[reply]

@Jacobolus: I have added citation needed tags to the article where I think they are needed. I have opened a thread at WT:GA to discuss the above interaction and ways to improve the GAR process. Z1720 (talk) 00:53, 15 June 2025 (UTC)[reply]

About half of these "citation needed" templates added here point at statements that in my opinion need no reference, along the lines of WP:BLUE. Of course it doesn't hurt anything to add extra references for well-known/trivial/self-evident statements, if anyone really feels like it, but not having them also is no real problem, and doesn't make the article any less "good". The others are also statements that look easy to verify, though it takes a while to do each one, and when done in a hurry the sources found are likely to be fairly mediocre and unhelpful to readers. Adding sources for these doesn't really seem urgent or the best use of editors' time, but it's probably at least marginally productive.

Frankly the several most problematic statements in this article are ones that already have footnotes, but the sources don't say what the statement claims; I don't think an audit of this type is going to fix any of those issues, and those take much more work to fix. For example, I think the claims about etymology we make here are not quite right but figuring out the actual story takes significantly more research effort. –jacobolus (t) 17:55, 15 June 2025 (UTC)[reply]

There is no short time limit. See Wikipedia:Good article reassessment/Fourteenth Amendment to the United States Constitution/1, now open for almost four months and with no indication of closing soon. Feel free to take as much time as you need, if you want to bring this article back to GA standards. ~~ AirshipJungleman29 (talk) 00:56, 15 June 2025 (UTC)[reply]

Having a look through the references, I think some of them should be removed:

Bogomolny, Alexander (1996): seems to be a promotional site for a logic puzzle book. It is not used as a citation so I think it can just be removed.
Dunham, William (1994), Jackson, Albert (1960), and Williams, Michael (1985) are not used as inline citations in the article. Should these be moved to "Further reading"?

Thoughts appreciated. Z1720 (talk) 01:01, 15 June 2025 (UTC)[reply]

Bogomolny's website Cut-the-Knot is generally great, but this particular page about "What is addition" (even if we include the sub-pages linked at the bottom) is nothing special. Since we don't currently cite it (perhaps we did at some point in the past, I didn't check) it can safely be removed from the list of citations. Feel free to move anything not currently cited to Addition § Further reading and also feel free to just trim any that don't seem particularly relevant or useful. –jacobolus (t) 03:13, 15 June 2025 (UTC)[reply]

I just took Dunham, Jackson, and Williams out entirely. None of these seems really fit for the Further reading section. My guess is that they were previously cited for some claim or other, but at some point the claim and/or specific citation was removed. –jacobolus (t) 03:31, 15 June 2025 (UTC)[reply]

The text abstract objects such as vectors, matrices, subspaces, and subgroups is problematical, because I'm not sure of the intended scope of the article. My first thought is to replaces it whith elements of abstract objects such as vectors, matrices, subspaces, and subgroups and add Direct sum to the See also section. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:54, 17 June 2025 (UTC)[reply]

Abstract objects

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)[reply]

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)[reply]

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)[reply]

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.^[a] 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)[reply]

"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)[reply]

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)[reply]

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)[reply]

Notes

^ But it might be a good idea to include Direct sum in § See also.

[1] But it might be a good idea to include Direct sum in § See also.

[a]