Talk:Addition/Archive 1

Archive 1

Split.

Okay, I've done the split. See Summation and Talk:Summation. As I write this, however, the dust has yet to clear... Melchoir 02:13, 3 December 2005 (UTC)

Still to do, possibly for someone else:

• Chainsaw "In music" section. I like music theory as much as anyone else, but come on.
• Determine where interlang links are appropriate in Summation.
• Add more explanation of what addition is.

Melchoir 02:28, 3 December 2005 (UTC)

Come on what? Hyacinth 08:18, 3 December 2005 (UTC)

Come on, as in the example I moved to Musical_set_theory#Addition was an overgrown example of arithmetic modulo 12. I replaced it with the comment, "In modular arithmetic, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory." which now appears in the Generalizations section. I hope that the Generalizations section makes it clear that there are countless different versions of addition indispensible to all kinds of fields.

In fact, I'm more than a little uneasy that you've linked to it from the top of Addition.

1. The notion of addition in musical set theory doesn't have its own article, and
2. the material linked to never defines addition,
3. nor does it use the word "addition" except in the heading you added, and
4. the word "sum" is just a link back to here. (now a link back to summation after re-redirect of sum)

Along with the mention in Generalizations, would you be happy with a See also link? Melchoir 18:29, 3 December 2005 (UTC)

Looks like you agree. Thanks! Melchoir 18:19, 4 December 2005 (UTC)

Of the four interlang links I found, two are pretty respectable. It looks like the German and Russian Wikipedias had the idea of separate articles a long time ago! Melchoir 07:56, 5 December 2005 (UTC)

Split?

I think this article should deal only with the binary (dyadic) operation x+y, and arbitrary sums should be moved to a separate page, possibly named Summation or Sigma notation or both. Melchoir 05:42, 28 November 2005 (UTC)

Also, once the split is done, we might want to merge Addition of natural numbers into Addition, where someone might read it. Melchoir 05:50, 28 November 2005 (UTC)

Strongly support splitting off Summation. Support merging Addition of natural numbers. --KSmrq^T 00:55, 29 November 2005 (UTC)

I agree, it seems like a good idea. My only worry is that Addition of natural numbers is technical in places, but I trust you can handle that. -- Jitse Niesen (talk) 12:48, 29 November 2005 (UTC)

I agree with a split. Also a reference to Series (mathematics), including the Taylor and Fourier series should be added.(Igny 18:14, 29 November 2005 (UTC))

Okay, thanks for your suggestions! I'll probably do it on Friday. Melchoir 18:57, 29 November 2005 (UTC)

I agree that you should outsource the sigmas, but I strongly disagree with "Addition of natural numbers" being incorporated into this article. That seems overly Bourbakist. The content of the article "Addition of natural numbers" certainly needs a better home, but it isn't here. Check out [[Category:Set theory]]. Silly rabbit 20:48, 29 November 2005 (UTC)

Well, then I won't do the merger yet, or perhaps at all; we'll see how Addition looks after the split to Summation and go from there. We'll still need to do something about Addition of natural numbers, possibly taking a hard look at Natural number itself. (Too many math articles seem to have catchall sections named "Properties"...) And Addition will still need a bit more discussion on its most fundamental example.

Oh, and for those of us (me) who aren't cultured enough, what do you mean by "Bourbakist"? Melchoir 22:38, 29 November 2005 (UTC)

See Nicolas Bourbaki  ;-) Silly rabbit 23:03, 7 December 2005 (UTC)

Holy crap, I always thought it was some person! Melchoir 23:37, 7 December 2005 (UTC)

More needed material

I've indicated where I think sections on history and algorithms might go. I hope I'm not defying this guideline. Melchoir 22:06, 3 December 2005 (UTC)

Never mind... Melchoir 00:57, 8 December 2005 (UTC)

Oh, and someone with a reference on combinatorics ought to have a look at what I've written in Related operations. Melchoir 22:07, 4 December 2005 (UTC)

test test Melchoir 19:33, 9 December 2005 (UTC)

Etymology

Does the source state that "addere" means "to give to"? Certainly, "ad" can mean "to" and "dare" means "to give", but that doesn't imply that "addere" means "to give to". Charlton T. Lewis, An Elementary Latin Dictionary, lists "to put to, place upon, lay on, join, attach" as meanings [1]. Furthermore, the form "addend" does not exist in Latin. As you say, the word is inflected; the canonical form "addendus", which is the masculine singular nominative. -- Jitse Niesen (talk) 02:37, 14 January 2006 (UTC)

Well, I know virtually nothing about Latin (Does it show?), so let me just quote. Schwartzman says:

add (verb), addition (noun), additive (adjective): from the Latin verb addere, itself a compound of ad (q.v.) "to" and dare "to give." When you add an amount to something, you "give more to" that something. The Indo-European root is do- "to give." Related borrowings from Latin include donate and condone "to give sanction or approval." A related borrowing from Greek is the dose of medicine given to a patient. In arithmetic, the "+" symbol...

He seems pretty confident about the giving. I originally wrote "give more to" to follow the source, but I decided the "more" wasn't justified without speaking of "an amount", so I deleted it, leaving "give to".

I guess I shouldn't be too surprised that addere has other meanings; if you'd like to add Lewis' list, be my guest.

As for addend not actually being a Latin word, I wasn't sure about that, so I kind of hedged. How should we put it? Melchoir 02:58, 14 January 2006 (UTC)

Actually, as long as I'm quoting, I should quote this entry:

addend (noun): from Latin addere "to add" (q.v.), with the suffix -nd, which creates a type of passive causative, so that Latin numerus addendus meant "the number to be added." In the statement 3 + 4 = 7, many Renaissance writers...

What the heck is a "passive causative"? Is it just a gerundive, or am I missing something? Melchoir 03:06, 14 January 2006 (UTC)

Well, I think I've fixed the passages in question. Melchoir 09:25, 28 January 2006 (UTC)

It is fine now, thanks; you're doing great on the article by the way (sorry for the late reaction) -- Jitse Niesen (talk) 14:46, 31 January 2006 (UTC)

Thanks! Melchoir 20:48, 31 January 2006 (UTC)

Commutativity

Would it be good to mention under commutativity that addition is only commutative for a finite number of terms or an absolutely convergent infinite series, but not that it is not commutative for a conditionaly convergent infinite series? --FurciferRNB 1 March 2006

Hmm... I think that's beyond the scope of the main body of the article, which deals with addition of two terms. Perhaps you could add a note under Other ways to add: Summation towards the bottom? I'm not sure how to phrase it. Melchoir 20:51, 1 March 2006 (UTC)

conjugations

Under the section Notation and terminology, addition and add are said to be conjugations of the latin verb addere. They are more properly derivatives... A conjugation is a changed form of a verb indicating aspect, person, number, etc like it says in grammatical conjugation, but a nonal form or a reuse of a verb stem in another language is a derivative. Verily, the Romans had a regularized form additio, from which we get addition.--Josh Rocchio 22:07, 20 March 2006 (UTC)

Hmm... interesting. Well, I guess I'll go fix it; natually, you're welcome to clean up any more mistakes you see! Melchoir 22:19, 20 March 2006 (UTC)

Sorry, I didn't see your edit. But I'm not sure derivation (linguistics) is the correct term either. I settled on "loanword derived from the Latin". -- Jitse Niesen (talk) 22:58, 20 March 2006 (UTC)

Well, I'm not sure that loanword is correct either, so I changed it to "word derived from the Latin", which echoes the second sentence of etymology ("Some words have been derived from other languages …"). Conclusion: it's dangerous to write about things one does not know. -- Jitse Niesen (talk) 23:05, 20 March 2006 (UTC)

Amen. When the article is good enough to send to peer review, I'm going to have to advertise it on quite a few WikiProjects for help. Melchoir 23:40, 20 March 2006 (UTC)

Sorry to be so late in checking back on this. Yes, a loan word is more like cologne or bologna. Addition is most certainly in the realm of linguistics considered to be a derivation of the Latin verb addere, though it seems the derivation (linguistics) needs another definition or a dismbiguation page, or perhaps I should, more concisely, start the derivation (philology) page. Thanks for fixing the error so quickly, fellas.--Josh Rocchio 04:38, 31 March 2006 (UTC)

Addition in analog computers

I would question the assertion that "Addition is not tremendously important to analog computers, whose essential function is integration.[23]" Analog computes are generally used to solve differential equations, not simple integration, and the RHS of most DE's of interest include the sum of more than one term. So addition is tremendously important. --agr 22:34, 18 August 2006 (UTC)

That makes sense. All I really meant by that sentence was to contrast with digital computers. I guess we could take it out, but then how do we transition from analog to digital? Melchoir 02:35, 19 August 2006 (UTC)

...okay! Is there anything else fishy in there? Melchoir 04:30, 20 August 2006 (UTC)

I'm not real happy with the sentence on adding machines. An analogy might be "plowing was so important that the earliest farm tool was called a plow." I'll try an edit.--agr 16:24, 21 August 2006 (UTC)

Fair enough. I was trying to make a point beyond naming, though, so I'll give that another shot. Melchoir 16:55, 21 August 2006 (UTC)

Oh, and I'll also restore "earliest automatic, digital computers", which is a stronger statement than "earliest mechanical calculators". My memory is a little hazy, but I believe this assertion is covered by the citation at the end of the paragraph. Melchoir 16:58, 21 August 2006 (UTC)

The madness of Addition

OK, now that I've been pointed to this article by another editor (whose good name I shall not sully by mentioning), I'm going to offer an opinion before even attempting to work on it. (Caveat: I am not a math person. I am a writer and editor outside of Wikipedia; those are the skills and perspective I'm bringing here.)

1. This article covers too much territory. It needs to be pared down to basics. Ideally, I think it should provide such a basic level of information that it can be used as a reference term elsewhere without overwhelming people when they click through to it.
2. I actually think non-mathematicians need to work on this article. I think this may be a case where too much knowledge is a bad thing. There's too much information and detail.
3. Addition is one of the most basic building blocks of math as I understand it. This article should reflect that. It should be simple, straightforward. At a glance, I'd say 80% of the content could be tossed, broken into separate articles, or reduced to "see also" or wikilinks.

I realize this is going against what people have created here. This is why I'm putting this on the talk page before getting all bold on it. I'd like some input on whether people think I'm balmy for this view. I'm not an innumerate person and yet I glaze over reading this article. Thoughts? --Pig^man_dialogue 00:34, 17 March 2007 (UTC)

I'm all for creating summary-style daughter articles. (But plain deletion is Bad and "see also" is a cry for expansion all over again.) Melchoir 00:54, 17 March 2007 (UTC)

Here's my thinking: When an article gets as large as this, it's a cry to be divided into discrete parts which can concentrate on explaining the specifics. I realize that, because of the very foundational nature of "addition", there is a desire to enumerate these many mathematical and scientific connections in the same article. However, the drawback to this approach is the reader may be overwhelmed with detail.

I believe the language in the article needs to be vastly simplified.

For example, I have to concentrate to understand the first sentence of the article. I have to really concentrate to understand the second sentence. It's not a brag to say I am fairly literate and well versed in the English language. And I already understand the concept of addition and the use of symbolic representative letters in math. Why is it so difficult? Perhaps it's a problem of translating math, a precise symbolic system, into less precise words. Beyond that point in the article there is an almost unremitting stream of specialized mathematical jargon/cant and terminology. (I'm using "jargon" in a non-pejorative manner here.) When a term is explained/defined with words whose specific contextual meaning is also difficult to understand, there's a problem. I suppose the many wikilinks are intended to provide additional clarification but it feels like a weak alternative to clearer original text.

I'm not even sure I could do a better job on the article but I feel these are valid concerns so I'm expressing them. I'm a writer, a wordsmith, if you will. I'm certainly not an advocate of writing to an overly simplistic, grade-school level. But if I'm having trouble comprehending the text, I've found this is a good indication that a large majority of other readers will also have trouble. I know my points above are radical. However, I also know there comes a point when line editing and tweaking sentences will not noticeably improve the readability of the article. I believe this is one of those times.

I have no intention of unilaterally making large changes to the article. I just think these are things to consider. --Pig^man_dialogue 02:57, 17 March 2007 (UTC)

You raise valid points that are equally applicable to many introductory-level math articles. It is unfortunately often true that the prose is too difficult or proceeds too quickly for the intended reader. I hope that you will consider making at least a few changes to illustrate how you would like to see the prose improved. Typically, the reason that things are phrased the way they are is that the original author didn't, or couldn't, think of a better way to say them. So some editing by a nonspecialist might inspire the rest of us in how to write the rest more clearly. Perhaps you could rewrite just the first paragraph - you almost certainly understand the material. CMummert · talk 03:08, 17 March 2007 (UTC)

Yeah, writing a good first sentence is especially hard. I was amused by Mathworld's solution: Addition is "The combining of two or more quantities using the plus operator", whereas Plus is "The addition of two quantities, i.e., a plus b." I was shooting for something a little more meaningful here! Melchoir 06:13, 17 March 2007 (UTC)

Indeed, first paragraphs in maths articles are always hard, I'm somewhat suprised that thiss has proved the case even for something as simple as addition.

Encarta has The arithmetic operation of addition is indicated by the plus sign (+) and is a means of counting by increments greater than 1. For example, four apples and five apples could be added by putting them together and then counting them individually from 1 to 9. Addition, however, makes it possible to add, or compute, sums more readily.

Britannica Combining two sets of objects together, which contain a and b elements, a new set is formed that contains a + b = c objects. The number c is called the sum of a and b

Simple English wikipedia has In arithmetic, addition is putting two or more numbers together. The sign for addition is "+". The name for this sign "+" is "plus".

As to whether its too long, ther is some very advanced material here, especially in the Addition of natural and real numbers, which makes many references to set-theoretic quantities. These could possibly be split off to formal definitions of addition. Its worth also comparing with Subtraction and Multiplication which are both too short and don't come close to comprehensive. --Salix alba (talk) 08:51, 17 March 2007 (UTC)

I realize the difficulty of explaining addition in plain prose. I think that's why I ranted a bit on the talk page rather than just attempting some changes and providing an example of clearer language. I'll take a whack at the opening para and see if I can make it better. For the record, I think the whole intro should be reduced to a plain para or two on the basic concept of addition. Info currently in paras three and four shouldn't be in an intro at all. My basic mantra for an intro is basic and simple. Despite what I said above about not writing to a grade school level, I believe an intro needs to be written as simply as possible without misrepresenting the subject. If there are wikilinked words/phrases in the intro, they themselves need to be easily understood without clicking through. I'm speaking only of the intro here, not the rest of the article. Ugh. I'm sorry if I appear to be speaking condescendingly to an undoubtedly intelligent group here. It's not my intent to insult anyone. Oh, and thanks for the other examples, Salix and Melchoir. It's very helpful to see how others define the term. --Pig^man_dialogue 19:23, 17 March 2007 (UTC)

Comment

If this is true (quoted from Addition):

Performing addition is one of the simplest numerical tasks, accessible to infants as young as five months and even some animals.

then why can't a person with too many college degrees understand the first paragraph without great effort? Anonymous 16:57, 18 March 2007 (UTC)

Musing philosophically (after edit conflit with paul below) -

Piaget 1965 - it is a great mistake to suppose that a child acquires the notion of number and other mathematical concepts just from teaching. On the contrary, to a remarkable degree he develops them himself, independantly and spontaneously. When an adult try to impose mathematical concepts on a child prematurely, his learning is mearly verbal; true understanding of them come only with mental growth.

My interpretation of this is that it is actually a hard thing to explain in words. When I've taught children basic arathmatic I've primarally used methods other than english paragraphs to explain the concepts - lots of manipulative materials like lego brick, and activities like counting squares and many many examples slowly leading up to a general theory. Bairly a word is written on the page.

The other problem is that mathematics is priamilly a constructive field, everything in mathematics builds on a simpler concept, hence addition first requires the idea of counting, 1,2,3,4... Then the idea of counting on hold up four fingers then raise 1,2,3 more fingers, now count how many fingers there are 1,2,3,4,5,6,7. We see reference to other concepts in the other intro paragraphs above, set is mentioned by Britannica.

Then we have the fact that addition covers several related things, addition of counting numbers is subitly different to addition of lengths.

So I posit that there is an intrinsic dificulty with plain english sentances which do not refer to other concepts and cover the range of things which addition covers. None of the other intro paragraphs above is entirely satisfactory. But then I am a child of New Math so my education was probably messed up! --Salix alba (talk) 19:08, 18 March 2007 (UTC)

I was thinking the very same thing! That is, that you were probably a child of New Math and that could account for the problem. Anonymouse 14:39, 19 March 2007 (UTC)

Addition of algebraic numbers

I think some attention should be paid to intuitionistic addition of algebraic numbers. There is a method, due to Kronecker, for adding such numbers by forming a common primitive element for the extension fields. There are other methods, using Newton's theorem on symmetric functions and the resultant. The most sophisticated approach (that I know of) is Trager's algorithm used in modern symbolic computation. I'll try to source these and include them in the article. Silly rabbit 15:48, 10 May 2007 (UTC)

Notation

In the Notation and Terminology section, it says that

"A column of numbers, with the last number in the column underlined, usually indicates that the :numbers in the column are to be added, with the sum written below the underlined number."

However, I've always been told that this means multiplication, not addition. Foxjwill 01:28, 10 September 2007 (UTC)

Associativity

I don't think that "one can add more than two numbers" is a good way to describe associativity. On the other hand, I'm not sure how to concisely describe it in laymen's terms. Thoughts? —Preceding unsigned comment added by 67.204.0.186 (talk) 03:08, 19 May 2008 (UTC)

Intro paragraph rewrite

OK, this is, of course, not as easy as I hoped. I feel a bit like a ass coming in and blustering about the difficulty in reading it and then struggling much more than I usually do in rewriting such a small section. Before anyone screams about the important points I eliminated, please consider that I attempted to focus solely on the very basic qualities of addition. I believe almost everything I took out was far too complicated for an intro. I also haven't looked carefully in the body of the article for the supporting documentation for the children and animals statement. I sure hope that's supported. Why would I leave something so peripherally related to addition like that in the intro and get rid of so much other info? Because it's human interest. "Oh, my child may know how to add before speaking? Wow, that's strange!" This is intended to draw people into the body of the article. It's called a teaser in print and TV. So let loose the slings and arrows of discontent if you've got them. Cheers, --Pig^man_dialogue 18:56, 18 March 2007 (UTC)

I admit I've got a few slings…

• I don't think it's a good idea to introduce "adding" and "total" in the first sentence along with "addition". The main danger is that they're read as parts of the definition, which would make it circular. Maybe putting them in italics would help clarify their role?
• "Combining" is vague. All binary operations could be described as combining two numbers — some quite meaningfully. My question is, how does addition combine its inputs in a way that distinguishes it from MAX, or subtraction, or averaging, or multiplication, or the Pythagorean sum…?
• "Equal simple amount"?

As for taking out things that are too complicated for an intro, just remember that the manual of style advises us that the lead should reflect the whole article — and I agree, and so do the folks at WP:FAC. So in the long term, some more work is going to have to be done there. Melchoir 19:45, 18 March 2007 (UTC)

By the way, the children and animals bit refers to Addition#Innate ability. Of course, you can't ask a five-month-old to compute 1 + 1 using symbols or even English words; the question has to be acted out. Melchoir 19:50, 18 March 2007 (UTC)

First para is actually readable now, even interesting. In fact I was lured into venturing down a few more paras for the first time and my brain didn't explode. Anonymouse 11:39, 20 March 2007 (UTC)

Sorry for the lateness getting back here on this. Life intrudes. I acknowledge the things you pointed out, Melchoir. Most of your critique comes down to the difficulty I have in translating a symbolic and number based transaction into a simple English phrasing. While I should not argue with the WP manual of style, I still contend that if people can't make it through the lead section easily, they are highly unlikely to go further into the article. That's what I think the target is for a lead section: to include enough of the complexity of the full article but without overwhelming the casual reader. You'll have to excuse me if I say the overload threshold for most general readers of the maths articles is going to be lower than many other types of articles. I'm basing this on mostly on my own perceptions but I believe it holds true.

Every one of your points is well taken: the circular nature of using "adding" to describe addition, "combining" is a poor substitute for what was originally "increasing" I believe, and "equal simple amount" was a paraphrase from a Merriam-Webster's Collegiate Dictionary definition (and a stunning failure of a phrase in my opinion.) I'm trying to think my way through to another way of expressing it. Argh. Perhaps I'm not as flash as I like to think. This is easily one of the most difficult tasks I've attempted on WP, requiring exceptional precision in the choice of words and phrasing. Thinking now, I'll be back. --Pig^man_dialogue 03:24, 21 March 2007 (UTC)

I think the children and animals statement probably over states the case. From what I can tell these experiments do something like: put one object behind a screen, then put another object behind it. Finally the screen is removed and the child is suprised if there is not two objects behind it. This ability is far removed from a complete ability for addition, even for low numbers like 3+5. Indeed there are counter experiments where children between 4-7 have problems with inclusion of sets, given a set of 3 boys and 5 girls the child will answer incorrectly when asked if there are more children than girls.

Just found an interesting example of a definition. Addition of numbers does not mean to increase but to group, join or rename a pair of numbers as a single number. The number idea is the same whether expressed as 3+2 or 5. ... (Richard Copeland - How children learn mathematics, p133) --Salix alba (talk) 10:29, 21 March 2007 (UTC)

Salix, the def in your last para is interesting and seems really quite accurate to me. It covers a range of possible examples. Any other people's opinions on it? Of course the problem is finding a way to paraphrase it in just as clear language without plagiarizing it. --Pig^man_dialogue 18:37, 21 March 2007 (UTC)

Folks, I'm going to bow out of this discussion. Please do whatever you think appropriate to the intro. This re-write is easily one of the more stressful experiences in my recent Wikipedia participation (and that's saying something!) Perhaps it's my own lack of ease with the broader math subjects but I can't seem to adequately grasp the best English expression of these concepts. I feel that I'm just poking at it without having a firm vision of outcome. For me, this is very unusual. Be assured my backing off has nothing to do with the company discussing it here. I just have to back off for my own well-being. --Pig^man_dialogue 18:09, 23 March 2007 (UTC)

Wow. The attempt to make the intro accessible has clearly gone too far. I came here by way of the Pages Needing Attention place, and yes, this does need attention. I read the first sentence of the article and fell of my chair. I'd argue that someone who can read the word "addition" knows what it is already. "For example, in the picture on the right, there are 3 + 2 apples — meaning three apples and two other apples — which is the same as five apples, since 3 + 2 = 5." should not be the second sentence of the article. I urge each to simply read the first paragraph, and judge whether the writing is encyclopedic or not.

I do see the problem, however - I can't think of a satisfactory solution. Leon math (talk) 04:27, 13 December 2008 (UTC)

...Well, feedback noted, but that's not very helpful...

I missed Salix alba's suggestion above; I suppose you could say something like "Addition means to group, join, or rename a pair of numbers as a single number." It's not perfect, though -- a good introductory definition would distinguish addition from other operations, while avoiding confusion between numbers and the objects whose size they measure. Melchoir (talk) 05:37, 13 December 2008 (UTC)

Deffinition on Mathematical logics

In the field of mathematical logics you can define all aritmetrics by creating a language with the normal things Natural, Rational, Real or complex numbers, +,-,*,/ and anything else you need. I would like to know how such a definition of + (and everything else looks) it should be on this page or on the general aritmetriks page.

Thank you for your time! —Preceding unsigned comment added by 83.176.244.189 (talk) 21:32, 16 March 2009 (UTC)

Qualification

I am not entirely sure what this paragraph is intended to address, but it seems to include ideas that aren't present anywhere else in the article. Kundip, can you please clarify exactly what you are trying to add? Publicly Visible (talk) 05:57, 4 September 2009 (UTC)

It is intended to directly addresses the process of addition. No matter what you increase the size of, put together, join, combine - whether numbers or even ingredients and so on - there is qualification. In all the definitions of addition this fundamental, this basic - is missing. There is no ´trying to add' there is actual addition because qualification is included. The word qualification should be in the primary definition. I have modified mine to reflect the main definition as my first one was deleted and I put my second attempt under the first definition so as not to put any noses out of joint. Even in old dictionary definitions this was missed. You cannot add a dog and a cat and call it two spoons or two cars or two dogs. You would automatically know itś two animals. You do not add one plus two and call it three ants. The answer is three numbers of the value one we shorten it and say three. kundip Kundip (talk) 11:09, 14 September 2009 (UTC)

Where are these ideas coming from? Melchoir (talk) 17:30, 14 September 2009 (UTC)

Addition is the mathematical process of combining quantities.

This definition does not state that there is an increase in size or quantity.

If one "combines" something - it may actually decrease in size which is subtraction.

It must state "so as to increase the size or quantity" to be addition.

The issue of "how" you combine is not addressed at all.

It just says "process of".

The prerequisite for addition is qualification.

It is signified by the plus sign (+). For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5.

This is not a definition it is an example.

In one edit of my definition I was referred to "Identical particles". I have pointed out that there is no such thing. Even if they were the same at some point in their growth or decay - you still have the problem that they occupy different spaces. If they occupy different spaces - they are not the same. There would be a minuscule difference in temperature between them - I could go on. I understand the usefulness of such concepts as explained previously. Mathematics would not work without it. Kundip (talk) 08:26, 15 February 2010 (UTC)

Please provide a citation to a reliable source that makes this claim. Melchoir (talk) 08:37, 15 February 2010 (UTC)

Re your latest edit, I don't see any references in this search (I also tried various permutations of the words.) Melchoir (talk) 17:56, 15 February 2010 (UTC)

Addition (mathematics) is the process or action of first qualifying then joining or combining under a common heading so as to increase in size.

The primary definition of addition (mathematics) https://secure.wikimedia.org/wikipedia/en/wiki/Addition

States that it is the the mathematical process of combining quantities.

The first step in adding anything is qualification. "We are going to add some numbers". We are going to count the fruit. How many items are there?.

Qualification is the first step carried out by anyone adding. You quickly correct anyone that has not qualified properly. e.g. "two cars plus a truck is three cars". Immediately you say "three vehicles". Test this out on almost anyone. Why do you do this? - The person has not added it correctly. How have they not added correctly? Qualification!

I defy you to let anyone add incorrectly: "Two apples plus an orange equals three apples". This immediately catches your attention. "Three pieces of fruit".

Addition is the mathematical process of qualifying then combining quantities. Is that a better definition? Kundip (talk) 07:03, 16 February 2010 (UTC)

No, because no dictionary or textbook I've seen contains it. One can find plenty of definitions of "addition" that mention combining but none for qualifying.

I think the root issue here is that you're confusing numbers with the collections they measure. Suppose I hold two apples in my left hand and one orange in my right hand. It occurs to me that I have three pieces of fruit in my hands. I might say to myself: okay, that makes sense, because 2 + 1 = 3.

However, I wouldn't say to myself: "2 apples + 1 orange = 3 pieces of fruit". That sentence would commit me to concluding that 1 apple = 1 orange, which for most purposes is untrue. The mistake is in overextending the words "plus" and "equals". If I really want to express the relationship between the sizes and types of the sets, I might say: "the union of a set of 2 apples with a set of 1 orange is a set of 3 pieces of fruit." Or: "2 apples and 1 orange are altogether 3 pieces of fruit".

In other words, if you're given two sets and you want to use the arithmetic operation of addition to learn something about how they join together, the first step you do isn't to "qualify" them. Instead, you take the cardinality of both sets, stripping them of all information about their individual elements.

Now, I'll admit that the sentence "Addition is the mathematical process of combining quantities" glosses over the distinction between numbers and sets. That's partly by design; we don't want to get too technical in the introduction. But if you prefer, we could make the distinction explicit with something like "Addition is a mathematical operation that represents combining collections of objects together into a larger collection". Melchoir (talk) 08:00, 16 February 2010 (UTC)

The "into a larger collection" piece is much better.

For the first part your argument fails, to me, on two counts. First even your own sentence above "It occurs to me that I have three pieces of fruit" is an immediate qualification before you have completed the action of addition. One cannot help oneself. Secondly the numbers have a qualification: 1 + 1 in mathematics is understood to be the joining or combining of two theoretical quantities that are the same in every possible way. As no two items are exactly the same this qualification is critical to make the wonder of mathematics work. The article you referred me to "Identical particles" admits that Identical particles "are particles that cannot be distinguished from one another" There are two names listed "identical particles" and "indistinguishable particles". This all means that they cannot see any differences at this stage in their research hence the two names. The article goes on to say "The fact that particles can be identical has important consequences in statistical mechanics" Again this is a critical element in making this area of science work. By stating that they are the same for the purpose for which you are using them gives one a stable platform to work off.

I thank you for taking the time to write a reply. I hope my work stays on this page as a matter of record. In any case I appreciate the immense work you do here. Kundip (talk) 13:21, 16 February 2010 (UTC)

Thanks, and you're welcome! But I have to ask: you wrote "1 + 1 in mathematics is understood to be the joining or combining of two theoretical quantities that are the same in every possible way". Where in the world did you get that idea? Melchoir (talk) 00:39, 17 February 2010 (UTC)

OK 1=1 https://secure.wikimedia.org/wikipedia/en/wiki/%3D "The equality sign, equals sign, or "=" is a mathematical symbol used to indicate equality. It was invented in 1557 by Welshman Robert Recorde. The equals sign is placed between the things stated to be exactly the same, as in an equation." I added (maybe incorrectly) "in every way" to emphasize the point. I added "theoretical" because there is no such thing as two identical particles. At the top of this page, https://secure.wikimedia.org/wikipedia/en/wiki/Identical_particles it says "This article does not cite any references or sources." Kundip (talk) 01:46, 17 February 2010 (UTC)

Oh, you're referring to the number 1. Yes, 1 = 1. Again, it is helpful to consider the difference between the numbers and the sets they measure. In the expression 1 + 1, both addends are identical; yet this expression can be interpreted as the number of elements in the union of two one-element sets, in which the elements are not identical, and indeed may have nothing at all in common. Melchoir (talk) 03:16, 17 February 2010 (UTC)

Firstly here is the qualification: "both addends are identical". Identical being the key word. Secondly "indeed may have nothing at all in common" adds strength to the part of my my definition "under a common heading". One finds a way to join or unite. The more precise the better. "Two brad nails" is better than "two nails" is better than "two thin pieces of metal" is better than "two items". Kundip (talk) 04:37, 17 February 2010 (UTC)

Let's take your intuition that it's useful to precisely describe groups of objects, and follow that intuition to its logical conclusion.

Given a nail x and a nail y, they are not just any two nails. Perhaps they are both brad nails. But they aren't just any two brad nails either. They will have something else in common: their lengths will both be less than 1 meter, they will both be made of a substance other than chesse, and so on. So they are two non-cheese, sub-meter, brad nails. It never ends. No amount of adjectives can completely specify the two of them. Ultimately, the most exclusive heading shared by x and y is simply that they are the elements of the set {x, y}.

Likewise a screw a, a screw b, and a screw c are not just any three screws; they are the elements of the set {a, b, c}.

If we put our nails and screws together, we get five thin pieces of metal. They are not five nails, nor are they five screws. But they aren't just any five thin pieces of metal, either... they are the elements of the set {x, y, a, b, c}.

The relationship between these sets has a name. It is called the union of sets. One writes

$\{x,y\}\cup \{a,b,c\}=\{x,y,a,b,c\}.$

The union operation is the mathematical tool whose job it is to join sets of objects under an perfectly precise common heading. Do you understand so far? Melchoir (talk) 07:22, 17 February 2010 (UTC)

Yes, I get that clearly. Kundip (talk) 14:10, 17 February 2010 (UTC)

Okay, on to numbers. The operation that measures the size of a set is called the cardinality; it takes a set and produces a number. For example, |{x, y}| = 2. Taking the cardinality of a set is an intentionally destructive action; we throw away all information about the set except its size.

Roughly speaking, taking cardinalities turns set union into addition. By that I mean, given disjoint sets S and T, we have |S U T| = |S| + |T|. Applying cardinality to the above equation, we derive the equation

$2+3=5.\$

So addition of numbers and union of sets are two different, although closely related, operations. And they are both operations: given two numbers, there is a unique number which we call their sum, and given two sets, there is a unique set which we call their union. Okay? Melchoir (talk) 01:54, 18 February 2010 (UTC)

OK, I understand that. I am not lost yet. Kundip (talk) 11:54, 18 February 2010 (UTC)

So which operation are you interested in? Melchoir (talk) 21:48, 18 February 2010 (UTC)

Was away for a week. Either operation is OK. As I understand it we are talking about some sort of increase. If I have to choose - I pick the harder to defend. Union of sets? Kundip (talk) 13:40, 25 February 2010 (UTC)

Re the: "union of sets". "union" Comes from unite or unit or one. This points out that one is trying to join something. If the result is more it is addition, less - subtraction.How does one unite? Give it a quality. i.e. Qualification. Any unity has some sort of name. —Preceding unsigned comment added by Kundip (talk • contribs) 01:53, 26 February 2010 (UTC)

example of columnar addition

I think the example of columnar addition would be more interesting if there was a "carry" in the operation. — MFH:Talk 07:41, 23 June 2011 (UTC)

Addition in group theory

Can we have a setion on addition in group theory please? Akin to the section in multiplication here. Explaining which sets forms groups under addition. Thanks PointOfPresence (talk) 09:40, 5 September 2011 (UTC)

Well, there's already a section on abstract algebra. Currently the last paragraph says this:

• The general theory of abstract algebra allows an "addition" operation to be any associative and commutative operation on a set. Basic algebraic structures with such an addition operation include commutative monoids and abelian groups.

I suppose you're saying it should be expanded? Melchoir (talk) 01:15, 6 September 2011 (UTC)

Sure, but I do think we ought to add a section to the addition article, just for completeness and for consistency with multiplication. PointOfPresence (talk) 11:43, 8 September 2011 (UTC)

Oh, that's sort of what I meant: expanding this article. Completeness and consistentency are good, but I'm not convinced that consistency with multiplication requires an exact analogy here. When we're talking about addition, groups aren't the most natural setting. It would make more sense to focus on modules and vector spaces as generalizations of real addition, and maybe commutative monoids and semirings as generalizations of cardinal addition. Perhaps in an article on subtraction, I'd expect to see more on abelian groups. In an article on multiplication, I'd expect to see groups but also monoids and rings and algebras. Melchoir (talk) 20:12, 8 September 2011 (UTC)

This article illustrates the problem with math articles on Wikipedia

Too much information, often presented in an esoteric fashion. Yes, the purpose of Wikipedia is information, but that information is pointless if the reader cannot understand it. I learned addition in first grade and now at 40 with a degree in mathematics, and I find this article challenging. Lets define information...information is defined as knowledge transferred or communicated. The word information is based on the word "inform", which is a verb that can be defined as "transfer knowledge". This is in contrast to the definition of "data" or "facts", which requires "processing", or "refinement" to become useful information. If Wikipedia is to truly be a knowledge base, we must take care to present our data and facts so that it is truly informative. I am not suggesting that we "dumb it down"....indeed, Einstein can be quoted as saying "You do not really understand something unless you can explain it to your grandmother." We can and should do better.

Tsk tsk, that's far too simplistic a view of imformation, it is measured by

$-\sum _{x\in \mathbb {X} }p(x)\log p(x).$

;-) I must admit on having a look at it the lead immediately would be a put off for anyone not a maths graduate. I think the Multiplication article is a bit better but not by a long shot. Dmcq (talk) 16:44, 19 July 2012 (UTC)

Carry

The Computers section describes "carry". That should be called Arithmetic overflow with a reference to that. Perhaps some of the description of "carry" should be merged into the Arithmetic overflow article. Sam Tomato (talk) 16:35, 15 November 2012 (UTC)

Carries are also mentioned in section "Decimal system". It is very strange that this notion that is fundamental for the practice of addition is not clearly defined in this article, and there is no link to the relevant WP article carry (arithmetic). About your suggestion, note that "carry" and "overflow" are very different concepts: a carry is a piece of information that is kept to be used later in another place; carries are 0 or 1 when adding two numbers, but may be larger when adding several numbers of multiplying a number of several digits by a number of one digit. On the other hand, "overflows" occur because computer arithmetic deals with integers of a fixed number of digits; overflow occurs when the result may not be represented with the fixed number of digits. The fact that the overflow bit may be, and is, used to store carries in multiple precision addition is an interesting property; it does not makes the notions identical. Thus I am against the suggested merge. D.Lazard (talk) 18:34, 15 November 2012 (UTC)

Simple animation?

Animation of the equation balance analogy showing: addition, subtraction, negation, collecting like terms.

This article is cluttered with a million images, how about one animation for a simple equation? Probably not. Feel free to take or leave... M∧Ŝc²ħεИ_τlk 22:21, 18 May 2013 (UTC)

I took six semesters as a math major (admittedly, I didn't do that well), and I cannot figure out what this animation is supposed to be showing (maybe it's the flashing that makes it impossible for me -- I did not grow up on television or computer games). So, from my perspective, this would be a terrible "addition" to the article. 211.225.33.104 (talk) 03:56, 10 June 2013 (UTC)

Definition

The current lede says additionis the operation that "represents...." Is that correct, or is it the operation that "produces..." or "results in..."? Kdammers (talk) 09:29, 18 June 2013 (UTC)

I agree. Moreover the article continue with "It is signified by the plus sign ...", when "it is represented by ..." seems more appropriate. D.Lazard (talk) 09:47, 18 June 2013 (UTC)

Adding 0-10

The graphic about adding 0-10 has the numbers and colors in the legend in exact opposite order of their order on the graphic proper. This is confusing.Kdammers (talk) 13:08, 9 December 2013 (UTC)

modular addition

One or two examples of modular addition would be quite helpful. Kdammers (talk) 13:09, 9 December 2013 (UTC)

Patterns

When referring to association etc., the article says addition follows patterns. This sounds pretty loose. Wouldn't it be better to call them properties or laws (as I was taught in high school)?Kdammers (talk) 00:51, 4 July 2014 (UTC)

References

Is there a better way to source the references? I tried to find a source listed in a footnote on learning (#33). It was in fact listed under cognitive. Maybe this is the best place for this particular source, which has a number of references to it -- I don't know. But why make it hard to find for some-one coming from the educational aspect of addition? For all I know, there are other cases, mutatis mutandis.Kdammers (talk) 00:55, 4 July 2014 (UTC)

"Sum"

This usage of Sum (edit | talk | history | protect | delete | links | watch | logs | views) , a redirect, is under dispute. A prior discussion exists at Talk:Sum (disambiguation), however it is mostly proceeding in the edit summaries of "sum". -- 65.94.40.137 (talk) 11:05, 26 January 2015 (UTC)

Further discussion is occurring at talk:summation -- 65.94.40.137 (talk) 11:05, 26 January 2015 (UTC)

An editor has asked for a discussion to address the redirect Sum. Please participate in the redirect discussion if you have not already done so. 65.94.40.137 (talk) 08:31, 27 January 2015 (UTC)

symbols for four operations

AT the bottom of the article, there is a colorful box with symbols for the four operations. The problem is that both the plus and the multiplication signs are two line segments set at right angles, AND the plus sign is tilted, so that it looks almost like a multiplication sign. Can this be fixed/Kdammers (talk) 02:58, 9 January 2013 (UTC)

This problem still plagues the math pages.Kdammers (talk) 00:08, 6 March 2015 (UTC)

All the image signs are slightly rotated; I really don't think it will confuse anyone (especially with the + sign below the word "Addition"), but I can see your point and if you would like to make/find an image we can use instead of the current green + sign, go ahead. But your problem is with the template ({{Elementary arithmetic}}), not this article, so your comments might be more suited to Template talk:Elementary arithmetic. — Bilorv_(talk)^(c)(e) 13:15, 7 March 2015 (UTC)

addition on computers

I have removed the C code aimed to simulate hardware addition. Its explanation was placed too far from the piece of code for being useful. Moreover, this is too technical here, as the reader of this section is not supposed to be able to read C code. A pseudo-code version could be useful, for expliciting the algorithm, if the shift, OR and AND operation would be given with their full name (without any C abbreviation that may be cryptic for the layman). D.Lazard (talk) 13:35, 16 September 2015 (UTC)

Agree with the removal. In fact, even if it's in pseudo-code, I think Adder (electronics) would be a more appropriate home for this level of detail than Addition. Melchoir (talk) 18:42, 16 September 2015 (UTC)

5.5 Complex numbers

Quotation:

"Using the visualization of complex numbers in the complex plane, the addition has the following geometric interpretation: the sum of two complex numbers A and B, interpreted as points of the complex plane, is the point X obtained by building a parallelogram three of whose vertices are O, A and B. Equivalently, X is the point such that the triangles with vertices O, A, B, and X, B, A, are congruent."

It is not very comfortable to read this passage without any real visualization of these vertices O, A and B :( -- Andrew Krizhanovsky (talk) 14:57, 18 January 2016 (UTC)

But there is an image there: File:Vector Addition.svg. There are a few images in that section in quick succession, so the image may be a bit below section 5.5 on your screen, but it is there. Admittedly, it doesn't label O, A or B, but it does show the vector addition being described. — Bilorv_(talk)^(c)(e) 15:52, 18 January 2016 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Addition/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Potential GA candidate. Salix alba (talk) 19:14, 29 September 2006 (UTC) A longer lead would help, as would some broader context: history, education, society. Geometry guy 19:56, 9 June 2007 (UTC)

Last edited at 19:56, 9 June 2007 (UTC). Substituted at 06:41, 29 April 2016 (UTC)

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