Talk:Whole number

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Integers and Whole Numbers[edit]

My son laugh a problem in his math homework that we are trying to figure out. It asks what the error is in the following statement: Jeff says that every whole number is an integer and that every integer is a whole number. Explain the error.Smcnell 03:40, 23 February 2006 (UTC)

"Because -1 is an integer but not a whole number." That's what I would write. --Ed Smilde
Every pig is a mammal but not every mammal is a pig --woot

1 is a whole number but the integers include the negatives i think and whole numbers do not — Preceding unsigned comment added by (talk) 09:08, 31 October 2015 (UTC)


If there's dispute in the mathematical world as to the meaning of "whole number", why do we present one view as correct? WP:NPOV, anyone? Proteus (Talk) 12:52, 1 June 2006 (UTC)


This Wikipedia page is completely screwed up. There's absolutely no dispute about the definition of a whole number. Whole number is an integer, which includes 0, all positive and all negative integers. Any decent book on math defines whole numbers in that manner.

There was a well-known dispute about whether 0 should be included into the definition of a 'natural' number. But there has never been a dispute about excluding negative integers from the definition of a 'whole' number.

whole number

whole number Mathematics. Any of the set of numbers including zero and all negative and positive multiples of 1.

Excerpted from The American Heritage Dictionary of the English Language, Third Edition Copyright © 1992 by Houghton Mifflin Company.

In my country, Canada, we are taught that whole numbers are 0, 1, 2, 3, ... so obviously there are different definitions out there, and hence "dispute".
The numbers you refer to are called integers. Why would we need another official name for the integers? 20:09, 23 October 2006 (UTC)
There is indeed disagreement. In my Irish primary school, the whole numbers were given as 0,1,2,3.... My mathematics dictionary (James & James) gives all three definitions, with 0,1,2,3,... as the first.--Malcohol 11:03, 25 October 2006 (UTC)

Not Screwed[edit]

The definition for whole number's just happens to be short. It's as simple as 0,1,2,3 etc. 20:46, 25 September 2006 (UTC)

Whole Numbers does not equal Natural numbers[edit]

This is high school stuff... —Preceding unsigned comment added by (talk) 06:18, 12 September 2007 (UTC)

Not everything they teach you in high school is necessarily the last word on the subject. Might as well get used to that early :-). --Trovatore 06:21, 12 September 2007 (UTC)
That depends on the author. H. A. Thurston in his book The Number System (1956) uses the term 'whole numbers' to mean natural numbers. -- (talk) 01:42, 24 April 2011 (UTC)
Thanks! —Preceding unsigned comment added by (talk) 23:19, 12 September 2007 (UTC)
Thanks for the reference. Chapter II of Thurston is titled "Whole Numbers": H.A. Thurston, The Number System, Blackie & Son Limited, 1956.
The Number System is available in a Dover edition.
-- (talk) 18:35, 7 October 2014 (UTC)

Whole numbers include 0, natural numbers don't[edit]

In primary school (United States) I was taught that there was a difference between Whole numbers, natural numbers, and integers. Natural numbers were {1, 2, ...}, whole numbers were {0, 1, 2, ...} and integers were {... -1, 0, 1, ...} - it seems like we should mention this distinction on this page unless it was unique to my education. Scott Ritchie (talk) 23:14, 24 November 2007 (UTC)

I agree. In elementary school I was taught Whole numbers = non negative intergers (0, 1, 2...); Natural numbers = positive intergers (1, 2, 3...). My daughter's text book shows exactly the same thing. Many others have testified the same on this page. Apparently these are the standard definitions taught in the US. Why its not mentioned on this page, I dont know. Surely there must exist a source confirming this. —Preceding unsigned comment added by Racerx11 (talkcontribs) 00:21, 18 August 2010 (UTC)
Oh, lots of sources. The problem is there are also lots of sources that contradict it.
This is the situation: Yes, primary/secondary-level math education in the United States uses the terms as you say, at least in my experience (there could certainly be exceptions somewhere).
Scholarly usage is different. Some mathematicians use the term natural number in a way that excludes zero; others, in a way that includes it. The term whole number is almost never used by mathematicians.
The writers of math texts for K-12 education in the United States seem to have picked one convention and stuck with it, in order to avoid confusing students unnecessarily, but here you see the downside of that choice — they've left their students unprepared to deal with the variety of conventions that occur in the literature.
In an encyclopedia article, it's not appropriate to favor the math-ed convention just to avoid confusion on the part of K-12 students. If anything we should gravitate towards scholarly usage, but as I've mentioned, there is no single convention in that environment either. So the best we can do is explain the situation, which is what this page is for. --Trovatore (talk) 18:50, 18 August 2010 (UTC)
Ok thanks, I understand. I should clarify I meant, "There must be a source confiming this is how US schools define whole number". My point is the situation isn't really explained. Could we put your explaination here as a lead in to the definitions listed in the article? I think it should be noted in the article that one convention is prefered by our education system and how "whole number" is a term rarely used by mathematicians. Its been suggested maybe this should just be a redirect to the natural numbers page, to a short paragragh explaining all this about whole numbers within the natural number article. As it stands now any reader visiting this page is going to be even more confused unless they happen to read the talk page to get the full story.Racerx11 (talk) 02:53, 19 August 2010 (UTC)
I guess that's not an entirely implausible solution. The problem with it is, when an editor links to whole number in some other article, he probably should really link to either natural number or integer instead; it's not likely that what he wants is a discussion of math ed in the United States. Wikipedia is not supposed to be a dictionary and I doubt that a discussion of the locution whole number is really very close to its mission. But I don't feel that strongly about it; a redirect to a section in natural number wouldn't be terrible. --Trovatore (talk) 08:58, 19 August 2010 (UTC)

A Whole Number Is...[edit]

A whole number is any non-negative integer, which includes 0. These numbers are whole numbers: 0, 1, 2, etc. —Preceding unsigned comment added by Jszivos (talkcontribs) 21:20, 9 November 2008 (UTC)

I agree with you and propose a revert from the current disambiguation page to the article at this version, as its consensus of references show that whole numbers mathematically have stood on their own as set W (the non-negative integers), distinct from the natural numbers N (the positive integers), and the integers Z (all integers). Who is with me? Prepare for dissent from Trovatore. — Preceding unsigned comment added by (talk) 19:28, 21 August 2012 (UTC)

Somewhat old response to both of you, but I have an idea to rectify the situation. From the reliable sources point of view, whole number might have reason to stand as an article. The version User: pointed out has reliable references and the bulk of which state "whole number" includes 0, 1, 2, 3 .... For the purposes of Wikipedia alone, this reason is enough to keep "whole number" as an article. The other alternative is to redirect to natural number and merge the content there, or to explain "whole number" and the related concepts there. (talk) 18:38, 30 August 2014 (UTC)
An actual article about "whole numbers" is the absolute worst possible solution. There is nothing whatsoever to say about whole numbers that isn't just talking about natural numbers (or integers, for those who use the term that way).
I am personally OK with a redirect to natural number. I think everything else can be explained at that article. However there's at least one contributor who doesn't think that gives enough prominence to the "integer" meaning. --Trovatore (talk) 02:46, 31 August 2014 (UTC)
natural number explains it sufficiently. We note that "whole number" is a synonym, and that should be sufficient. Any further discussion on "whole number" can be made on natural number including its use in nonscholarly literature. (talk) 20:09, 31 August 2014 (UTC)
That's fine with me. --Trovatore (talk) 21:42, 31 August 2014 (UTC)
I am going to post a note on talk:natural number for the implementation. (talk) 05:44, 1 September 2014 (UTC)

Should this article just be a redirect?[edit]

I've just removed duplicate reference to "nonnegative integer" and disambig template from the article. But what's left is almost nothing! Perhaps it should just be a redirect page. Mitch Ames (talk) 13:02, 25 February 2009 (UTC)

You shouldn't have removed these, because the term apparently is used in all these ways, which is the point of the disambig. I have reverted. --Trovatore (talk) 20:44, 25 February 2009 (UTC)
I added references to the article--in comments--showing the three ways "whole number" has been used by mathematicians. If people believe that references are OK on a disambiguation page, they can be incorporated into the visible text. If not, at least they will be seen by people who go to edit the article, and maybe there will be fewer back-and-forth changes to it.--BrianH123 (talk) 13:29, 19 June 2009 (UTC)

Explanation for the confusion[edit]

On the occasion of another edit today that mistakenly removed one of the three meanings, I thought I'd leave here my explanation of where they all come from. This is all conjecture.

Original meaning (presumably)

The straightforward meaning of the term is integer: A (real) number is "whole" if it doesn't involve any fractions, i.e. if it is one of the numbers ..., -2, -1, 0, 1, 2, ...

In schools: Since English has the more popular Latin word integer, the term whole number is redundant if used in this sense. In schools it makes sense to introduce only one word for integers, so whole number is not used in the sense of integer.

In research level mathematics: The literal German translation is ganze Zahl, which is the only German word for integer. This may contribute to the continued use of the word with this meaning in research level mathematics.

Most common meaning

The most common meaning seems to be that of non-negative numbers 0, 1, 2, ... There may be a French connection, since (according to Wikipedia) French uses the following terminology: entier relatif = integer, entier positif = non-negative integer, entier négatif = non-positive integer. With such a terminology it's not entirely clear whether whole / entier is understood to refer to all integers or just non-negative integers.

With the traditional definition of natural numbers as 1, 2, 3, ..., there was no simple term referring to 0, 1, 2, 3, ... So it makes sense to use one of the arguable French meanings of whole number and define them as the non-negative integers.

In schools: It seems that this is the standard definition in many English-speaking schools.

Positive integers

This meaning may be caused by mistranslations from French. The French word positif means non-negative, and plus grand que means greater than or equal. Interpreting positif incorrectly as positive, we get a definition of the whole numbers (entiers positifs, i.e. 0, 1, 2, ...) as 1, 2, 3, ... In connection with the version of the definition of natural numbers that includes 0, this fills an obvious gap in the terminology. This definitions seem to be rare.


One thing that is missing on this disambiguation page is usage advice. People want to find one definition here. If we present three they are unhappy. If we had sources supporting my conjectures, then we could prioritise the definitions and write something like this:

In school mathematics, a whole number is always a nonnegative integer, i.e. one of the numbers 0, 1, 2, ... In other contexts the term may also occur as a synonym for integer. [Footnote: According to a rare third definition, the whole numbers are the positive integers 1, 2, 3, ...]

This could perhaps be added to integer, and the present article be turned into a redirect. Hans Adler 22:41, 20 August 2009 (UTC)

The term "Whole Number" is a part of math learning.[edit]

Student textbooks for at least the last 4 decades in American education have used the term "Whole Number" on average in at least 5 grade levels. Usually from grade 4 through 8. Whereas the term "Natural Number" appears only in 9th and 11th grade materials. It is sad that writers for Wikipedia discredit it, by showing a lack of understanding what is really going on in the classroom.

Jim kelly

I was introduced to the terms "Whole Numbers"(0,1,2..) and "Natural Numbers"(1,2,3...) at the same time, well before the 9th grade. This was about 3 decades ago in a US school.Racerx11 (talk) 00:39, 18 August 2010 (UTC)
I assume it was your teacher who introduced the word "Natural Number", as I have been checking for the presents of 1,000 terms ("Natural Number" being one) in student's K-12th grade textbook series for at least 40 years (one of the functions of Do you remember the series being used?
Jim Kelly
Could you explain your point please? Perhaps you are trying to push one of the three meanings as the only "correct" one? If so, I have never seen any of the textbooks you are referring to, so I have no idea which of the three meanings you think is the correct one. If I were allowed to dictate the content of this article in order to unify terminology, I would define whole numbers as all integers, because that meaning is etymologically closest to the terms and it's also the correct translation ganze Zahl, the only term for integers in German.
Or perhaps you want the article to say something like the following? "In the US education system, the term whole number always refers to ..." That would be an excellent addition to this page, although (1) we would need a reference for that fact (not just to a textbook or syllabus defining the whole numbers in this way but to someone who says it's like that in the US), and (2) this kind of information is strictly not permitted on a disambiguation page per our formal guidelines. (Not that I would mind it, though.) Hans Adler 11:31, 7 September 2010 (UTC)
PS: Re-reading earlier discussions on this page, it now seems clear that you were referring to the definition of the whole numbers as 0,1,2,... . My comments in the section above this one still apply, especially under the heading "Conclusion". Give me the sources, and I will turn them into an article. But I can't write an article based on other people's personal experiences. In fact, I am not even allowed to do so based on my own. See WP:Verifiability. Hans Adler 11:39, 7 September 2010 (UTC)
Uh yeah not sure what happened. My comment above was directed at the user who initiated this section and that users comment is now gone. So to answer your question, no I dont have a point and therefore can't explain it. I was simply trying to help someone else. Do you know if you can pull up the edit history for talk page in order to retrieve the deleted post I was responding to? Otherwise I honestly can't remember precisely what I was talking about. I think the user was talking about when these concepts were introduced to math students and he seemed to somehow believe it was in the 9th or 10th grade for most students and maybe something about how this has changed over the years. I don't know why his original comment was deleted and the section he created remains.Racerx11 (talk) 16:34, 30 October 2010 (UTC)
I've restored the deleted material. Algebraist 16:46, 30 October 2010 (UTC)
Thank youRacerx11 (talk) 17:16, 30 October 2010 (UTC)
And to Hans Adler it appears that you were also refering to the same deleted material as I. Sorry I got really confused there for a while.Racerx11 (talk) 17:30, 30 October 2010 (UTC)

Usages among mathematicians seem to vary. Among mathematical logicians, the term "natural number" seems to mean "nonnegative integer" (thus including 0), but some others reserve the term for strictly positive integers. I think I've seen "whole number" used to mean "integer", thus including negative integers, but not including non-integers. Michael Hardy (talk) 21:16, 7 May 2011 (UTC)


Nobody of you three provided a solid reason for your reverts. Heck, you did not even provide any falsifiable reason why my edits were wrong! How can I argue with a person whose only argument is "I don't think that..." ? My text is based on references to books. Max Longint (talk) 00:22, 7 May 2011 (UTC)

No one is arguing against your content, and therefore the references are irrelevant. This is an organizational question, not a content dispute. The longstanding status, which seems to have reasonably wide acceptance, is that whole number is to be a disambig page, not an article. (Some would even like to make it into a redirect.) Disambig pages are navigational aids, not places to put content, no matter how well-referenced. --Trovatore (talk) 00:26, 7 May 2011 (UTC)

This is crazy logic. What is wikipedia but new content? How references are irrelevant? Since you refuse to dicsuss the content, you are nothing but a bully who has no respect to other contributors. And I no longer want to edit. Max Longint (talk) 00:30, 7 May 2011 (UTC)

No-one is bullying you. It was asked reasonably, given the WP:3RR policy, that you explain your editing, and develop a consensus. Mephtalk 00:37, 7 May 2011 (UTC)
I don't see what to explain. I don't know what is wrong with my text besides an unexplained refusal to accept it. Consensus requires dialog, not stonewalling. Max Longint (talk) 00:53, 7 May 2011 (UTC)
I think I have explained my position clearly, although not on this page. Let me rephrase it carefully here. The term whole number is used in different ways by different people, but in no case does it mean anything interestingly different from concepts treated elsewhere.
Specifically, it can mean positive integer, nonnegative integer, or simply integer. For the first two, we have the natural number article, whereas for the last one, we have integer. Any discussion of whole numbers themselves (as opposed to the phrase "whole number") belongs in those articles. The phrase "whole number" is not interesting enough to have an encyclopedia article about, WP not being a dictionary and all that. --Trovatore (talk) 01:30, 7 May 2011 (UTC)

I support this revision; it makes the point that there are three definitions without belaboring matters which are better treated at the linked articles (integer and so on). See WP:DISAMBIG for the style to follow. As for the references, having them in comments seems like a decent compromise in terms of being able to show to editors why this is a disambig without boring readers with references which are just about terminology. Kingdon (talk) 01:44, 7 May 2011 (UTC)

Wikipedia is an encyclopedia, not a dictionary. We organise our articles primarily by topics, not by terms that refer to them. Terms that can refer to several topics tend to be a problem. I don't have a big problem with Max Longint's changes, but we have a lot of bureaucracy fans who tend to go crazy if something in article space doesn't fall neatly in one of the three categories as (1) a proper article, (2) a disambiguation page, or (3) a redirect. Therefore any hybrid between a proper article and a disambiguation page, as proposed by Max Longint, is automatically unstable. We can't have yet another article on this topic, per WP:CFORK, so it must be a disambiguation page. Hans Adler 08:29, 7 May 2011 (UTC)

I'm by no means a bureaucracy fan, but I do indeed think that no middle ground can be tolerated between an article and a disambig page. They have completely different functions.
In any case I don't think that's the issue here; I think Max was trying to make it an article, not some middle-ground thing. My view is that it doesn't deserve an article. --Trovatore (talk) 11:01, 7 May 2011 (UTC)
Max Longint, I've just looked up my Collins English Dictionary which is usually quite a good guide to British and International English, and it gives the definition 1. an integer. 2. a natural number. I'd agree with most of the contributors on this page that both are wrong - it just shows how variable things are and that yes, maybe we don't want an encyclopedic article about it.
It's a shame that on one of your first edits you've run into both an exceptional article (disambiguation) and some of the more "robust" editors. Better luck on your next effort! Chris55 (talk) 14:36, 7 May 2011 (UTC)
Color me skeptical that Max is a new editor. If he actually is, then I probably should have approached some elements of the discussion differently. --Trovatore (talk) 20:57, 7 May 2011 (UTC)
[revised next morning] At a disambiguation page we should accept listings liberally. It is not the place for argument whether or demonstration that a particular listing is appropriate (although the disambiguation's Talk may be the place for that). So it really isn't the place for References.
There is scope for a disambiguation page to include a preface longer than the current one-liner and to include See also. In a manner of speaking, those features make a very moderate "hybrid" of a disambiguation and an article.
A hybrid page that is closer to a regular article may be useful, and remain valuable for years, but that shouldn't happen where numerous editors are willing and able, as here. Given the editors, something like the following should happen.
At one of the disambiguation target pages, normally one should be able to learn why that page is a target, so the ambiguous term should appear, and explicit discussion of its usage is appropriate. In particular, there should be some discussion at the target page if there is any evident issue whether the ambiguous term (eg, whole number) really is ambiguous in a way that fits the target (eg, integer). (If there is no discussion in the target page, check the target's Talk.) --P64 (talk) 19:32, 8 May 2011 (UTC)
This seems to be a normal case, so the ambiguous use of "whole number" should be covered, and perhaps sourced, in the target pages integer and natural number. —continued—
I was unable to work out what you were saying. The last paragraph was especially cryptic, I was unable to even parse it. Could you use simpler English please. Dmcq (talk) 20:36, 8 May 2011 (UTC)
Thanks. I have revised in a way that changes the order of the paragraphs too.
There is a serious problem here now: no proper target for "non-negative integers" or "positive integers". Both of those listings include piped links to Sign (mathematics) (which explains non-negative and positive without mention of whole numbers). Instead they should not be linked at all. I will rewrite them to make natural number the target for both.
Natural number does cover "whole number" succinctly in the lead paragraph, which does minimally satisfy one normal expectation of anyone who follows those two disambiguation links. (That lead paragraph is unusually redundant. Its revision may be in progress.)
At the moment there is no coverage of "whole number" at integer.
I wonder whether some pages should include a note on terminology as a separate section, perhaps just before See also. --P64 (talk) 15:57, 9 May 2011 (UTC)
I see, this disambiguation page should point to natural number instead of the section within sign. I hadn't noticed it was pointing at sign. That would cover the first two cases and has the exct same problems whole number has with zero. I'll go and change the disambiguation. Dmcq (talk) 16:13, 9 May 2011 (UTC)

Alternative version[edit]

[This is my version. I depart after two edit conflicts with Dmcq and suffering exceptionally slow service at this site.--P64 (talk) 16:34, 9 May 2011 (UTC)

Whole number is a term with inconsistent definitions by different authors. All distinguish whole numbers from fractions and numbers with fractional parts.

Whole numbers may refer to:

See History of natural numbers and the status of zero for some more information.

Seems okay to me. Much better than sending them to sign. Dmcq (talk) 17:33, 9 May 2011 (UTC)
Done. This replaces the entire visible content of the page. The long hidden comment remains, documenting all three uses.--P64 (talk) 13:40, 11 May 2011 (UTC)

Maybe an undefined but understood term![edit]

Most preschooler in certain English speaking societies know what a “whole dollar” is, not a “natural dollar” or an “integer dollar”. In those societies the words “whole number” is to arithmetic as the terms “point”, “line”, or “plane” is to geometry. Mathematics has an intuitive base, please respect the term “whole number”. It is necessary in the learning process. Jim Kelly

I'm really not sure what your point is. I gather that you would like to write an article about the term "whole number"? But Wikipedia is not a dictionary and does not exist to document terms. There are a few accepted exceptions for words considered to be particularly interesting phenomena as words (for example thou) but surely whole number does not fall in that category. --Trovatore (talk) 19:31, 2 October 2011 (UTC)


This term is not ambiguous, per WP:DABCONCEPT. To the contrary, there is apparently merely a dispute as to the actual meaning, but agreement that the term refers specifically to some set of integers. There is no set of disaparate classes of things (movies, albums, ships, people, planets) bearing the name. Rather, there is one type of thing bearing the name, with different ideas about the scope of that one type of thing. Perhaps it could be listed as an SIA, but the better practice would likely be to explain the dispute (whether live or merely historical) in the article itself, rather than leaving it to be found only by those who edit the page. bd2412 T 14:56, 24 May 2012 (UTC)

Seems ambiguous to me. Why should we have an article about it? Is there some source that says something useful about it as opposed to natural number or integer or do you think those two articles should be merged? Dmcq (talk) 15:10, 24 May 2012 (UTC)

It's good to check the article history before proposing this sort of change. The page used to be an article (although not a very good one): see this version. Then it was changed to a disambiguation page--diff, following discussion at Talk:Natural_number/Archive_1#Merge_whole_number_here. There's further discussion above, under the heading Reverts, which seems to end in consensus for keeping it as a disambiguation page. Jowa fan (talk) 02:14, 25 May 2012 (UTC)

I'm utterly opposed to making it an article; that's complete nonsense. However bd2412 does have somewhat of a point that it's not a classical disambig either. Has anyone considered possibly making it a Wiktionary redirect? That would (at least to some extent) address the needs of anyone who enters "whole number" into the search box. As for internal links to whole number, of course there should not be any; they should be changed to point to integer or natural number as the case may be. --Trovatore (talk) 02:21, 25 May 2012 (UTC)

By the way, I disagree that WP:DABCONCEPT is relevant. That guide talks about different instantiations of some "broad concept", such as a triangle center, where there are interestingly different ways of finding a point in a triangle that is in some sense central. But there is no "broad concept" here at all; some speakers are using whole number to mean one precise thing, and some to mean some other precise thing. It's purely a piece of nomenclature; no article can be written about it that is not essentially a dictionary entry. --Trovatore (talk) 02:37, 25 May 2012 (UTC)
I agree. My main concern is that I don't see any way to write an "article" on the topic without engaging in lots of original research and speculation. Each author has a particular convention, but they don't justify or explain it in a way that we could cite here, they just use it. — Carl (CBM · talk) 11:43, 25 May 2012 (UTC ::I say the error is that integers are whole numbers because not every integer is whole. For example, -11.8 is an integer but not a whole number

Cut the Gordian knot?[edit]

So right now we have three entries in the disambiguation table, each of which has a single bluelink, namely integers.

I have to say that seems a little silly. An awful lot more effort has been spent on this page than it's really worth.

So how about this simple alternative?

The reason not to redirect whole number straight to the section is that most occurrences of whole number in WP articles are most likely going to be talking about natural numbers, including 0. The correct target for that concept is simply natural number, not a discussion of terminological issues. (Ideally, no one would ever link to whole number at all, and that's probably the biggest downside of my proposal — as long as whole number is a disambig page, bots will notify you if you link to it, whereas if it were a redirect, they wouldn't.)

Thoughts? --Trovatore (talk) 04:53, 3 May 2014 (UTC)

The problem with simply redirecting to "natural number" is that "natural number" is never used to refer to negative integers, but there are respected mathematical authorities for whom "whole number" includes negative integers. See the hidden references on the edit page. I was the one who added the references back in 2006. I even had a discussion on the talk page in 2006 with someone who had your point of view until he saw the references. I originally added the references to the visible content of the page but was told that references shouldn't be on a disambiguation page, so I put them in comments. Because these references aren't visible until you go to edit the page, this topic keeps coming up. BrianH123 (talk) 23:07, 3 May 2014 (UTC)
Right, I know that usage exists, but I think it's a minority usage, and anyway I believe it's discussed at the section where I proposed to point the hatnote. --Trovatore (talk) 01:31, 4 May 2014 (UTC)
I think just the act of making this page a redirect to natural number tells the visitor (or strongly implies) that the two terms have the same meaning. The visitor would then have to read through six paragraphs of "History of Natural Numbers and the Status of Zero" to learn, in passing, that the term he was originally interested in, for many mathematicians, includes negative integers, which are definitely not part of the picture for natural numbers. As for "whole number" = "integer" being "minority usage", I don't know that anyone has ever conducted a survey, but my personal experience is probably in line with yours. I was always taught that "whole number" was a non-negative integer. But if we're interested in the common man's definition, at least one dictionary (Webster's Third New International) has only one definition, integer, and arguably, that should be the sole definition because "whole" in this context means no fractional part, and -123 has no fractional part just as surely as 123. Perhaps the reason we were taught that "whole number" is 0, 1, 2, 3, etc., is because the notion of fractions is introduced to children before the notion of negative numbers (if I recall correctly and if my education is representative, two big assumptions). If I had my way, this page would be turned from a disambiguation page into a short article with content similar to the Wolfram MathWorld article (hopefully not plagiarized, and leaving out the Z set terminology) and the references we have made visible. We would discourage growth of this page ("whole number" being more of a grade school term) and encourage the visitor to see the article on integers and natural numbers. As long as this is a disambiguation page and the references are hidden, we're going to have to live with these recurring discussions. I agree with you that too much time has been spent on this page, and I think the reason is because the evidence that there are three definitions in use by respected authorities is hidden unless you edit the page. BrianH123 (talk) 16:32, 4 May 2014 (UTC)
Well, my next preference would be a Wiktionary redirect, I guess. There is nothing mathematical to say about the locution whole number, and Wikipedia is not a dictionary, so I think an article, even a short one, is out of place here. --Trovatore (talk) 19:43, 4 May 2014 (UTC)

Redirect to natural number?[edit]

The calls for a redirect to natural number are many and varied. "whole number" and "natural number" are synonyms. It is stated on natural number that some "natural number" = integer in some definitions, resulting in "whole number" = integer in some instances. The current page is so simple it lists these definitions. Objections? (talk) 16:33, 29 August 2014 (UTC)

The page already links to natural number, so I do not understand what you are proposing. And natural number does not mean the same as integer under any definition I am aware of – an "integer" may be negative, a "natural number" may not. Maproom (talk) 06:18, 1 September 2014 (UTC)
I am proposing to redirect this article to natural number. At the end of 6th paragraph of natural number#History and the status of zero, it states "while others use it in a way that includes both 0 and the negative integers, as an equivalent of the term integer" with a reference. If you edit whole number, you will notice a number of references which use whole number as synonymous to integer. Per wikipedia policies, I dont think we should have 2 articles discussing the same topic. WP:CONTENTFORK may be relevant here. (talk) 17:06, 1 September 2014 (UTC)
I see. I hadn't realised that this was an article; I had mistaken it for a disambiguation page. In my view it ought to be a disambiguation page, referring the reader to natural number for positive-only and for non-negative uses of "whole number", and to integer for uses of "whole number" which may be negative. At present, it lists all three types of "whole number", but confusingly, all three are linked to integer. Maproom (talk) 07:16, 2 September 2014 (UTC)
References, though, are inconsistent in their usage. For the purposes of WP:RS, we have to document the use in reliable sources. We cannot use our own definitions. Lots of discussion on this topic are found in the above threads. One editor quoted that we cannot use our own observations due to WP:V. (talk) 17:09, 2 September 2014 (UTC)
@Maproom: You were right the first time; it's a disambiguation page. It's tagged as a disambig page, and it uses the disambig-page format.
It's just sort of a not-very-good disambiguation page, insofar as all three links point to the same place, and it's mostly the wrong place.
I don't quite agree with the statement that "we have to document the use in reliable sources", mainly because it assumes that we have to document the usage at all. Encyclopedias are for explaining their subject matter, not for documenting usage. However, it doesn't make much difference in practice, because I do think this usage should be documented, just that it doesn't justify having an actual article to document it — it can be worked in to articles that are not primarily about documenting usage.
I support the redirect to natural number, with the appropriate explanations at that page. --Trovatore (talk) 21:13, 2 September 2014 (UTC)
Coming from the natural number article, here.
This is a disambiguation page for an ambiguous term. That is how it should be according to WP policy. Redirecting this would be a bad idea, as "whole number" doesn't always mean "natural number". Also, this page does not actually link to natural number though it really should. I'm not sure who thought it was a good idea to have three links to integer, but frankly: It's kinda dumb. I apologize for my abruptness if anyone involved here is responsible for that, but I stand by my statement. Three links to integer, with no links to natural number or Sign_(mathematics)#Terminology_for_signs is not at all how this page should be. MjolnirPants Tell me all about it. 15:23, 3 September 2014 (UTC)
Sure, "whole number" doesn't always mean "natural number", just as much as "natural number" doesn't always mean "integer", though depending on the reference, it does. I don't see how this couldn't this page be redirected to "natural number", as they are used ambiguous and synonymous, when the only way out of this problem is to explain the usage on "natural number". On the contrary, this is a clear violation of WP:CONTENTFORK for these reasons. As to redirecting to Sign (mathematics), I would oppose it because "whole number" has much less to do with negative and positive values than natural number. (talk) 18:33, 3 September 2014 (UTC)
The proposal to redirect to natural number is a standard mechanism — see WP:PRIMARYREDIRECT. There is no violation of "WP policy". --Trovatore (talk) 18:39, 3 September 2014 (UTC)
Oh, you are quite right. Theres less of policy violation rather than policy execution. (talk) 18:51, 3 September 2014 (UTC)
@Trovatore: see WP:D, which says Disambiguation in Wikipedia is the process of resolving the conflicts that arise when a single term is ambiguous—when it refers to more than one topic covered by Wikipedia. So you're saying that "Whole number" is entirely synonymous with "natural number?" Because if not, a disambiguation page is called for by that passage (the opening sentence) of WP:D. The term "whole numbers" may refer to natural numbers (which can itself have one of two meanings, both of which are discussed on that page quite handily) or integers. That's the very meaning of disambiguation. The page as written now perfectly matches with this, it's just the linking which is wrong.
Also, to the IP editor: I never said this page should redirect to Sign (mathematics), I said it should link to it. Similar to the way the lead at natural number links to it; using it to provide definitional information in terms which don't have wikipedia articles, such as "non-negative integers". MjolnirPants Tell me all about it. 15:28, 4 September 2014 (UTC)
Not at all. I'm saying that natural number is the primary topic for the search term whole number, not the only meaning. In that case, the search term is supposed to redirect to the primary topic, with some provision at that article to resolve the ambiguity for anyone who has a different notion in mind, usually a hatnote. --Trovatore (talk) 18:35, 4 September 2014 (UTC)
I don't think it's ideal, because I've heard the term used to refer to negative numbers many times. However, I could live with it, as long as it's made clear that there is ambiguity to the term. MjolnirPants Tell me all about it. 18:45, 4 September 2014 (UTC)
Sign (mathematics) is not used as a link in natural number anywhere. natural number is synonymous to whole number per the following on natural number:

Likewise, some authors use the term whole number to mean a natural number including 0; some use it to mean a natural number excluding 0; while others use it in a way that includes both 0 and the negative integers, as an equivalent of the term integer.

— Weisstein, Eric W. "Counting Number". MathWorld. (talk) 08:05, 5 September 2014 (UTC)
1: Your quote flatly contradicts your claim and reinforces what I've said here. In fact, it is exactly what I said here, only re-phrased. Maybe you should have read it before copying and pasting it, because "X can means Y, Z or N," is obviously not the same thing as "X always means Y," especially when "Y sometimes means Y, and other times means Z," is true, but not stated here.
2: Natural number contains a link to non-negative in the phrase "non-negative integers," just as I originally posted. Non-negative is a redirect to Sign (mathematics)#Terminology for signs. MjolnirPants Tell me all about it. 13:13, 5 September 2014 (UTC)
I shall include the previous sentence:

The term counting number is also used to refer to the natural numbers (either including or excluding 0). Likewise, some authors use the term whole number to mean a natural number including 0; some use it to mean a natural number excluding 0; while others use it in a way that includes both 0 and the negative integers, as an equivalent of the term integer.

It states that a counting number is also used to refer to a natural number (synonymous). The next sentence starts with "likewise". This word "likewise" connects the term "whole number" to the previous idea explaining that the ideas in both sentences are analogous. The prose does not indicate "Y sometimes means Y, and other times means Z", nor does it differentiate "X can means Y, Z or N", but lastly, this isn't important as, as I have mentioned, we have many references which uses "whole number" in different definitions but consistent in the single paper being published. (talk) 18:13, 5 September 2014 (UTC)
It states that a counting number is also used to refer to a natural number (synonymous).
Synonymity is not the issue, exclusivity is. "Hare" is also used to refer to rabbits. "Cockroach" is also used to refer to palmetto bugs. "White" is also used to refer to Caucasian ancestry. "Cold blooded" is also used to refer to non empathic personalities. "Green" is also used to refer to cyan. "Round" is also used to refer to spherical (or cylindrical) objects. Just because a word is ambiguous doesn't make it synonymous with one of its uses. "Big" is exclusively synonymous with "large," because anytime you use the word "big," you could substitute it with "large" without changing the meaning. That is not true with "whole number" and "natural number," when -as your source admits- "whole number" may be used to refer to all integers, all non-negative integers, or all positive integers. That makes it an ambiguous term.
Finally, you need to scroll up and read my last response to Trovatore, because you're arguing (badly) for something I already agreed to, thereby accomplishing nothing beyond convincing me of your inability to argue well. MjolnirPants Tell me all about it. 22:06, 5 September 2014 (UTC)
No, no, there's no misinterpretation of the source. The definition of synonym is quite broad and narrow at the same time. Words are grey unlike the black and whiteness of math. (talk) 02:44, 6 September 2014 (UTC)
Who are you arguing with? It can't be me, because you're not responding to anything I've said, but something different. MjolnirPants Tell me all about it. 13:58, 8 September 2014 (UTC)

Redirect Target[edit]

Any change to this redirect's target should be discussed on this page before being made. This is a section in which such discussions can occur. MjolnirPants Tell me all about it. 01:03, 5 October 2014 (UTC)

I think we should go back to some version of the disambiguation. Whether the term refers to positive integers, non-negative integers, or all integers is genuinely ambiguous, and the reader is not well-served by a redirect to any of these locations. Sławomir Biały (talk) 14:42, 6 October 2014 (UTC)
I tend to agree, however the consensus the last time this was discussed was to redirect to natural number. As such, I'm content to let that stand until we can achieve a consensus for making this a disambiguation page. MjolnirPants Tell me all about it. 16:04, 6 October 2014 (UTC)

Discussion moved from Talk:Natural number[edit]

Ah why doesn't positive integers redirect to integers?

Ah, and why doesn't whole numbers redirect over there also, as there is a discussion of whole numbers there. Now MjolnirPants has sent me a talk note saying that whole numbers are unrelated to Integers. Can you or anyone else providing the reasoning that lead to this?

In reading the comments about whole numbers, here and elsewhere, I have noticed a couple of things. Firstly, you don't find the set of 'whole numbers' referred to in formal works, but in contrast it is common in lower grade texts.

'Whole' itself is used as a adjective to mean there is no fractional part. Hence if the adjective is applied before the number zero is taught, wholes are positive integers. If it is applied before negatives are taught, whole is non-negatives. Otherwise it is identical to integers.

The word integer itself is Latin from 'untouched' apparently thus undivided and whole. I.e. this concept of wholeness is central to integers, why not direct over there? And if not there, and there must be an explanation of school books etc, why not give it a wikipage. Why muddle the Natural numbers pages with a new issue concept of fraction and whole? Thomas Walker Lynch (talk) 13:12, 7 October 2014 (UTC)

Good points. "Whole number" is a grade school term. I doubt it needs an entire article to itself. And I also doubt we need an article on "positive integers".
The Peano Axioms you copies are the wrong Peano Axioms (they are Peano's Axioms, and only some of them). I'll try to fix it. Rick Norwood (talk) 15:08, 7 October 2014 (UTC)
Thanks, I don't see the modern list on the Peano's axioms page then? I liked their explanation of why zero is commonly included, as one needs an additive identity. Can that go somewhere? Thomas Walker Lynch (talk) 16:02, 7 October 2014 (UTC)
1. I most certainly did not say that whole numbers were unrelated to integers and the evidence is right there on your talk page of that. What I said was that 'natural number' is more closely related than 'integer'. I said this due to the fact that the integers include negative numbers, and there are few (if any) definitions of 'whole number' which include negative numbers. Please attempt to at least maintain the appearance of honesty and cooperation, I think you'd be surprised at how easy I am to get along with when you're behaving civilly and reasonably.
2. The redirect to this page was arrived at by a consensus. A single dissenting voice -even if it is your own- does not override that.
3. Redirects exist to help people find what they are searching for by allowing for a wide variety of article titles to link to a single page. In this case, "whole number" is indeed a grade school term that does not deserve its own article. There is an indexed article by that name because most people don't know more than grade school math and still use the term, and it is a redirect to this article precisely because it does not deserve its own article. The etymology and precise definitions of the words 'integer' and 'whole' are irrelevant. It is how the terms are used which is important here. So while the term 'whole number' may indeed at one point have been a synonym for 'integer', it is no longer used that way, and thus the redirect reflects current use.
4. If there is a discussion of the term elsewhere which you think is very useful, feel free to copy it here. I would suggest summarizing it and including it in the lead paragraph.
5. This discussion does not belong here. I created a section to discuss that redirect on the appropriate page: Talk:Whole number. I will give you enough time to read this before I move this whole discussion to the appropriate page. Please do not reply here, but on the page I linked to. I will happily refactor the combined discussion there. Again, all discussion of where Whole number should redirect to should be held on Talk:Whole number. MjolnirPants Tell me all about it. 15:30, 7 October 2014 (UTC)
Here I am asking why the positive integers redirect here. I was also curious to know your view on whole numbers not being related to integers. I didn't see that to be the same issue, but sure move it up if you like. I can see that.
Yeah, positive integer seems too small to be a page to itself. But whi is it not pointing to integer? Thomas Walker Lynch (talk) 15:50, 7 October 2014 (UTC)
As I have already explained once and will not explain again: I did not say that 'whole number' was not related to 'integer'. Read my response above, and read my initial comment on it if you still have trouble understanding this.
As far as the issue of what page to redirect to goes, there are three possible meanings of the term 'whole number':
  1. Non-negative integers.
  2. Positive integers.
  3. Integers.
Of those three, the first two are the most common usages. In my own experience, I have never seen 'whole number' used to refer to negative integers, but other editors have cited sources which purport to do so. The first two definitions are by far the most common, and Natural number covers both of those definitions. Therefore, it was decided by consensus to redirect to Natural number with a hat note that explained that 'whole number' redirects to that page, but could also refer to 'integer', along with a link to Integer. That was the most logical conclusion, given that there was no consensus to leave Whole number a disambiguation page.
My personal choice would be to make Whole number a disambiguation page, with three entries as shown above. The first two would link to Natural number and the last to Integer. Barring that, however, the current situation is ideal from where I sit. MjolnirPants Tell me all about it. 16:48, 7 October 2014 (UTC)
I agree with MjolnirPants. I am waiting for the extensive discussion at Talk:Natural_number to die down, in case anything relevant to this page develops there. Maproom (talk) 11:22, 10 October 2014 (UTC)