# Wikipedia:Articles for deletion/Totient function/Proofs

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*The following discussion is an archived debate of the proposed deletion of the article below.***Please do not modify it.**Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was **keep**. **krimpet✽** 03:45, 16 December 2007 (UTC)

### Totient function/Proofs[edit]

AfDs for this article:

- Totient function/Proofs (edit | talk | history | protect | delete | links | watch | logs | views) – (View log)

Wikipedia is not a manual, guidebook, or textbook. See Policy Ra2007 (talk) 19:41, 10 December 2007 (UTC)

**Comment**: Also, Totient function/Proofs might be intended for Euler's totient function (in case concensus is keep/move). Ra2007 (talk) 20:18, 10 December 2007 (UTC)

**Comment**: How about converting the article to PDF and adding a link on the page for Euler's totient function -Zahlentheorie (talk) 22:21, 10 December 2007 (UTC)

**Keep**: Proofs of an important function are certainly worth keeping. -- Masterzora (talk) 23:28, 10 December 2007 (UTC)**Delete**: Transwikify to some other wiki project. Ra2007 (talk) 16:51, 11 December 2007 (UTC)

**Comment**: I really think making a PDF of the article and linking to it should make everybody happy. This is not difficult. And BTW, what other wiki project did you have in mind? -Zahlentheorie (talk) 19:15, 11 December 2007 (UTC)

**Delete**: Wikipedia is not a textbook. "It is not appropriate to create or edit articles which read as textbooks, with leading questions and step-by-step problem solutions as examples." I agree that it could be transferred to another wiki project. --SimpleParadox (talk) 20:20, 11 December 2007 (UTC)

**Comment**: These proofs do not "read as textbooks, with leading questions and step-by-step problem solutions as examples." In fact, I can understand a deletion if they did, but they don't. -- Masterzora (talk) 07:16, 12 December 2007 (UTC)**Reply**: The page addresses the reader directly using phrases like, "Next observe that" and "we get" and "as we saw earlier." Those are phrases used to teach a subject matter by building empathy with the reader. The leading questions may not be present on the page, but they are nonetheless being answered as if they were. As I said, the page is still worthy of being kept somewhere on wiki, just not on Wikipedia. Cheers. --SimpleParadox (talk) 17:48, 12 December 2007 (UTC)- See WP:TONE, which is about not using the first person in articles, but which states:
*"we" may be used in mathematical contexts.*See also We#Atypical uses of we for this use in mathematical proofs, which is absolutely standard usage also outside the teaching context – perhaps even more so. Take for example Andrew Wiles' celebrated proof (21MB!) of Fermat's Last Theorem. This is most definitely not teaching material, but it uses "*we*" all over the place. The very first example of a proof in our article on mathematical proofs also uses the word "we" in this way. --Lambiam 09:27, 15 December 2007 (UTC)

- See WP:TONE, which is about not using the first person in articles, but which states:
**Reply**: Proofs require some form of transitional phrases such as those. The fact that they also appear in textbooks doesn't mean anything at all. There is nothing about such phrases that is particularly textbookish. -- Masterzora (talk) 19:31, 12 December 2007 (UTC)**Reply**: I disagree. You should also consider the "original research" implications of this proof. Ra2007 (talk) 21:43, 13 December 2007 (UTC)**Reply**: What OR implications? Are you stating that the proofs are all original research? Even if we assume that someone did prove these specifically for the article, I have seen most of them in class and, if I had spare time, I'm relatively certain I could source the proofs. Even if they couldn't be sourced, I'm of the position that the verifiability his high enough to offset the OR-ness, anyway. -- Masterzora (talk) 00:11, 14 December 2007 (UTC)**Reply**: Is it unreasonable to assume that uncited proofs are original research? If not OR, cite them. And then, if cited, the proof becomes a wholesale quote. Encyclopedias do not have mathematical proofs, do they? If the proof is notable, describe it (after establishing notability with third party RS). Just my thoughts. As is, WP is not a publisher of original thought, manual, guidebook, or textbook. Guidebooks and how-to texts belong in Wikibooks, Recipes belong in Wikibooks. Ra2007 (talk) 16:46, 14 December 2007 (UTC)**Reply**: I think there are many cases to assume that uncited proofs are OR. Specifically, if it's something new or novel, it's probably OR. If it's older and nothing special, then I wouldn't say you're necessarily wrong to assume the author to have done the proof from scratch his or herself, but it's not bound to be original thought, nor something that they they just independently came up with. We can also cite it without quotes, easily enough. Find a source that uses the same method, cite that source with the current proof. Thus, it's not a direct quote, but it's still sourced. As for encyclopedias not having mathematical proofs: that argument doesn't make much sense to me. After all, encyclopedias don't have a lot things that Wikipedia does (and should) have. And, as I said before, I don't see how it fits into the category of "original thought, manual, guidebook, or textbook" material any more than something like absolute value or any of the other mathematical articles. -- Masterzora (talk) 21:36, 14 December 2007 (UTC)

- The behavior of the nominator, and "TableManners" and "SimpleParadox" is offensive. This is not good-faith participation in discussions. I do not contribute content to articles on how to do open heart surgery because I do not know anything about that. (I might fix a typo in such an article, or find the famous surgeon John Smith mentioned with no link to the article about him and add the link, etc., but I don't explain to the reader how to do surgery.) But those named here differ from me in that respect. Euclid's proof of the infinitude of primes, written in about 300 BC, is much celebrated, comprehensible to 15-year-olds, and very beautiful, and it would be strange to find an encyclopedia considering it unworthy of inclusion. Cantor's diagonal argument was a very unexpected advance, and considering it unworthy of inclusion in any encyclopedia would be profoundly weird. We have conventions on Wikipedia, long discussed by those knowledgeable in the subject concerning how to write and how to organize and how to title, articles on mathematical proofs. We have hundreds of articles devoted mainly to proofs. We have many thousands of articles containing mathematical proofs. People not familiar with those facts and who've never given them half a second's thought should not step in and lecture us condescendingly about these things as if we've never thought of them. Why was THIS particular "proofs" article chosen, rather than a policy discussion proposing deletion of ALL of them? People think I'm being rude by calling "illiterate" a person who thinks the only way to include a proof that has appeared in the literature is by copying it verbatim. That one could adapt such a proof to the level of the audience or background, while it remains the same proof, seems alien to this person. Could any fact be more obvious? To explain these things is to do remedial tutoring for weak undergraduates. They shouldn't be using this page to demand such tutoring. Michael Hardy (talk) 17:52, 15 December 2007 (UTC)

**Comment**: I see nothing in this proof that suggests problem-solution textbook-type material. It's a proof, not a lesson. Tparameter (talk) 01:33, 16 December 2007 (UTC)

**Keep**Mathematics without proofs is nothing. JRSpriggs (talk) 05:48, 15 December 2007 (UTC)**Keep**per JRSpriggs. What exactly is the objection to this article? I haven't been able to figure that out by reading everything above. Michael Hardy (talk) 05:52, 15 December 2007 (UTC)**Comment**If this is made into a PDF, then how will people edit it?? Michael Hardy (talk) 05:52, 15 December 2007 (UTC)**Comment**Why should we tolerate people who write things like "Encyclopedias do not contain mathematical proofs, do they?" asking to be treated with the same respect that good-faith participants in discussions like this are entitled to? That's wrong. We should consider banning that user. Michael Hardy (talk) 06:12, 15 December 2007 (UTC)

**Comment**Please cite a violation of Wikipedia policy by said user in support of banning him, or withdraw your statement. This article is about whether proofs of totient functions should be in Wikipedia. If a certain user uses fallacious logic, by all means criticize the logic. But please refrain from ad hominem attacks. Beetle B. (talk) 23:39, 15 December 2007 (UTC)

- Someone wrote above: "And then, if cited, the proof becomes a wholesale quote." Why do illiterates who write idiotic crap like this feel entitled to be treated with the same respect that honest people should get? That's just wrong. It is sickening to see the people who hang around the AfD discussions always feeling their entitled to push people around, when those they're pushing around differ from them in that they have some professional expertise in the subject matter and those feeling so entitled are illiterate and dishonest. Michael Hardy (talk) 06:17, 15 December 2007 (UTC)
- Ack, Michael, a user being misinformed or new to mathematics on wikipedia does not constitute a basis for banning said user. It is important not to bite new users in such a way. They are the lifeblood of the project. We all (well, most of us) made mistakes when we first arrived here; it would be a terrible thing if all of us were banned for out first error in judgment. —Cronholm
^{144}06:41, 15 December 2007 (UTC)

- Ack, Michael, a user being misinformed or new to mathematics on wikipedia does not constitute a basis for banning said user. It is important not to bite new users in such a way. They are the lifeblood of the project. We all (well, most of us) made mistakes when we first arrived here; it would be a terrible thing if all of us were banned for out first error in judgment. —Cronholm

**Keep**The nominator seems to be confused about the difference between a*textbook*and any piece of text containing proofs. I can see how reading this article can be very challenging, especially for those without mathematical training. However, the decision to banish all proofs from Wikipedia would be a major policy decision and could only be made after a careful consideration at the highest level. At present, the policies do not explicitly preclude proofs, and*de facto*, there are many other articles of this type. Arcfrk (talk) 07:22, 15 December 2007 (UTC)**Keep**. The "Wikipedia-is-NOT" argument does not apply here. This is not the kind of material you'd find in a manual, guidebook, or textbook. WikiProject Mathematics has created these articles named XXX/Proofs to keep the parent articles manageable and easier for people not interested in the proofs (see Wikipedia:WikiProject Mathematics/Proofs); merging all these back into the adjunct articles will not improve Wikipedia. --Lambiam 08:18, 15 December 2007 (UTC)**Keep**Nominator's reasoning fails to stand up to scrutiny. This article is not written like a textbook, and does not breach "NOT" Woody (talk) 10:25, 15 December 2007 (UTC)**Rename**as "Totient function identities". These are notable enough to deserve a separate article, but such an article needs to be properly named and properly written, like any other article.*Geometry guy*11:30, 15 December 2007 (UTC)transwikify to Scholarpedia. Sorry folks, but other stuff (proofs) exist on Wikipedia is not a good enough argument. TableManners (talk) 15:21, 15 December 2007 (UTC)**Speedy delete**- That "other stuff" that "exists", exists as a result of policies that have been discussed at length, calling for it to exist. "TableManners", your behavior is offensive. I do not add content on how to do open heart surgery because I know nothing about that subject. But you do. As seen above. Michael Hardy (talk) 17:35, 15 December 2007 (UTC)
- Please try and stay civil. People are allowed to disagree with one another. Woody (talk) 17:39, 15 December 2007 (UTC)
- I have no problem with people disagreeing with me. I find the behavior of the nominator and two of the discussants offensive. I've commented on this above and copied it onto their talk pages. Michael Hardy (talk) 17:57, 15 December 2007 (UTC)
- You've mentioned it a number of times, but have not indicated what is offensive about their comments. Yes, you disagree with them, but what offended you? Again, if there is inappropriate behavior at hand here, please cite Wikipedia policies that they are violating.Beetle B. (talk) 23:45, 15 December 2007 (UTC)
- My comments above, beginning with the words "The behavior of the nominator", says what offended me. What specifically do you find insufficient in that paragraph? Michael Hardy (talk) 03:16, 16 December 2007 (UTC)

- You've mentioned it a number of times, but have not indicated what is offensive about their comments. Yes, you disagree with them, but what offended you? Again, if there is inappropriate behavior at hand here, please cite Wikipedia policies that they are violating.Beetle B. (talk) 23:45, 15 December 2007 (UTC)

- I have no problem with people disagreeing with me. I find the behavior of the nominator and two of the discussants offensive. I've commented on this above and copied it onto their talk pages. Michael Hardy (talk) 17:57, 15 December 2007 (UTC)

- Please try and stay civil. People are allowed to disagree with one another. Woody (talk) 17:39, 15 December 2007 (UTC)

- That "other stuff" that "exists", exists as a result of policies that have been discussed at length, calling for it to exist. "TableManners", your behavior is offensive. I do not add content on how to do open heart surgery because I know nothing about that subject. But you do. As seen above. Michael Hardy (talk) 17:35, 15 December 2007 (UTC)
**Comment**. Most of the time proofs are not necessary in encyclopedic articles (there are a few exceptions though). It is preferable to have proofs in a subpage than in the main page, but this is a "sweep under the rug" strategy long-term. Ideally the proofs should be transferred to Wikibooks or some other place, but either way, eventually dedicated proof subpages will have to go. Oleg Alexandrov (talk) 17:48, 15 December 2007 (UTC)**Comment**a general comment on AfD's concerning such articles. i would second Salix Alba's comment [here] that it should be decided on a case by case basis. (so i disagree with Oleg's comment above.) to come to a sensible conclusion, or to have a valid reason to start a AfD in the first place, some kinda mathematical competence is required. otherwise one is likely to start making painfully ridiculous statements and suffer the wrath of Michael Hardy, :-). the question is whether the proof is sufficiently non-trivial to justify a subpage. just blindly quoting bureaucratic guidelines is really a bad way to go about this business. Mct mht (talk) 18:56, 15 December 2007 (UTC)

- A case-by-case discussion is good indeed. My point is that one can't stay in the Article name/Proofs framework forever. Articles worthy of keeping should stand on their own as independent articles (with a proper name), as suggested by Geometry guy. Others should be deleted. And one should think think very carefully when spending a lot of effort in creating new proofs subpages. Their value can be rather marginal. Oleg Alexandrov (talk) 21:27, 15 December 2007 (UTC)

**Keep/Rename**per Geometry Guy. There's no edict barring proofs from Wikipedia. Some encyclopedias don't contain proofs. Some don't contain animated GIF images. "This article contains proofs" is not a reasonable deletion rationale. --Cheeser1 (talk) 21:46, 15 December 2007 (UTC)

**Keep**as improvable to encyclopedic quality. In a very quick scan of the mathematics featured articles listed at Wikipedia:WikiProject Mathematics I did not notice any proofs. In other words, the articles like this one that are identified as 'proofs' aren't very good as articles, and the best articles usually don't contain proofs. I don't yet see this as blanket justification for deleting 'proof' articles. This one has room for improvement, so let it be improved. Decide in the future whether this is a dead end, and we can't improve articles like this one up to the standards of the best articles. I know that Cantor's diagonal argument is not yet featured, and it *does* contain sketches of proofs, and I think it's a good example of what can be done. EdJohnston (talk) 21:52, 15 December 2007 (UTC)

**Comment**. I agree with the case-by-case approach. Proofs are not inherently unencyclopedic, and there is great value in including them in Wikipedia: don't forget that Wikipedia is not paper and that Wikipedia's goal is to contain "the sum of all human knowledge" (subject to WP:NOT, WP:NOR and WP:V, of course, but proof articles only tend to violate these if they are not notable or are badly written). Proofs can be included in encyclopedia articles. They can also be separate articles, but such separate articles must be notable and coherent in their own right. (I see no reason to make them a general exception to WP:N.)

- The whole subpage experiment (now more than two years old) was an interesting experiment, but ultimately, these are articles, not subpages, and so must stand up as articles in their own right. Calling them subpages just leads to bad writing, in which the context and statement are not well explained. For example, this article uses the same notation for greatest common divisor as for ordered pair, but does not explain it. Other "/Proofs" articles are worse, whereas the "Proofs of X" articles are generally better, because they are more self-contained.
- My test is whether a reasonable article could be written if it were not regarded as a subpage (for one more time, mainspace subpages do not exist!). In this case, I think a reasonable article on "Totient function identities" could be written, so I say "Rename". In the case of the AfD for Boy's surface/Proofs, I don't see the case for an independent article, and so that content should be transwikied and/or merged, and the article deleted.
*Geometry guy*22:57, 15 December 2007 (UTC)

**Delete**. I feel only notable**proofs**should be kept in Wikipedia - not proofs of notable**theorems**. The proof of infinitude of primes is notable - it's often the first proof by contradiction many encounter. Cantor's proof is also notable (and again, may often be the first of its kind seen by students). Both of these may also have had a great deal of historical significance. The proofs provided in this article are in no way special. Yes, totient functions are important, which is why there is an article on them. The proofs of its various properties are just details. I agree that it should be transwikified - Wikibooks if there is a book on number theory being worked on there. Beetle B. (talk) 23:56, 15 December 2007 (UTC)

**Delete**the proof is incorrect. we need accurate proofs on wikipedia if at all.

**Delete**unless sources can be found for the notability of these proofs, and not just of the facts that they prove. I strongly disagree that proofs and proof articles have no place in Wikipedia; I think that proof that 22 over 7 exceeds π, for instance, is a fine article. But that article, in contrast to the present one, provides sources that attest to the notability of that specific proof, and has a name that makes it clear that it is an article about a proof rather than an appendix to some other article. Without such sources, I am having a difficult time justifying the continued existence of the totient proofs article. Little damage will be done to mathematics or Wikipedia by deleting the article; the facts in question will continue to have proofs that can be found in the number theory textbooks. It is plausible to suggest a merge, back to the totient function article, but the reason this sort of material was removed from the article in the first place remains valid: they clutter up the article making it difficult to read and even more difficult to find the important facts about totient functions among the unimportant details of exactly how to formulate the induction hypotheses etc. —David Eppstein (talk) 00:21, 16 December 2007 (UTC)

**Keep**per Michael Hardy per JRSpriggs. Proof of notable thing is good enough. Lack of substantial reason to delete exists as well. Tparameter (talk) 01:07, 16 December 2007 (UTC)

**Keep**because, as voiced above, the presence of proofs does not make something "a manual, guidebook, or textbook." The conventions of a field must be respected, if we wish to write in an encyclopedic manner. --Starwed (talk) 01:17, 16 December 2007 (UTC)

**Keep**As above, you can't have math without proofs. This does not make it "a manual, guidebook, or textbook." Kevin143 (talk) 01:35, 16 December 2007 (UTC)

**Keep**per Lambiam and Kevin143. CRGreathouse (t | c) 02:12, 16 December 2007 (UTC)

**Comment**I withdraw my opinion. In the future, I will ask Michael Hardy before I submit an opinion, mostly because I do not like being bullied. TableManners (talk) 02:37, 16 December 2007 (UTC)

- That
*I*do not like being bullied is why I wrote what I did. Michael Hardy (talk) 03:18, 16 December 2007 (UTC)

- That

*The above discussion is preserved as an archive of the debate.***Please do not modify it.**Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.