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 delete. There's a powerful argument here that there's no authoritative source for the use of this term in the math world. We need to be very careful to avoid putting our stamp of approval on things, because then *we* become the authoritative source, whether we like it or not. -- RoySmith (talk) 22:53, 10 September 2016 (UTC)[reply]

Cyclic function (edit | talk | history | protect | delete | links | watch | logs | views) – (View log · Stats)

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Non-notable mathematical term. The AoPS source is not reliable because it is a blog. GeoffreyT2000 (talk) 20:14, 19 August 2016 (UTC)[reply]

Note: This debate has been included in the list of Mathematics-related deletion discussions. North America¹⁰⁰⁰ 20:23, 19 August 2016 (UTC)[reply]

• Keep - Hit "scholar" in the list of links above and youwill find numerous academic papers discussing this term. Firkin Flying Fox (talk) 21:14, 19 August 2016 (UTC)[reply]

Nothing jumps out in those search engine hits as the subject of this article. Most of them seem to be incidental combinations of the words "cyclic" and "function". Sławomir Biały (talk) 00:48, 21 August 2016 (UTC)[reply]

• Merge to Iterated function#Abelian property and Iteration sequences. This topic occurs in a few different places on WP: Cyclic function, Cyclic order#Cyclic Functions, and Iterated function#Abelian property and Iteration sequences. My impression is that math and physics folk talk of iterated functions and periodic orbits, whereas computer science folk talk more of cyclic functions. The best content development and context for cyclic functions appears to be in the Iterated function#Abelian property and Iteration sequences section, so that would seem the best target for a merge. --Mark viking (talk) 23:43, 19 August 2016 (UTC)[reply]

  Comment. That doesn't seem a suitable redirect target to me. What is described at Iterated function#Abelian property and Iteration sequences only refers to the pointwise behaviour of functions, not to that of the iterated function. Take for example the permutation (bijection) on the positive integers whose decomposition in cycles is (1 2)(3 4 5)(6 7 8 9)... Let's call it π. Then for any positive integer i, the orbit i, π(i), π²(i), ... is a cycle. Yet π is not a cyclic function, since πⁿ(n²) ≠ n² for all n > 0. By the way, the section Cyclic Functions in the article Cyclic order was recently added by the creator of the article under discussion here. I've never encountered the term in the sense used here, and doubt that it is in significant use for this concept, so I'd be inclined to remove that section. For a very different meaning, see here.  --Lambiam 22:20, 20 August 2016 (UTC)[reply]

• Comment Whatever happens, the current "definition" seems to be somewhat original to me. There are many uses of "cyclic" in the literature, which range from just meaning a function that oscillates, such as sine, to meaning a multivariable function that takes the same value if the variables are shifted in a cyclic fashion. The AoPS source seems problematic, and I hope they do not become the next MathWorld in terms of making up original terminology. — Carl (CBM · talk) 22:53, 20 August 2016 (UTC)[reply]

Comment If the concept lacks a standard name, is that a reason why there should be no article about it? The article need to have some name. This is about functions that generate a finite cyclic group under the operation of composition. Michael Hardy (talk) 23:17, 21 August 2016 (UTC)[reply]

Yes, if it is not covered in any literature we can find, we shouldn't have an article on it. Otherwise we would have articles on all sorts of unremarkable mathematical topics. The general standard is that we should only have an article once there is enough interest in the literature to justify one. — Carl (CBM · talk) 23:33, 21 August 2016 (UTC)[reply]

• Comment The notion seems useful, but I don't think the name "cyclic function" is standard. I edited the article slightly but I don't know that it's enough to save it. - CRGreathouse (t | c) 05:34, 21 August 2016 (UTC)[reply]

Comment If the concept lacks a standard name, is that a reason why there should be no article about it? The article need to have some name. This is about functions that generate a finite cyclic group under the operation of composition. Michael Hardy (talk) 23:16, 21 August 2016 (UTC)[reply]

• Delete. Nonnotable concept. The concept would, at first sight, appear to be most of interest in discrete mathematics, in particular for functions on finite domains. But the latter are easily seen to coincide with the bijections. I can't think of any interesting properties (beyond being the generator of a finite cyclic group under composition, which by itself is a somewhat boring observation) that applies to these "cyclic functions" in general, which may go a long way to explaining why we can't find anything about them in the literature under any name.  --Lambiam 20:57, 23 August 2016 (UTC)[reply]
• Keep and modify as editors above have noted other definitions in sourced literature that should be mentioned. There is clearly no standard definition of the term, but one of an encyclopedia's main uses, especially in technical work, is to be a guide when something is encountered in a publication that doesn't give adequate context, such as for example in an isolated excerpt from the Bostock/Chandler textbook above. SamuelRiv (talk) 15:10, 25 August 2016 (UTC)[reply]

Well, there are a bunch of unrelated uses of the term. In many cases, these uses derive from the definitions of the English words "cyclic" and "function". That is a very poor basis for an article. If there are established "technical definitions" of the term, that requires sources, which I'm not certain exist. Sławomir Biały (talk) 15:54, 25 August 2016 (UTC)[reply]

Given that the original source is AoPS, the right place to look for sources would be in the math competition literature. I have a relevant book or two at home, I will try to remember to see if I can find anything there. --JBL (talk) 16:56, 25 August 2016 (UTC)[reply]

• Okay, I just found a decent reference. — Preceding unsigned comment added by Vivek378 (talk • contribs)
  • The issue is that this term seems to be made up by the Art of Problem Solving site, so pointing to a book by the same author doesn't show much. We had similar issues with MathWorld, which liked to make up terminology not used in the actual literature. If there is no source independent of AoPS that uses this term in this way, then I would view the article as a neologism, and so I would be in favor of deletion. I did some quick searching, but I could not find a reference apart from AoPS. — Carl (CBM · talk) 13:54, 28 August 2016 (UTC)[reply]
  • Well yes, but the people who wrote it are different. Besides, there is the meriam webster reference. — Preceding unsigned comment added by Vivek378 (talk • contribs) 01:39, 4 September 2016 (UTC)[reply]
• Delete, as per above: it doesn't seem to be notable, it seems to be the invention of a single person, with no other citations. More seriously though: no examples at all are given, aside from involutions. I can actually think of a pile of additional examples, all well known from the study of topological groups. However, these additional examples are "well known" or "obvious" or have famous, distinct names and theories of their own, e.g. cyclic groups. So, for this article: no theory is developed: what can one do with 'cyclic functions'? Do they have any interesting properties? Are they applied in any field of study? It sounds like an idiosyncratic invention with no depth to it. 67.198.37.16 (talk) 20:55, 28 August 2016 (UTC)[reply]
• Weak delete. I'm still not convinced there is a notable topic for an article here. The sources cited in the current article are clearly pretty marginal (an Art of Problem Solving blog post, a dictionary, and an entire book entitled "Intermediate algebra" also published by AoPS). Such sources alone do not establish notability. Even the most permissive criteria actually require independent sources, and we do not have suitably independent sources here. The chant of "Google it" turns up very little of relevance to the subject of this article. For example, one of the google hits refers to the "cyclic function of the kidneys". That has nothing whatsoever to do with the subject of this article. Many other Google and scholar hits are of this kind, or are incidental combinations of the words "cyclic" and "function". So, absent more solid and specific sourcing, I am inclined to vote delete. Sławomir Biały (talk) 11:51, 4 September 2016 (UTC)[reply]

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.