Talk:Fixed point (mathematics)

Pre- and postfixed points switched
Davey/Priestley are simply wrong™ on this. The earlier, better reference is Cousot&Cousot, 1979, http://www.di.ens.fr/~cousot/COUSOTpapers/publications.www/CousotCousot-PacJMath-82-1-1979.pdf, where the the prefixed and postfixed points are defined correctly™. Changed.

Requested move 8 April 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: not moved. Favonian (talk) 07:55, 30 April 2022 (UTC)

Fixed point (mathematics) → Fixed point of a function – An RM discussion was just closed with no consensus for the suggested WP:PRIMARYTOPIC title of for this article. However, the closer of that discussion also suggested further discussion of the article title, and I saw no expressions of support for the current article title in that discussion (e.g., due to ambiguity with Fixed-point arithmetic, an alternative to Floating point that is also a matter of mathematics). When the RM was closed, more than a month had passed by since I had suggested, and no one ever responded to that suggestion – even after I highlighted the suggestion in another comment directly about the lack of response after 12 days. The proposed title is more clear and also provides WP:NATURAL disambiguation. There was clear opposition to as the title. —&#8288;&#8202;&#8288;BarrelProof (talk) 21:50, 8 April 2022 (UTC) — Relisting.  Heart  (talk) 03:57, 16 April 2022 (UTC) — Relisting. Favonian (talk) 08:34, 23 April 2022 (UTC)
 * Support. When I saw the title my first thought was of Fixed-point arithmetic. YorkshireExpat (talk) 11:16, 16 April 2022 (UTC)
 * Oppose. Not every function has a fixed point.  The wording seems to suggest it does. Walrasiad (talk) 23:50, 21 April 2022 (UTC)
 * I don't see how that is implied at all. —&#8288;&#8202;&#8288;BarrelProof (talk) 18:29, 22 April 2022 (UTC)
 * Note: WikiProject Mathematics has been notified of this discussion. Favonian (talk) 08:34, 23 April 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Oppose. Disambiguation from Fixed-point arithmetic could be done with a hatnote, if the hyphen seems not sufficient. Moreover, fixed-point representation of numbers is not mathematics, but computer science. So, in this case, "(mathematics)" is not an incomplete disambiguation. On the other hand, "of a function" is a too restrictive for the following reason: in many cases, the fixed point that is searched is not a fixed point of the function under study, but a fixed point of an auxiliary function or process. For example, Newton's method for finding a zero of a function consists of searching a fixed point of an auxiliary function. In other cases, the fixed point that is considered is not the fixed point of a usual function, but it is a fixed point of a functional, that is a function on function spaces. In these two cases, "fixed point of a function" could confuse a non expert reader. D.Lazard (talk) 10:11, 23 April 2022 (UTC)
 * I think arithmetic, including fixed-point arithmetic, is clearly part of mathematics, although it can also be part of computer science. —&#8288;&#8202;&#8288;BarrelProof (talk) 00:48, 24 April 2022 (UTC)
 * Arithmetic is mathematics, but fixed-point arithmetic is a part of computer arithmetic, which is computer science. By the way, computer arithmetic is a well established subject, which lacks of a true article, instead of a redirect to a very narrow part of the subject. It is because computer arithmetic, floating point-arithmetic and fixed point arithmetic are not parts of (mathematical) arithmetic that a dab hatnote is useful. D.Lazard (talk) 07:35, 24 April 2022 (UTC)
 * Oppose. "Invariant point" is much more unusual language and should not be the title. "Fixed point of a function" is better but not optimal, since fixed point theory in functional analysis is often in context of operators and multifunctions, extending beyond the domain of functions. So I think hatnote would be best solution. Gumshoe2 (talk) 14:36, 24 April 2022 (UTC)
 * Oppose The current title seems the least bad out of all the suggestions made so far. XOR&#39;easter (talk) 19:51, 24 April 2022 (UTC)

Pre- and postfixed points switched back
I think the Smyth-Plotkin 1982 usage is more common than the Cousot-Cousot 1979 usage. They seem equally natural to me. — Preceding unsigned comment added by 147.188.201.12 (talk) 21:44, 21 July 2022 (UTC)


 * Well there is also Shamir's 1976 thesis which says a prefixedpoint is p ≤ f(p), and accompanying 1977 paper "The convergence of functions to fixedpoints of recursive definitions". The Cousot 1979 paper cites Shamir's paper so this is probably why they agree. There are still people using Shamir's definition, e.g. (cites Cousot) and  (probably copied from Wikipedia). In  Pitcher uses Shamir's definition and remarks "Warning: in [Gun92], [the post-fixed-point] is the definition of a pre-fixed-point." This implies that Pitcher considered both definitions and decided to use Shamir's definition, but unfortunately he doesn't explain why.
 * I guess I agree, overall prefixedpoint as f(p) ≤ p does indeed seem more common. But it would be nice to have a source which thoroughly compares the two definitions, however briefly, and comes to a conclusion. But Pitcher is not that source. --Mathnerd314159 (talk) 02:10, 22 July 2022 (UTC)
 * I should also mention Shamir's justification for his definition: a prefixedpoint is a function which is "almost" a fixedpoint, but is less defined. This "less defined" is similar to the meaning "before" of pre-. It is also similar to the use in preorder, which is almost a partial order but is not antisymmetric. In contrast the Smyth-Plotkin definition has no justification in that paper or in Davey-Priestley. Mathnerd314159 (talk) 03:31, 22 July 2022 (UTC)
 * Per the justification for the "modern" definition is that the location of the symbol f is before the inequality sign in the term “f (x) ≤ x”. Mathnerd314159 (talk) 05:11, 22 July 2022 (UTC)
 * The analogy to "preorder" is not helpful, as it works equally well for each usage of "prefixpoint". 147.188.201.13 (talk) 20:51, 23 July 2022 (UTC)
 * But well done for finding all these sources. 147.188.201.13 (talk) 20:52, 23 July 2022 (UTC)

Requested move 4 October 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: no consensus. (closed by non-admin page mover) — Ceso femmuin mbolgaig mbung, mellohi! (投稿) 20:04, 23 October 2022 (UTC)

– After my edits this article is about the usage of fixed points in a range of areas, such as math, computer science, and logic, with a brief mention of the physics definition, so it is not just about mathematics anymore and is more suited to be at Fixed point. Looking at the dab stats it seems that it is 50-50 fixed point (mathematics) and fixed-point arithmetic, so no help there in determining a primary topic. As argued in the previous RM though, the primary topic of the term "fixed point" is the sense described on this page. "Fixed-point" uses a dash, for one thing - looking at a dictionary they are clearly separate. Also, in terms of long-term significance, the usage in computers is relatively recent and niche, and the usage as a point that is fixed has been around for centuries and is still going strong in every high school math classroom. Also the close last time as no consensus seems pretty suspicious by my count - the only actual oppositions were No such user and BarrelProof who preferred moving to invariant point, and they were rebutted by eviolite and also opposed by Felix QW. So if this page doesn't become the primary topic then Wikipedia's RM process is just broken. Mathnerd314159 (talk) 04:09, 4 October 2022 (UTC) — Relisted.  P.I. Ellsworth &thinsp;, ed.  put'r there 10:32, 14 October 2022 (UTC)
 * Fixed point (mathematics) → Fixed point
 * Fixed point → Fixed point (disambiguation)
 * Oppose: sorry, I still think of Fixed-point arithmetic. YorkshireExpat (talk) 19:33, 4 October 2022 (UTC)
 * Per WP:NWFCTM it doesn't matter what you first think of. Mathnerd314159 (talk) 02:02, 6 October 2022 (UTC)
 * Well WP:5P5 to that. As someone with a fairly general technical education including maths, computer science, and physics, I regard myself as a well read layman in this topic, and don't think it's unreasonable that others would think the same way as me. YorkshireExpat (talk) 17:27, 6 October 2022 (UTC)
 * Oppose: The computing topic is not any more niche than topic in the analysis of mathematical functions. Computing may be a more recent topic, but computing seems unlikely to fade away in importance anytime soon. Any simple search will show that the computing terms "fixed point" and "floating point" are often not hyphenated in practice. If the dab stats are showing a 50-50 split in the selection between the two disambiguated topics, that indicates there is WP:NOPRIMARY topic and the dab page is doing its job of helping people find what they want when what they want is statistically unclear. —⁠ ⁠BarrelProof (talk) 23:02, 4 October 2022 (UTC)
 * Honestly I'm not sure what's up with the stats. Outside of WP, a simple Google Books search shows 52 out of 430 results with the computing usage. (At page 43 Google stopped matching text in books and just started recommending based on topic), confirming that the computing usage is quite niche. The standard definition was used in diverse areas such as fiction, astronomy, railways, and patents. It was even used in a computing magazine to describe computing square roots via iteration. Meanwhile the computing usage was used with.. well... computers. Similarly if we look at Ngrams and charitably assume that fixed point in the computing sense and floating point were used equally, subtracting that out the standard sense was only briefly below the computing sense around 1990 and since then it has rebounded to 3x the usage.
 * As well the hyphenation there is also the adjective-noun distinction - in the computing usage, fixed-point is always applied to a noun, so you get fixed-point signal processing, fixed-point arithmetic, fixed-point numbers, etc. In fact users use various names to get to the page such as fixed-precision arithmetic and fixed-point number. So FPA can't be a primary topic because it would be an incomplete title. (WP:TITLEPTM) Mathnerd314159 (talk) 03:08, 6 October 2022 (UTC)
 * Support As mentioned above and in the last Requested Move discussion, the computing use is differentiated by a hyphen and is a partial title match, since it is rarely used as an adjective outside of set phrases such as fixed-point arithmetic. Felix QW (talk) 19:17, 6 October 2022 (UTC)
 * This is the first non wiki link I get when I Google 'fixed point'. No hyphen. YorkshireExpat (talk) 21:12, 6 October 2022 (UTC)
 * Yeah, but that article also has obvious grammatical issues. "The use of fixed point data type is used widely in ..." Mathnerd314159 (talk) 21:32, 6 October 2022 (UTC)
 * Here is a real example: . This was on page 8 of Google Scholar results for "fixed point", quite buried. Most results were of course for the mathematical meaning, but all the fixed-point arithmetic results before then used the dash. Mathnerd314159 (talk) 21:42, 6 October 2022 (UTC)
 * Comment: I linked this discussion in Wikipedia talk:WikiProject Mathematics and Wikipedia talk:WikiProject Computing to hopefully get a wider variety of views. Mathnerd314159 (talk) 21:24, 6 October 2022 (UTC)
 * Support: Per WP:NOUN: "Fixed point" [of a function] is a noun, whereas in the computing sense, it is an incorrectly dehyphenated adjective with the real noun omitted (I see I am independently making the same point as Felix QW above). We should not be using titles in the sense of an adjective simply because it brings to mind a topic by suggestion.  There is no other topic that competes as a possible primary topic.  We should not be supporting what amounts to illiteracy on WP.  —Quondum 22:01, 6 October 2022 (UTC)
 * The grammatical accuracy of the page title(s) is not what's in dispute. It's what topic people expect to get when they type 'fixed point' into the search bar, and whether or not the extra click from the dab page is wasted or not. YorkshireExpat (talk) 16:58, 7 October 2022 (UTC)
 * That is what disambiguation hatnotes in articles are for, but rather what the primary topic is (and my argument here is that the arithmetic sense is disqualified). We should not use search bar behaviour to decide article titles.  Besides,the person looking for Fixed-point arithmetic gets an extra click either way.  The person looking for the fixed point of a function gets one less click if not sent via a dab page.  —Quondum 17:53, 7 October 2022 (UTC)
 * But there are more pages being dabbed. YorkshireExpat (talk) 18:17, 7 October 2022 (UTC)
 * The additional dab links seem pretty tangential, and can go through an extra click to get to the dab page. —Quondum 18:51, 7 October 2022 (UTC)
 * Maybe to you, but remember WP:NWFCTM ;) YorkshireExpat (talk) 08:32, 9 October 2022 (UTC)


 * Oppose. There is no primary topic, but I'd support some move since the current title can easily be confused with fixed-point arithmetic. Vpab15 (talk) 15:23, 12 October 2022 (UTC)
 * I'd propose fixed point (invariant) or also invariant point which was suggested in previous discussion. Vpab15 (talk) 15:25, 12 October 2022 (UTC)
 * Invariant point was also clearly rejected last time. Quoting: '"Invariant point" is far too rare for fixed points to be "commonly called" that for WP:NATURAL purposes.' Similarly invariant is too unusual a word to be used as a subject specifier for fixed point (invariant); it will just read like fixed point (*gibberish*). Mathnerd314159 (talk) 23:23, 15 October 2022 (UTC)
 * Support, though not very strongly. I can see there's good competition for the name but there is no stronger one for the precise name. In fact I'm a bit surprised a couple of other uses like in sci-fi aren't mentioned as well in the disambiguation.. I would not move it to a title like invariant point - that is simple not used anywhere nearly as much. NadVolum (talk) 11:47, 19 October 2022 (UTC)


 * Oppose - There is no clear WP:PRIMARYTOPIC here so Fixed point needs to remain a disambiguation page. Renaming Fixed point (mathematics) may be appropriate but I don't have any useful input to share on that.
 * ~Kvng (talk) 16:09, 22 October 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.