Talk:Glossary of mathematical symbols/Archive 3

Restructuring finished$$$$
I have finished to replace table entries by glossary entries. Some work is still needed for including some symbols that were lacking in the preceding version and to improve the structuration in sections. This should be much easier than with the structuration in tables, because of the modularity allowed by glossary structure.

The hard part of this restructuring work was to find the information that was lacking (or badly provided) in the previous version, namely, for each symbol
 * An accurate short definition that allows an user who already know the symbol to retrieve its exact meaning
 * Links allowing beginners to find detailed desciptions of the meaning of a symbol and of the technical terms that are used in the short description
 * Syntax and semantics of the use of symbols, allowing distinguishing with different meaning. In particular, the meaning of an operator can generally be deduced from the nature of its arguments. This is why many descriptions start by "if $a$ and $b$ are ..., then ... denotes ...".
 * Indication whether the use of a symbol is standard, standard in a specific area of mathematics, common, or occasional. The marginal uses have been removed. It should be noted these indications are generally lacking in the relevant articles. Therefore, I have considered as marginal all uses that are mentioned in an article on a topic, but not used elsewhere in Wikipedia. Therefore some errors are possible. For example, Hadamard product mention notations $$\circ$$ and $$\odot$$ for the Hadamard product of matrices; after some search, it appears that $$\circ$$ is normally used for the Hadamard product of matrices, while $$\odot$$ is used for the Hadamard product of series (which has not a WP article).

Also, I have renamed the article as a "glossary", as this reflects better the content.

Finally, I have removed the use of Latin and Greek letters as symbols. For variables and numerical constants, these uses are the object of linked articles. There are so many uses of letters for denoting specific functions, that this can not described here, and requires a separate article, that, unfortunatly, is lacking. D.Lazard (talk) 11:15, 13 January 2021 (UTC)

Bourbaki dangerous bend symbol
I noticed this symbol when adding the Glossary to Mathematical notation (astounding that it was not already there in any incarnation). It doesn't really qualify as a mathematical symbol as defined in the opening sentence of this article but thought I should mention it "for completeness", as my high school maths teacher liked to say. --John Maynard Friedman (talk) 11:11, 14 January 2021 (UTC)
 * It can naturally be added in section "Abbreviation of English phrases and logical punctuation" where I have grouped symbols that do not appear normally in a formula. By the way, I am not sure of the best title of this section. Maybe, "Symbols that do not belong to formulas" could be better. D.Lazard (talk) 14:53, 14 January 2021 (UTC)
 * Yes, I think that title will work better, especially after you add the dangerous bend. --John Maynard Friedman (talk) 15:38, 14 January 2021 (UTC)

Mathematical symbols / glossary list
Shouldn't the last two items in the symbol column on the list NOT be identical, (both are shown as bar over X)? I believe the complex conjugate, (last entry) is bar over Z; although I was formally educated awhile back, I'd like to think I keep current. :-) Thank you for your attention in this matter, RM11 2601:645:201:F7B0:28C6:B898:5FB1:FD35 (talk) 16:01, 21 June 2021 (UTC)

Remove judgement on symbol usage
Can we change the phrase: "Often used improperly in plain text as an abbreviation of..." to something less judgmental such as "Often used in plain text as an abbreviation of..." AlastairL (talk) 02:00, 19 August 2021 (UTC) Alastair

Proposal to merge from List of mathematical symbols by subject
List of mathematical symbols by subject seems to have been spun off of this article / translated from the German circa 2014. It's meant to have a different classification scheme so readers can choose whichever one is easier. For better or worse, the lists have ended up with more or less the same classification scheme. This article has also been converted from table to glossary format. To avoid a lot of work converting to the other article, and because it does not seem to have achieved its intended purpose, I propose merging that article into this one. -- Beland (talk) 02:24, 10 January 2021 (UTC)
 * Strongly oppose merge: The article "List of mathematical symbols by subject" is meant to be a glossary. It does not define the terms and is not meant to define them. It is organized by subject because that makes navigating the article easier than say, one long list sorted by Unicode number. Its purpose is to list mathematical symbols and their LaTeX, Unicode, HTML, etc. code; it is not meant to define them. Similarly, this list of Latex/Unicode/HTML code would not fit well in a glossary because listing code is not the purpose of a glossary. That is why I strongly oppose the merge of "List of mathematical symbols by subject" into "Glossary of mathematical symbols".  Mgkrupa  16:55, 22 May 2021 (UTC)
 * Support move to Help: namespace: Let's be clear about the purpose that the article "List of mathematical symbols by subject" serves. It is meant to help people writing math formulas find the symbols that they need. It is meant to be used as a technical help/reference article. For this reason, I suggest that instead of a merge, this article be moved into Wikipedia's "Help:" namespace. That is: Mgkrupa  16:55, 22 May 2021 (UTC)


 * New Proposal: Move "List of mathematical symbols by subject" to "Help:List of mathematical symbols by subject".


 * Notice: BTW there is a debate about the proposed move to the Help: namespace here: Talk:List of mathematical symbols by subject. Mgkrupa  21:11, 23 May 2021 (UTC)


 * I support move to help space. Then each can link to the other and gives two ways of getting access to information. --John Maynard Friedman (talk) 19:18, 22 May 2021 (UTC)

Apart relation
The "apart relation" has been recently added by in. I have removed it for the following reasons: D.Lazard (talk) 15:05, 15 December 2021 (UTC)
 * Probable WP:OR: Google scholar does not provide any hit for this meaning of "apart relation".
 * WP:UNDUE: It seems that this notation is used only in one specific approach of constructive mathematics and proof theory. In other words, it is not standard, even in constructive mathematics. So mentioning it would give it a undue value to it.
 * WP:TECHNICAL: The notation has been added in a section aimed to be read by a very large audience, which ignores generally constructive mathematics.
 * Common sense: As many many symbols have ever been used in mathematics, only those that have been widely used have their place here. In other words, if a symbol is so rare that it cannot be used without being defined again, it is not useful here, since, if readers encounter it somewhere, it will certainly be accompanied by a definition or a link to a definition.


 * If you wish to keep constructive mathematics from this page, fine. Though you should probably consider a move to Glossary of common mathematical symbols.
 * But your incompetence at searching doesn't give you licence to shade fellow contributors. Good day. Paradoctor (talk) 15:45, 15 December 2021 (UTC)
 * OK, I confused "apart relation" and "apartness relation". So, I stroke the item "Probable WP:OR". However the other items remain. D.Lazard (talk) 08:59, 16 December 2021 (UTC)

Tables needed.
This page needs some serious cleaning. It needs tables with symbols in the left column and definitions in the right. I don't have time for it, but maybe the people who wrote this page would care to clean this disgusting mess up. 2604:CB00:536:C800:6087:66A1:26E1:EAF3 (talk) 15:51, 28 February 2022 (UTC)

Missing Definitions
"·" also represents the spinor. Since I came across this within the first few symbols, I have no doubt this list is absent many more definitions. Icm done with this page. Icm off to find a real website that has a proper list of symbols and definitions because I donct have time for this garbage. 2604:CB00:536:C800:6087:66A1:26E1:EAF3 (talk) 16:01, 28 February 2022 (UTC)

Is "
" truly sometimes used as the assignment operator? ==

In section "Equality, equivalence and similarity," the "==" is listed as one possible assignment operator in programming languages. Is this perhaps an error? I've always understood that "==" was created to make it clear that assignment is not intended, but rather equality testing. Should I "be bold" and correct this, or is there some language making very confusing use of "==" to denote assignment? — Preceding unsigned comment added by Dfgriggs (talk • contribs) 14:24, 24 March 2022 (UTC)
 * As far as I know, == is sometimes used to define/assign a function, but I cannot remember which programming language use it. However, as this is not mentioned in Assignment (computer science), I have removed it. D.Lazard (talk) 16:28, 24 March 2022 (UTC)

What are the different meanings of "≦" referenced in this article?
I had to laugh when I came to this page specifically to find out how else "≦" is used, other than as a synonym of "≤", and saw this single entry: "1. A rarely used synonym of ≤. Despite the easy confusion with ≤, some authors use it with a different meaning." The different meanings/usages need to be specified. It is fine to note that the other uses are not common, assuming that this is the original reason for omitting them from the page, but an encyclopedia entry should not say "and there's some other stuff we won't tell you about." Nodero (talk) 17:59, 27 March 2023 (UTC)


 * As far as I know, the other uses, if any, are generally author specific. As, apparently, no reliable source is available, I’ll edit the entry. D.Lazard (talk) 18:16, 27 March 2023 (UTC)

Under Set Theory "subset" and "proper subset" refer to the wrong definition number
I made my title a statement rather than a question, but I'm not entirely sure there is some other context I do not get here. The subset item refers to "second definition" which is actually the proper subset under set inclusion. I'm assuming this is just a mistake and it is meant to be the converse?

Dv-id.061 (talk) Dv-id.061 (talk) 16:06, 28 March 2023 (UTC)


 * I do not see any mistake: when $$\subset$$ means subset, one needs $$\subsetneq$$ for proper subsets, and when $$\subset$$ means proper subset, one needs $$\subseteq$$ for subset. It rather well known that teachers prefer often to use $$\subset$$ for proper subsets only, and professional mathematicians prefer to use $$\subset$$ for “proper or equal subset”. D.Lazard (talk) 17:15, 28 March 2023 (UTC)

Potentially confusing wikilink markup
The symbol is displayed as <. This is disturbingly similar to. No doubt there are many similar cases. It seems to me that we should do something to mitigate this problem. Suggestions? Such as unlinking the symbols and putting a explicit article tag on the next line? 𝕁𝕄𝔽 (talk) 16:34, 4 November 2023 (UTC)


 * On my browser (Safari on a laptop), the link is underligned only when hovered, similarly as for every wikilink. However, I understand that it may be confusing on some devices. By the way, I was not very happy of having different colors for the symbols. So I have implemented a variant of your suggestion for.
 * I suggest a similar change for all linked symbols, but, just now, I have not the time to do it myself. Could you do it (if you agree with the suggested format)? D.Lazard (talk) 17:50, 4 November 2023 (UTC)
 * That was using Chrome on Android and ChromeOS. I get the same using Firefox on Windows. Bing on Windows doesn't underline but changes the colour to light blue.
 * Ok, I will work through the article over the next few weeks. Hopefully others will join in. --𝕁𝕄𝔽 (talk) 18:33, 4 November 2023 (UTC)
 * I have done the Arithmetic operators section, please verify before I do any more. All fairly straightforward except the radical symbol, two instances. --𝕁𝕄𝔽 (talk) 20:33, 4 November 2023 (UTC)
 * Thanks. However the first argument of the template term is an anchor, and it is an error to systematically replace its value with "less", as you did. I have fixed this and improved two wikilink targets. D.Lazard (talk) 10:11, 5 November 2023 (UTC)
 * So that explains why I couldn't find the word less as a documented argument in template:term . Another case of Less is more, I suppose. I'll do another block and check back again. --𝕁𝕄𝔽 (talk) 10:48, 5 November 2023 (UTC)

Equality, equivalence and similarity
Section done. Three points to raise: Anything else? --𝕁𝕄𝔽 (talk) 12:11, 5 November 2023 (UTC)
 * I guess we can't do anything about it short of revising term but the identity symbols rendered in bold face are just smudges.
 * You might want to add a sentence on "triangle equals" to equals sign and move the anchor equals sign that I added, which just links to the list of Unicode code points. If it is enough to simply paste a copy of the definition from the Glossary, I can do that?
 * For ≈, I changed your "approximation" to the Unicode name "almost equal to". This area is a bit of a mess of nomenclature: Unicode has "Approximately equal to" and "Almost equal to" (see infobox) but the text says The approximately equals sign, ≈, was introduced by British mathematician Alfred Greenhill. Clarification needed?


 * Rendering of the "content=" parameter: My opinion is that special symbols must not be rendered in Unicode since they are poorly rendered or even not rendered at all on some browsers. Symbols that have the same rendering in raw html and inside math are such special symbols. So, in the case of a poor rendering with math, the best is to use latex in the "content" parameter.
 * IMO a link is useful inside the content parameter only if the target of the link contains some text about the symbol (not its mathematical meaning that must be linked in defn templates). A link to a list of Unicode symbols is not sufficient for being linked. This is the reason of my removal of links to "triangle equal" and "triangle def".
 * For ≈, the linked article is not about the symbol, but about its mathematical meaning. So, the link does not belong to the content parameter. Moreover, the given definition is misleading since it hides the fact that different authors use different symbols for this meaning.
 * D.Lazard (talk) 18:27, 5 November 2023 (UTC)

Progress review after four blocks done
This exercise is proving rather more time-consuming than either of us had anticipated. But reviewing the changes and your subsequent revisions, I think a reasonable conclusion and way forward is that I should only change those lines what begin with an underlined symbol. The result would be that the symbol is shown without an underline but is named, linked and thus underlined in the entry title. I'll do another block on that assumption and we can review again. --𝕁𝕄𝔽 (talk) 10:58, 10 November 2023 (UTC)
 * That was relatively painless. The only question arising from it would be that (in the Comparison section), I would have defaulting to making a link at $≤$ to less than or equal to in the entry header. I guess you decided that to do so would be redundant given that it is in the first line of the body? --𝕁𝕄𝔽 (talk) 11:23, 10 November 2023 (UTC)

This discussion began with the fact that some symbols were confusingly underlined. This came from the fact that some symbols were linked to articles on the symbol. It is recommended in Wikipedia to avoid linking symbols, when possible (just now, I does not have in mind the relevant page of the Manual of Style). The solution to the problem is to display in the templates term both the symbol and the common name of the symbol, and to link only the symbol name. However, this can only be done if the symbol has a commonly accepted name; otherwise, no name and no link must be provided. Also, the link to the mathematical article where the use of the symbol is defined must be in defn and not in term, since a symbol can have several very different uses.

We must not invent names for unnamed symbols, sine this would be WP:OR. The Unicode names of symbols are designed for the internal use of the Unicode system. A Unicode name is not an indication that the name is commonly used in mathematics. So, IMO, a Unicode name alone is not sufficient for linking a term. However, I am open to give somewhere the Unicode name, if the latex symbol is also given. For avoiding overbolding, this could be done with the format LaTeX: \approx   Unicode:U+2248 ≈ ALMOST EQUAL TO
 * LaTeX: \approx   Unicode:U+2248 ≈ ALMOST EQUAL TO

just before the other defns, which should be numbered even there is only one.

There needs further discussion and will require some work to be implemented. D.Lazard (talk) 14:24, 10 November 2023 (UTC)
 * Yes, I was coming to the same conclusion: for example, $≤$ has two meanings, only one of which is "less than or equal".
 * So let's return to where we started, which was to remove the underlines that are potentially confusing. That is easily achieved by unlinking them.
 * There is a separate question on whether we provide information about how to reproduce them and, despite WP:NOTGUIDE, I can see value in doing that. I can see that taking time and discussion (for example, I would prefer that we use unichar (thus, for your example, though I wouldn't defend including the html= given that mess! and perhaps to include the nlink= is maybe "leading the witness" by preselecting the target article. That would leave us with, which is your first suggestion without the shouting ). I like idea of providing the latex code sample, I think that will help a lot of neophytes.
 * As I think we have already dealt with the most egregious cases, would you prefer to suspend work on the change as it stands, until you have time to look at it properly? --𝕁𝕄𝔽 (talk) 15:08, 10 November 2023 (UTC)

I in List of mathematical symbols by subject and Glossary of mathematical symbols
in BOTH pages i do miss the 'I' for Irrational numbers, as i learned on school 85.149.83.125 (talk) 12:42, 13 August 2023 (UTC)
 * I cannot find any sources that use that notation; if it's a thing, it seems rare. It's also not mentioned on Irrational number. Are you sure you're not thinking of imaginary numbers? -- Beland (talk) 20:31, 24 August 2023 (UTC)
 * 85.149.83.125 is probably thinking of $$i$$ (so yes, imaginary numbers). --𝕁𝕄𝔽 (talk) 19:04, 26 October 2023 (UTC)
 * No, I think that the IP is thinking of $$\mathbb{I}$$ for the set of irrational numbers (that is, $$\R$$/$$\Q$$); that's a use I recognize from many years ago, and it seems that others do too: see this blog from 2007. If we can find reliable sources using this, then it's worth adding to the list too. Klbrain (talk) 14:56, 31 December 2023 (UTC)
 * A quick Google search for "set of irrational numbers" turns up multiple instances of $$\Q'$$ so not looking good for $$\mathbb{I}$$, sorry. --𝕁𝕄𝔽 (talk) 23:06, 21 March 2024 (UTC)

Replace box as placeholder symbol with dotted circle?
The convention in articles about diacritics is to use (as in this example: ). This article currently uses the box symbol □ as place holder, but the symbol has a given mathematical meaning (d'Alembert operator): might it be sensible to replace it with something innocuous? Would dotted circle fit the bill? 𝕁𝕄𝔽 (talk) 15:48, 8 December 2023 (UTC)


 * ✅ A dotted circle sounds reasonable to me. I don't think a dotted circle is used in mathematics, while a hollow box is. The note in the article '(here an actual box, not a placeholder)' would benefit. WhoAteMyButter  ( 🏔️talk │ ❄️contribs ) 16:23, 22 March 2024 (UTC)
 * We need a placeholder that can be rendered in latex. I do not know if this is possible for the dotted circle. If it is not possible I am strongly against the use of the dotted circle, which is a special symbol whose usage is discouraged in Wikipedia. D.Lazard (talk) 17:56, 22 March 2024 (UTC)
 * It is certainly not "strongly discouraged in Wikipedia", it is a standard and essential facility of unichar to demonstrate combining diacritics, used in hundreds of articles. The character exists in Unicode only to be an unambiguous place-holder, it should not be reused for anything else. So in theory, it would be ideal – but the fact that it is not in the LaTeX repertoire] kills the dead in its tracks. Pity.--𝕁𝕄𝔽 (talk) 18:21, 22 March 2024 (UTC)
 * For the record, the use of special Unicode symbols are not discouraged in articles on typography, diacritics and Unicode. But the use of special symbols are discouraged in other articles when they are not correctly rendered in all browsers and all fonts. See, for example, MOS:CURLY and MOS:BBB. D.Lazard (talk) 18:42, 22 March 2024 (UTC)
 * The VisualEditor's formula window tends to use lowercase a, b (and also x, y); see File:VisualEditor formula-en.png (a, b). May that be a starting point? Most readers are familiar with basic, single-letter variables as placeholders ($$ax^2$$, anyone?). WhoAteMyButter  ( 🏔️talk │ ❄️contribs ) 20:11, 22 March 2024 (UTC)
 * For not being confusing, one must use a placeholder that does not appear normally in any formula. I suggest $$\diamond$$ (\diamond) or $$\blacksquare$$ (\blacksquare), with a slight preference for $$\diamond.$$ D.Lazard (talk) 21:26, 22 March 2024 (UTC)
 * I feel as if that would confuse readers more, as I doubt anyone has encountered a $$\diamond$$ before as a placeholder (and would understand what it is trying to convey). A (albeit thin) black square $$\blacksquare$$ is also used as a tombstone.
 * Furthermore, some symbols are used with more than 1 variable (Leibniz's notation) so I feel that using 1 symbol across them would lead to confusion over seemingly identical variables. I'm not sure if using a, b, c across different symbols would lead to as much confusion. WhoAteMyButter  (🌷talk│🌻contribs) 21:42, 22 March 2024 (UTC)
 * In mathematics, a tombstone is never used inside a formula. So it does not matter if it appears here as placeholder. Also, a placeholder must not be confused with a variable. In particular, it must be clear in the introduction that a placeholder is used for marking the place of a variable or any mathematical expression, and several occurence of the same placeholder in a formula does not imply that it takes the place of the same expression (see ). As, in mathematics, lettters are used for variables, and two occurences of the same variable represent the same value, the use of variables as placeholders would be the best way for making the article confusing. Thus a placeholder must be a symbol that is never used in formulas. Dotted circle would be a good choice if it would exist in latex. So, if the placeholder must be changed, $$\diamond$$ seems the best choice ($$\blacksquare$$ would give too much visual emphasis to the placeholder). D.Lazard (talk) 22:22, 22 March 2024 (UTC)
 * That makes sense to me – I understand now. I'd support a diamond, then. WhoAteMyButter  (🌷talk│🌻contribs) 22:35, 22 March 2024 (UTC)

At a second thought, it seems less confusing to keep the square box as a placeholder. Firstly, it is already used commonly as a placeholder for unicode characters that cannot be displayed by the browser. So, its use should be less astonishing than the diamond for many readers. Secondly, the use of square box in mathematics is limited to the d'Alembert operator, which belongs to theoretical physics and more specifically to theory of relativity. So, one cannot encounter this symbol without a good mathematical background, and one may expect that readers with such a background would not search here for this symbol. D.Lazard (talk) 09:32, 23 March 2024 (UTC)
 * As OP, I must agree with D.Lazard's conclusion. A placeholder must be self-evidently "non-significant", which means that we can't choose our own convention arbitrarily. The only credible option is dotted circle which we can't use unless and until LaTeX adopts it. --𝕁𝕄𝔽 (talk) 14:18, 23 March 2024 (UTC)