Talk:Glossary of mathematical symbols/Archive 2

Top versus transpose
Are these different symbols? Richard Pinch (talk) 13:59, 11 October 2008 (UTC)
 * I think so... top uses the down tack symbol (⊤), transpose uses the letter T. Alksentrs (talk) 14:08, 11 October 2008 (UTC)

Templates
I've been creating a template which I hope will make editing the table easier, if used.


 * The template: User:Alksentrs/Template:Row of table of mathematical symbols
 * A short test article: User:Alksentrs/Table of mathematical symbols (monolithic; using template)

Should this be used in the article? (After renaming it to something like Template:Row of table of mathematical symbols.)

Alksentrs (talk) 20:53, 15 October 2008 (UTC)


 * Does anybody care? Shall I just do it? Alksentrs (talk) 13:37, 25 October 2008 (UTC)


 * I think this is a useful suggestion -- so yes, be bold. --Daniel Mietchen (talk) 15:58, 25 October 2008 (UTC)


 * I've just finished the conversion (at last). Now we can think about messing with the template (rearranging columns, etc). Alksentrs (talk) 01:22, 22 November 2008 (UTC)

Euclidean Vector symbols
In the wikipedian article Euclidean_vector, the "Representation of a vector paragraph" shows the following symbols that are not mentioned in this table of mathematical symbols wikipedian article. Maybe a vector is not considered a "mathematical symbol"?
 * (...) A circle with a dot at its centre (Unicode U+2299 ⊙) indicates a vector pointing out of the front of the diagram, toward the viewer (...).
 * (...) A circle with a cross inscribed in it (Unicode U+2297 ⊗) indicates a vector pointing into and behind the diagram. (...)

Thanks for your attention. Maurice Carbonaro (talk) 11:38, 16 January 2009 (UTC)
 * This article is mostly limited to the symbols used in mathematical formulas. In Euclidean vector, ⊙ and ⊗ could be described as “mathematical symbols”, but for vector diagrams.
 * What do you mean by Maybe a vector is not considered a "mathematical symbol"? A vector is an object which combines a direction and a length. A symbol is just a picture which represents something. You can represent a vector with a symbol, but that won't make the vector into a symbol. Alksentrs (talk) 16:49, 16 January 2009 (UTC)

What is mathematics then?
Hi Alksentrs! thanks for answering me! That's a good point you made:
 * You can represent a vector with a symbol, but that won't make the vector into a symbol.

Well I wonder what do we universally mean for mathematics then... because in ancient ages mathematics was strictly connected with astrology and cosmology (please also see Astrology and astronomy article). According to the wikipedian article...:
 * (...)The word "mathematics" comes from the Greek μάθημα (máthēma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study".(...)

Talking about "learning", "studying" etc. we should then take a look to who was Pythagoras. According to the wikipedia article...:
 * '' Pythagoras of Samos (...); born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mystic and scientist;

Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC.''
 * (...) He was the first man to call himself a philosopher, or lover of wisdom. (...)
 * (...) In pythagorean cosmology it was used the monad symbol. Please take a look at right picture please. (...)

. Said that I noticed that there are astounding similarities with:
 * The sun symbol ([[Image:Sun symbol.svg|22px]]) which is considered a very important part of astrology.

And it could also be interesting to see the Circled dot and Sun cross wikipedia articles. Thanks for your attention. Maurice Carbonaro (talk) 11:09, 19 January 2009 (UTC)

symbols used in early 20th century quantum mechanics
Looking at Sources of Quantum Mechanics by B. L van der Waerden, there are symbols that I have not seen explained/interpreted: v with a single dot over it, p. 262 other letters with double dots over them

Somewhere we need to collect and explain these elements of discourse that may otherwise be or become unknown to readers. P0M (talk) 03:31, 30 May 2009 (UTC)
 * I found it. A single "dot accent" indicates the derivative with respect to time, so x-dot is the first derivative and it gives the x component of velocity. A double dot accent indicates the second derivative with respect to time, so x-dot is the x component of acceleration. It looks like this convention goes back to Newton. P0M (talk) 14:28, 30 May 2009 (UTC)

rowspan with template
Removed: replaced with divs because rowspan is annoying when selecting the text on it (it would go: name, explanation, example, row below name...) revert if there was a reason to have it (assuming not) -- 6Sixx (talk) 07:05, 11 June 2009 (UTC)

Dirac notation
I dispute the claim that the notation of <|> for an inner product originates in computer science. This is Dirac's notation, invented in the early 20th century. I am pretty confident that this precedes any computer science usage by a considerable interval. 128.223.231.9 (talk) 22:14, 31 July 2009 (UTC) Justin
 * The page doesn't claim that. The reference is just to show that the description (i.e. $$\langle\ |\ \rangle$$ is the inner product in Dirac notation) is true. Alksentrs (talk) 22:39, 31 July 2009 (UTC)
 * You are correct. The article does not necessarily claim the origin of the notation.  I also didn't take much care to distinguish between angle brackets and less-than/greater-than symbols ($$\langle\ |\ \rangle$$ rather than  < | >). I guess what I should have said is that I find this text a bit confusing:
 * "v〉 and (u"
 * If the statement regarding computer science is meant to apply only to inner product notation framed by less-than/greater-than symbols (which also commonly appears in physics documents typeset in HTML) perhaps this should be more carefully distinguished from the angle bracket form. If the two notations are considered synonymous then the phrase "are primarily from computer science" appears to imply one of two things; either that computer science is the primary source of this notation (i.e. that it originated in this field) or that it contains the primary usage of such notation (i.e. that it can be shown that this notation occurs with greater relative frequency in this field than in any other).  I find either implication a bit troubling without further support.  Wouldn't this be better avoided by simply saying "less-than and greater-than symbols are commonly used in computer science"?  71.236.215.87 (talk) 18:13, 4 August 2009 (UTC) Justin
 * I have removed from the symbol column, and have changed the wording slightly:
 * "As 〈 and 〉 can be hard to type, the more “keyboard friendly” forms are sometimes seen. These are avoided in mathematical texts."
 * This should be better. Alksentrs (talk) 00:37, 6 August 2009 (UTC)

Irrational's symbol
so ya see wat is irrational's symbol —Preceding unsigned comment added by 64.150.215.120 (talk) 22:59, 9 September 2009 (UTC)
 * There's no standard symbol for the set of irrational numbers. You could use $$\mathbb{I}$$, $$\mathbb{J}$$, $$\mathbb{Q}'$$ or $$\bar{\mathbb{Q}}$$, but make sure you state which notation you are using. Or just use $$\mathbb{R} \setminus \mathbb{Q}$$. Alksentrs (talk) 01:32, 28 September 2009 (UTC)

non-parallel
could someone please help me find the symbol for non-parallel, if there is one. —Preceding unsigned comment added by HawkE65 (talk • contribs) 10:19, 17 October 2009 (UTC)
 * "Not parallel" is probably something like $$\not\ \!\parallel $$ (a slash through a double vertical bar). Also, please add new sections at the end of talk pages, not the middle. Alksentrs (talk) 13:40, 17 October 2009 (UTC)

♯
Is ♯ really used for #? I've never seen that and it is not explained. Cheers, — sligocki (talk) 02:12, 4 December 2009 (UTC)
 * In mathematics and computer science, ♯ and # are often used interchangeably. I think # is more popular though, as it's easier to type. Alksentrs (talk) 03:29, 4 December 2009 (UTC)
 * Do you know of an example in which the sharp symbol is intentionally used? The only example I know of is actually the opposite, the C sharp programming language is usually spelled C#. Thanks, — sligocki (talk) 03:44, 4 December 2009 (UTC)
 * I believe a (19-century?) mathematician used ♯ and ♭ to mean maximum and minimum, but this didn't catch on. Alksentrs (talk) 04:18, 4 December 2009 (UTC)
 * But this article implies that ♯ is synonymous with # for cardinality and connected sum which I don't believe. Cheers, — sligocki (talk) 04:48, 4 December 2009 (UTC)
 * (Re: your [citation needed]s) When ⊃ is used instead of ⇒, I think it is describing the relationship between the associated models. That is, if $$\phi \Rightarrow \psi$$, $$\mathcal{M} \models \phi$$ and $$\mathcal{N} \models \psi$$, then $$\mathcal{M} \supset \mathcal{N}$$. Or something like that (I'm not a logician). Alksentrs (talk) 13:34, 4 December 2009 (UTC)

Shouldn't pi also have the value for pi? I.e., 3.141592653589793. . . ? Geometrian (talk) 03:25, 14 December 2009 (UTC)Geometrian
 * Originally, the article did have pi, but then it was removed (see and ), and recently a different meaning for π was added. Really, the meaning(s) of symbols like π, e, d, δ etc shouldn't be in this article, but be in the Greek letters used in mathematics and Roman letters used in mathematics articles. But, by this logic, we'd have to remove ℕ, ℤ, O, ∑, ∏, Δ, T, etc as well, so I'm not sure how strict this should be. Alksentrs (talk) 23:29, 15 December 2009 (UTC)

Common and Tex/HTML
"This is a listing of common symbols found within all branches of mathematics" Which it more or less is. However is the intention to give the universal or near universal uses? Or all uses? Or common uses? Because the article seems a little confused, mentioning Heyting algebra, but otherwise only talking about very large and general fields (in most cases almost equivalent in reality to "everywhere").

In terms of typography, the distinctions between HTML and TeX are doubtless important, this oes not seem to be the right article to bring them up.

Rich Farmbrough, 19:47, 14 December 2009 (UTC).
 * The intention is to give all uses. But to do so would probably require splitting the table up a bit. I added the TeX column for people using MSIE or with dodgy fonts installed. Alksentrs (talk) 23:39, 15 December 2009 (UTC)

Why is the equivalent symbol not here....???
Top half is omega and the bottom minus....???--222.64.27.154 (talk) 01:35, 20 March 2010 (UTC)

If this convention is replaced by a new standard, please show the history of the edition--222.64.27.154 (talk) 01:43, 20 March 2010 (UTC)
 * Its unicode U+224F &#x224f; see Unicode mathematical operators. I'm not sure if its very common in mondern mathematical notation, "≈" is more common see Approximation.--Salix (talk): 09:11, 20 March 2010 (UTC)

!congruence not included
negative of congruence is not included —Preceding unsigned comment added by Userdce (talk • contribs) 18:03, 19 June 2010 (UTC)

Add "action" to \cdot ?
It's rather common to denote any kind of actions by [latex]\cdot[\latex] (let it be group actions on spaces, ring/algebra actions on modules, or any other kind). Maybe this should be added? --Roman3 (talk) 10:06, 23 June 2010 (UTC)

Such That Symbol
Doesn't the symbol: ϶ also mean "such that" which I don't see listed?70.170.26.14 (talk) 08:09, 9 July 2010 (UTC)

TeX
A lot of people have complained about not being able to see the symbols; I created a test version of this article and of the row template in which both HTML and TeX can be used: User:Alksentrs/Table of mathematical symbols (testing). Should I use this in the main article? (The idea was stolen from the French version.)

PS: I can see every HTML symbol except ∧ (U+2227: Logical And, $$\and$$), which appears like this: ∘ (U+2218: Ring Operator, $${}^{^\circ}$$). Bizarrely, it does appear properly in the edit box. I'm using Firefox 3 on WinXP and have Code2001 installed (but the culprit may be “MS Reference Sans Serif”). Does anyone else have this problem?

Alksentrs (talk) 00:04, 27 November 2008 (UTC)


 * There was no response, so I'm adding a TeX column. Alksentrs (talk) 15:12, 5 December 2008 (UTC)


 * Finished. Comments? Alksentrs (talk) 16:25, 5 December 2008 (UTC)
 * Hello, I am from romanian wikipedia. Please tell me, is it obvious to add a column with TEX-CODE, or should I look elsewhere ?? Bogdan188.25.53.122 (talk) 20:52, 6 September 2010 (UTC)

I second that. Please include a column of TeX (or, better yet, LaTeX code).66.90.218.114 (talk) 03:30, 12 October 2010 (UTC)

ISO 31-11 standard
Should notations that adhere to the ISO 31-11 standard be mentioned specifically? I.e. mentioning that { ∣ } is a standardized notation while { : } is not. --BiT (talk) 23:08, 29 October 2010 (UTC)

Canonically isomorphic
The symbol "=" is - at least in algebraic and analytic geometry - often used to denote objects which are canonically isomorphic. I imagine the same is true in other disciplines which use algebraic objects as a tool of classification (e.g. cohomology groups in algebraic geometry), where the actual algebraic object in question doesn't matter as much as its isomorphism class.

One also quite regularly abuses "=" to mean isomorphic in the sense of manifolds (e.g. differential, complex, algebraic).

Actually, a fun article might be written about all the different ways in which the symbol "=" is abused. —Preceding unsigned comment added by 81.220.155.201 (talk) 22:37, 21 November 2010 (UTC)

Plus-Minus
The statement "x=7 and x=3" is false from the logical point of view and thus it should be changed into "x=7 or x=3". — Preceding unsigned comment added by Bcserna (talk • contribs) 14:12, 11 January 2011 (UTC)

This is the wrong place, but
Where do I go to talk about the MATH markup in the wiki? I simply can't get it to look nice, and I'm wondering if it's my browser, my markup, or something else. Maury Markowitz (talk) 19:55, 18 January 2011 (UTC)

Linking to pages about the symbol?
I propose we add links to pages about the symbols themselves, rather than just about the concepts they represent. This is both interesting, as well as helpful to learn more about the symbol itself and its origins. The HTML symbols themselves could easily be made into a link:
 * =

This would also help to alleviate the problem of people being unable to see the symbols, as most of the pages about symbols themselves have pictures of the symbol. A great many of the symbols do have pages exclusively about them. Scientific29 (talk) 22:12, 11 January 2011 (UTC)
 * Done! Thanks whoever did the first half!Scientific29 (talk) 04:48, 27 January 2011 (UTC)


 * How about making the first usage of any symbol on many or all mathematics articles an HTML version linking to that symbol's page? Or a link to its representation in this table?  I can't think of a good reason why most or all of the symbols used in the articles are non-hyperlink versions.

Requested move
Table of mathematical symbols → List of mathematical symbols — Per Manual of Style (stand-alone lists), the standard naming convention is List of ____. The change would also make it more consistent with List of logic symbols. --Cosmopolitan (talk) 04:32, 26 March 2011 (UTC)
 * Moved. Courcelles 02:15, 31 March 2011 (UTC)
 * Support: If we are not using the 'table' nomenclature anywhere else we should get rid of it here for consistency. –CWenger (talk) 17:22, 27 March 2011 (UTC)
 * Support: Alksentrs (talk) 13:23, 28 March 2011 (UTC)

Deletion of DeTeXify link.
If someone opens DeTeXify a JavaScript will be activated which will take 100% CPU power for Bitcoin mining. This is not something a visitor would expect and should probably be deleted or at least a warning should be included. 91.67.56.182 (talk) 18:32, 31 May 2011 (UTC)

After the German Blogger Felix von Leitner Blogged about DeTeXify and Bitcoin JS Miner, the Script was removed from the Site. But they might include the script again. --91.67.56.182 (talk) 12:05, 1 June 2011 (UTC)

Pedantry
Shouldn't multiplication use &sdot; sdot instead of &middot; middot?

183	middot	·	middle dot = Georgian comma = Greek middle dot

8901	sdot	⋅	dot operator

dot operator is NOT the same character as U+00B7 middle dot

http://www.htmlcodetutorial.com/characterentities_famsupp_69.html — Preceding unsigned comment added by 96.224.64.67 (talk) 16:15, 7 June 2011 (UTC)

Links to LaTeX commands
This page would be much more useful if there were also links to the related LaTeX commands in the LaTeX Wikibook! I cannot do it since I am unable to find many of the symbols in the Wikibook :-( — Preceding unsigned comment added by 131.212.12.225 (talk) 21:54, 30 July 2011 (UTC)

Tilde - please check on discussion on Tilde, Talk:Tilde pages
Hi. The Tilde article is currently internally contradictory regarding the meaning of ~ in mathematics, as discussed in Talk:Tilde. Could someone please check on this? Thanks! Allens (talk) 14:33, 5 November 2011 (UTC)
 * The article lists more than one meaning for the symbol. That's not the same as a "contradiction". Jowa fan (talk) 00:27, 6 November 2011 (UTC)
 * For the information of others - the difficulty isn't it meaning multiple things; it's that someone was claiming in the article that some of the established uses of ~, including ones specified in the article, were incorrect. Allens (talk) 02:28, 6 November 2011 (UTC)

Semidirect Product - strange symbol, not defined
"N ⋊φ H is the semidirect product of N (a normal subgroup) and H (a subgroup), with respect to φ." This last character before the period really confused me until I went into edit mode and saw the 'lowercase letter O overstruck with a vertical bar' ( which, by the way, is not defined in this list ). It looks totally different (albeit a little prettier) in most fonts, including Times New Roman and Arial; it looks normal (like a symbol I recognize) in Symbol and most monospaced fonts. Another argument for images rather than fonts? — Preceding unsigned comment added by AFbrat1972-MN (talk • contribs) 24 Nov 11
 * φ is the Greek letter phi. Alksentrs (talk) 15:20, 27 November 2011 (UTC)

Another use of the symbol #
See: http://en.wikipedia.org/wiki/Primorial. — Preceding unsigned comment added by Reddwarf2956 (talk • contribs) 14:44, 13 February 2012 (UTC)


 * Done (on 2012-03-03). — Quondum☏ 14:17, 9 April 2012 (UTC)

\bigcup
Needs an entry. -Stevertigo (t | c) 23:06, 27 May 2012 (UTC)

Criteria for order
How can Karp reduction be listed before addition? - Anonymous 190.31.128.203 (talk) 22:19, 4 April 2011 (UTC)

I agree. How the list is sorted must should be explicitly stated. — Preceding unsigned comment added by 80.99.93.173 (talk) 08:27, 4 July 2012 (UTC)

Phrasing
Possible phrasing issue at the not symbol... "A slash placed through another operator" — Preceding unsigned comment added by 129.78.32.21 (talk) 00:52, 6 September 2012 (UTC)

⊕ Overriding union
Overriding union, mentioned in the article on Functions, is missing. — Preceding unsigned comment added by 173.11.133.155 (talk) 17:40, 5 December 2012 (UTC)

Truth and Falsity symbols
⊤ and ⊥ mean "Truth" (or tautology) and "Falsity" (or contradiction) in logic. --AndreRD (talk) 15:47, 23 January 2013 (UTC)

Aloud
Some indication as to the way the symbols are read aloud should be given. — Preceding unsigned comment added by 46.65.2.139 (talk) 13:21, 18 March 2013 (UTC)

Edit request on 21 March 2013
The question mark symbol is also used for IF following a logic statement and the first option is true, second is false...  ? :

70.39.231.44 (talk) 18:00, 21 March 2013 (UTC)


 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made.. The fact that it's part of Java's syntax is not quite the same as saying that it's a mathematical symbol. Favonian (talk) 19:43, 31 March 2013 (UTC)

Many unicode mathematical symbols not covered in this article.
There are three sets of mathematical symbols contained in the Unicode character set. Presumably each of these characters had to have a justification presented to be accepted for inclusion in unicode. It would be nice if all of these symbols, with an explanation of their use, perhaps based on the unicode submission, were included in this article. I often need new symbols for my own use, and if an exiting symbol for that use exists I'd rather use that than invent something new; it would be nice if this article were a comprehensive list. FreeFlow99 (talk) 15:27, 2 April 2013 (UTC)
 * Mathematical operators and symbols in Unicode does show all the symbols without explanation. Unicode.org does give each symbol a specific name and use, but I've not found details of inclusion criteria. Some pages like Miscellaneous Technical (Unicode) do go into greater detail which might be an idea for the mathematical unicode pages, but it is quite a bit of work to do. --Salix (talk): 16:41, 2 April 2013 (UTC)

Special arrows missing
What about the arrow symbols meaning injection, surjection and bijection? — Preceding unsigned comment added by 2.33.16.227 (talk) 16:25, 13 August 2013 (UTC)

Suggested addition
I suggest that someone who knows how might want to add ≶, ≷, ⋚, and ⋛. Thanks. Duoduoduo (talk) 16:10, 31 October 2013 (UTC)
 * I would suggest that those aren't single symbols, although they are in TeX and UNICODE, but are shorthand for stacked cases. — Arthur Rubin  (talk) 21:13, 31 October 2013 (UTC)
 * But the list here already includes the stacked symbols ≤ and ≥. Duoduoduo (talk) 21:47, 31 October 2013 (UTC)
 * Those are stacked symbols, but they don't represented stacked cases. The usage:
 * A ≶ B if A&minus;1 ≷ B&minus;1
 * is shorthand for the two statements:
 * A < B if A&minus;1 > B&minus;1
 * A > B if A&minus;1 < B&minus;1.
 * There is no similar referent for ≤ or ≥. — Arthur Rubin  (talk) 22:01, 31 October 2013 (UTC)
 * I really don't care that much -- it was just a suggestion. But ≶, ≷, ⋚, and ⋛ are used not only for stacked cases, but also as either-or statements. For example, the expression for the slope of a curve can be followed by ⋚0 to show that it can be any of them depending on the parameters or the value of x. It doesn't have to be followed by "as" or "if". Duoduoduo (talk) 13:29, 1 November 2013 (UTC)
 * As another example, when a model is being specified the modeler can say "where the parameter a⋚0", to show that it is unrestricted on the real line, or "where the parameter a≶0 but not =0." Duoduoduo (talk) 13:48, 1 November 2013 (UTC)
 * Your first note is wrong: They are only used for stacked cases.  The second note is confusing; when it isn't used for stacked cases, "≶" should be replaced by "≠". — Arthur Rubin  (talk) 17:18, 1 November 2013 (UTC)


 * Occasionally (but admittedly seldom) in applied math contexts people use "a≶0 but not =0" when they are trying to emphasize the fact that a is not restricted in sign as much as the fact that it is non-zero. As for your comment Your first note is wrong: They are only used for stacked cases., that's wrong; perhaps you've never seen it, but in economics "⋚0." appears whenever a comparative static derivative, usually from an n×n system, is given explicitly in terms of a variety of parameters and it can be positive, negative, or zero depending on parameter combinations. In that context there's no point in saying "as ... ⋚ ,,," because that would simply repeat the same information. Duoduoduo (talk) 19:04, 1 November 2013 (UTC)
 * I'd like to see an example of use in economics, to see whether it is really a mathematical symbol which does not represent stacked cases. (As an aside, ≶ or ⋚ may make sense in cases of partial orderings, and might be used in Winning Ways, although it doesn't seem to be.  It does use the symbol that may look like. $$\vartriangleleft \shortmid$$ or $$< \!\shortparallel.$$ — Arthur Rubin  (talk) 03:52, 2 November 2013 (UTC)


 * Sorry I can't be of any help with references -- way back when I retired I trashed my entire collection of photocopied papers, and where I live now I have no access to a good library. Duoduoduo (talk) 17:34, 2 November 2013 (UTC)

Another "such that" symbol
I saw my math professor using this symbol for "such that": Link here — Preceding unsigned comment added by 31.147.119.182 (talk) 09:55, 8 November 2013 (UTC)
 * I can't say I've ever seen that. Ever seen it in a published paper?  — Arthur Rubin  (talk) 06:10, 9 November 2013 (UTC)
 * I see that the list already includes a similar symbol ∋ from mathematical logic with this meaning (which it says is declining in use). Perhaps it is a distortion of this? — Quondum 06:44, 9 November 2013 (UTC)
 * I've never seen it in a published paper. I've only seen it from that math professor, but she didn't explain that symbol, so maybe only she use it to distinguish it from ∋ (which can also mean "contains"), but its also possible that somebody else use it also (but until now, I didn't see other math professor using it). --31.147.105.41 (talk) 15:14, 10 November 2013 (UTC)

$$ \mathbb E$$ (capital E set)
I came across the symbol $$ \mathbb E[f(x)]$$ in another Wikipedia article on stochastic math, and came here to find it, but it was absent from the list. Could someone who knows what it means add it? Source: http://en.wikipedia.org/wiki/Stochastic_approximation 167.164.3.140 (talk) 13:47, 9 April 2012 (UTC)
 * $$ \mathbb E$$ (blackboard bold E) means expected value. Alksentrs (talk) 14:18, 15 April 2012 (UTC)
 * I have added it. - Letsbefiends (talk) 06:27, 23 November 2013 (UTC)

Switch TeX and HTML Columns
Some symbols shown in the HTML font are not immediately recognisable. To facilitate quick scrolling, I put forward that we should switch the columns. This may seem like a small difference, but for people with bad peripheral vision who scroll quickly, it makes a big difference.

Example: Try to find the product symbol, $$ \prod $$, quickly looking at the HTML column. It looks very much like other symbols, and not it all like it is usually represented in textbooks.

24.215.98.204 (talk) 10:13, 28 December 2013 (UTC)

Logical Mirror Symbols
All directed logical symbols can also be used in their mirror form. It is not only allowed for arithmetic such as "1 1" to use mirrors. But also for logic "swan -> white" and "white <- swan". Unicode, Tex etc.. has all the symbols for it. For a real life use of <- see for example here:

http://artint.info/html/ArtInt_128.html

More evidence is found in ISO 31-11:


 * ⇒ 	p ⇒ q 	implication sign 	if p then q; p implies q
 * Can also be written as q ⇐ p. Sometimes → is used.

https://en.wikipedia.org/wiki/ISO_31-11

Jan Burse (talk) 16:04, 29 December 2013 (UTC)

↯ for "contradiction"
The zigzag or lightning arrow, ↯, is used (also) as meaning "contradiction" in fairly many academic places, such as proofs on boards also slides, but also some printed/prepared material. The main fact is already stated in ↯. A book example is given in Proof by contradiction.

Various internet discussions show that there is some preference for the use of ↯:
 * http://tex.stackexchange.com/questions/28192/is-there-a-contradiction-symbol-in-some-font-somewhere
 * http://forums.xkcd.com/viewtopic.php?f=17&t=15928
 * http://math.stackexchange.com/questions/160039/contradiction-any-symbol-for
 * http://www.gamefaqs.com/boards/576216-maths-marathon/55021543
 * http://comments.gmane.org/gmane.editors.lyx.general/63920

I will shorly re-add the entry for ↯. — Preceding unsigned comment added by 157.181.98.186 (talk) 00:34, 9 January 2014 (UTC)

Incorrect / Superfluous use of := symbol?
In the section about summation symbol, the example $$\textstyle 1^2+2^2+3^2+4^2$$ is shown as equal by definition to $$::=1+4+9+16$$. I am assuming the two colons are a typo. Is equal to (=) not a more correct symbol here? I saw that it has been used in other examples also where it seems superfluous to me. So I might be wrong but I could not find clarity about its use. Is this by design? Poojac20 (talk) 23:10, 14 March 2014 (UTC)

Reorganize
I would like to propose reorganizing this list to make it easier for readers to find entries. At the very least I would separate letter-based symbols from the rest and alphabetize them. Preferably I would do a more elaborate taxonomy, as follows:


 * 1) Symmetric relations (=, etc.)
 * 2) Unsymmetric relations (<, >, etc.)
 * 3) Operators (+, etc.)
 * 4) Brackets ( [, ], etc.)
 * 5) Set theory (This is a natural grouping. I'd cross reference to here, e.g. union U, element-of E, from Latin letters, inclusion from unsymmetric relations)
 * 6) Other symbols
 * 7) Latin letter-like symbols (I would list e.g. dagger and the perp symbol under T)
 * 8) Hebrew and Greek letter-like symbols (e.g. co-product under Pi)
 * 9) Letter modifiers (a-bar, a-hat, etc.)

I'd also suggest adding a short list of basic symbols, say through high school math, at the beginning. As this is a major reorg and a lot of work, I'd like to get some consensus first. Comments?--agr (talk) 15:19, 14 July 2014 (UTC)


 * You might also consider an arrangement by subject, such as I did in de:Liste mathematischer Symbole. Best wishes, --Quartl (talk) 15:33, 14 July 2014 (UTC)


 * Yes: organization by subject makes sense, and I'd prefer this. One is usually looking for the meaning of a symbol within a subject area, and such a structure would make use of the table easier. There will be some duplication (same symbol used in multiple areas, with or without nuances specific to the subject area). —Quondum 16:43, 14 July 2014 (UTC)

It might be good to have two lists, one by subject and one by symbol type. The later, which could be made from what we already have, as I suggested, would be useful if one did not know what subject to look under. Sometimes one encounters in an article on one subject an unfamiliar symbol from a different subject. (What motivated me was the symbol E in the article on the Traveling salesman problem. I guessed it might be expected value, but I had to scroll to the very end of this article to confirm that.) For a List of mathematical symbols by subject article, it would be fairly easy to translate Quartl's very nice de:Liste mathematischer Symbole into English. The hard TeX and table stuff would not have to change at all. But I wonder if there are any MediaWiki or external tools that could make this a multilingual page?--agr (talk) 18:28, 14 July 2014 (UTC)


 * The proposed reorganization seems like an improvement, but I have this particular qualm: Some of the sections seem to be named after the _meaning_ of the symbols ("unsymmetric relations", etc.) and others after their typographical features (Greek letters, symbols with bars) etc. Having two different ways of classifying them --- by meanint, or by typography --- might make sense if if the whole set of symbols appears in both classifications.  But otherwise it seems rather infelicitous. Michael Hardy (talk) 18:36, 14 July 2014 (UTC)


 * Having just gone through this list to find a specific symbol (∑ to correct the above mentioned problem) I am in agreement that reorganization is needed. Organization by subject makes sense if the user knows the proper name of the subject in which the symbol appears. Some symbols are not tied to a specific subject, such as ∑, so how does a user know that they can find it in just about any subject? I think that any organization is going to need to have a great deal of redundancy (or at least internal links). I support the idea of having a short list of the more common symbols followed by subject specific symbols arranged by subject. Organization within these groupings is going to be problematic no matter how it is done if the sections have any length to them. I would tend to want to use a scheme that has already appeared in the literature, so that someone else can shoulder the blame when the complaints roll in. Bill Cherowitzo (talk) 18:49, 14 July 2014 (UTC)

I agree that if we have one list by subject, the other list should be entirely typographical. My thought with unsymmetric relations was that many symbols visually point to the right or left, e.g. > and < but also set inclusion, logical inference, etc. I think they make a grouping that would be easy to search through. Similarly there are a number of variations on the equals sign, that form a natural grouping, and so on. Here is a revised proposal:

This in addition to translating the German by-subject list.--agr (talk) 22:22, 14 July 2014 (UTC)
 * 1) Basic math symbols
 * 2) Symmetric symbols
 * 3) Symbols based on equality "="
 * 4) Symbols based on arithmetic operators (+, -, X, /)
 * 5) Other symmetric symbols
 * 6) Asymmetric symbols
 * 7) Symbols that point left or right (<, >, etc.)
 * 8) Other asymmetric symbols
 * 9) Brackets ( [, ], etc.)
 * 10) Symbols based on letters
 * 11) Latin letter-like symbols (I would list e.g. dagger and the perp symbol under T)
 * 12) Hebrew and Greek letter-like symbols (e.g. co-product under Pi)
 * 13) Letter modifiers (a-bar, a-hat, etc.)
 * I've started translating the German article as List of mathematical symbols by subject. Help welcome. Mostly it involves translating the interpretation for each entry and finding an appropriate article link to replace the German one. Translate one section at a time and perhaps start from the back so we don't work on the same entries. Proof reading of the translated portions is also welcome.--agr (talk) 04:32, 15 July 2014 (UTC)
 * Translation is now finished, but proofreading is still necessary. --Quartl (talk) 08:37, 15 July 2014 (UTC)
 * Wow! Thank you, that was a lot of work. I guess further discussion of the new article should move to its talk page.--agr (talk) 10:07, 15 July 2014 (UTC)

I've reorganized this article to separate the letter based symbols from the rest. I'll wait for any comments before reorganizing the rest of the symbols.--agr (talk) 16:33, 15 July 2014 (UTC)
 * I've completed the reorganization using a simplified version of the scheme I proposed. Proofing and comments welcome. --agr (talk) 14:15, 16 July 2014 (UTC)

Unclear intro sentences
The Intro says:


 * For example, depending on context, "≡" may represent congruence or a definition. Further, in mathematical logic, numerical equality is sometimes represented by "≡" instead of "=", with the latter representing equality of well-formed formulas.

The characters "≡" and "=" both display as equal signs on my browser (OS-X 10.9.4 Safari Version 7.0.5 (9537.77.4)). I'm not clear as to what was intended here. Anyone know?--agr (talk) 18:43, 27 July 2014 (UTC)


 * Probably your browser doesn't display the characters correctly. The first character is the triple bar while the second one is the standard equals sign. Best wishes, --Quartl (talk) 19:01, 28 July 2014 (UTC)
 * Thanks. The triple bar was too small on my browser. I made it bigger, " ≡ ", in the two sentences and added a link to triple bar. Let me know if it is too big on your browser. If so, maybe we should use TeX.--agr (talk) 20:29, 28 July 2014 (UTC)

Greater than or equal to or equal to or less than
Reading through a book and WTF do these symbols mean? Please add them to the article. http://i.imgur.com/7goZk5a.png — Preceding unsigned comment added by 96.224.66.189 (talk) 02:01, 21 October 2014 (UTC)


 * I wonder whether such a symbol is even standardized. There is a Unicode symbol (&#x2A8B; U+2A8B LESS-THAN ABOVE DOUBLE-LINE EQUAL ABOVE GREATER-THAN) re is a similar Unicode symbol (&#x22DA; U+22DA LESS-THAN EQUAL TO OR GREATER-THAN). Without a reference, I am not going to include it, but my guess is that the meaning of "$with π_{ij} &#x2A8B; 1⁄2 according as V_{i} &#x2A8B; V_{i}$" is a shorthand for less than in both cases, or equal in both cases, or greater than in both cases. —Quondum 03:28, 21 October 2014 (UTC)

ℸ
Hi! Over on Wiktionary, we're trying to figure out if ℸ has ever actually been used as a symbol for the "fourth transfinite cardinal". (See wikt:WT:RFV.) Our resident mathematicians haven't seen it used that way, but one of them suggested asking you folks. Have you ever heard of it? If so, I presume it could be added to this (WP) article. I've also posted this query to Talk:List of logic symbols. -sche (talk) 21:45, 22 February 2015 (UTC)

Wiki Math markup
A useful addition would be a column for the wiki markup to generate a specific symbol. Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:29, 12 April 2015 (UTC)

X bar
If I'm not mistaken, in programming logic a number with a horizontal line over it means 'not' of that number, similar to the use of the exclamation mark. —Preceding unsigned comment added by 124.150.95.62 (talk) 13:05, 12 April 2011 (UTC)

mathematical formulae of derivatives Bindas prem (talk) 03:23, 26 July 2015 (UTC)

Legendre/Jacobi symbol
I noticed that there is no entry for Legendre symbol/Jacobi symbol. If someone has the time to add it, feel free to do so.46.223.230.227 (talk) 00:06, 21 September 2015 (UTC)

Update HTML Column
As of HTML5 MathML is part of HTML. Consequently, one should update the HTML colum using MathML and use HTML5 standardconform notation. Feedback is very welcome. In that context I would like to make users aware that users can use MathML rendering even today, by selecting the MathML rendering mode. Also the reduction to only one row seems to be an option to me: For example Which looks like that to me https://www.dropbox.com/s/7e2h5lbrsmfqqbl/Screenshot%202015-11-08%2013.50.39.png?dl=0 --Physikerwelt (talk) 12:52, 8 November 2015 (UTC)

NTIME "k"
What does the "k" represent? I don't see it listed anywhere. Thanks.

NTIME

$$\mbox{NP} = \bigcup_{k\in\mathbb{N}} \mbox{NTIME}(n^k)$$

kencf0618 (talk) 15:08, 21 November 2015 (UTC)
 * It just the variable. In the union it will take every value. The Summation article describes this type of notation best. Here it will mean the union
 * $$\mbox{NTIME}(n^1) \cup \mbox{NTIME}(n^2) \cup \ldots$$
 * --Salix alba (talk): 15:53, 21 November 2015 (UTC)

⊑
I was looking for ⊑ in order theory, as used on Kleene fixed-point theorem. Wikipedia almost certainly requires more articles like the present one, but dedicated to specific areas of mathematics. Such articles will be of much assistance to students who are newcomers in the respective areas of mathematics. JMK (talk) 12:41, 6 January 2016 (UTC)

Wikipedia motto: we don't mind giving an explanation of any kind when reverting more than 5 hours of your work
I won't bother anymore with Wikipedia. The 5 1/2 hours I put on this table was to motivate people to write sleek looking HTML+CSS mathematical expressions, especially using the template. I had the intention of improving the already existing templates to facilitate writing HTML+CSS integrals. You don't even need to block the I.P., I'm not editing anymore for Wikipedia, ever. — Preceding unsigned comment added by 132.204.242.47 (talk) 00:40, 10 March 2016 (UTC)
 * I reverted your edits because I viewed this diff, which was enough to suggest you were vandalising the page. (eg - repetitive use of CSS, all caps, hidden notes embedded in templates, frownie faces, ...) Wiki text should not generally contain CSS, and articles should not contain any of these elements. I didn't inspect the style changes, which may or may not be productive edits. (A cursory inspection of your changes to the integral entry seems like an improvement, at least on my desktop browser.) My suggestion to you: revert my edit, but prune the commentary. Mind  matrix  02:28, 10 March 2016 (UTC)


 * Most of my time was spent on doing grunt work on the page, i.e. clean up the inconsistent spacings and alignment of the [wikitables] wikitext (a very time consuming and boring task: am I too obsessive about clean wikitext...?). Is that something that Wikipedia wants to be done, since it is only visible in the wikitext, not on the rendered page?


 * What I would like to see on Wikipedia is beautifully rendered HTML+CSS (with templates only; thus not requiring JavaScript to be enabled on the browser, as is the case with MathJax, which converts the LaTeX code into HTML+CSS via JavaScript, and has the annoying flash of unstyled content issue) [inline text] style mathematics, since the LaTeX rendered PNG images don't look that great for inline mathematics (e.g. vertical alignment is often wrong, the PNG images too obviously look like that have been badly spliced into the text...), though LaTeX rendered PNG images work well for display math.


 * To produce beautifully rendered HTML+CSS, it is necessary to use a lot of CSS (for positioning, kerning, fine control of spacings, font-size and what not...) For example, look at the examples on the template: the only way to make the mathematics look sleek is to firstly (and consistently) use the  template (which should be used thoughout Wikipedia for all [inline] text style mathematics) and then to use a dollop of CSS in the  template (which I was tentatively trying to figure out for the integrals on this page, before trying to improve the code of the  template, after which I could just remove the added CSS that was needed to sleekly render the integrals on this list). Also, when the purpose of some wikitext in a template is not obvious, I consider it good practice to add comments (what you refer as "hidden notes embedded in templates" I guess...) for the benefit of ulterior editors. I understand that commentaries don't belong on article pages (only on templates). Should I try to improve the  template? Of course, I would need to log on for that!


 * P.S.: I never use ALL CAPS (ouch!) or frownie faces... (Oops! Sorry I did use a frownie in a comment... which I rarely do! No more.)


 * Also, would it be too much of a burden on the server if the whole list used the template throughout? — Preceding unsigned comment added by 132.204.181.137 (talk • contribs)


 * I will do as you suggested: "revert my edit, but prune the commentary." (And I will also remove the CSS that I used to improve the presentation of the integrals.) (And, if you have no objection, I will sprinkle some CSS in the template to make the integrals look nicer.) Thanks. — Preceding unsigned comment added by 132.204.181.137 (talk • contribs)
 * I haven't been involved with the development of that template. Perhaps you can ask on the template's talk page, or at Wikipedia talk:WikiProject Mathematics. Mind  matrix  20:43, 11 March 2016 (UTC)


 * You may want to review Manual of Style/Mathematics, Rendering math, and maybe Help:Displaying a formula. You may also want to start a discussion at Wikipedia talk:WikiProject Mathematics regarding your typesetting ideas, which will likely elicit input from a broader spectrum of editors interested in mathematics articles. Mind  matrix  20:43, 11 March 2016 (UTC)


 * I brought back my edits, then I meticulously pruned my comments and CSS that you wanted me to remove from my edits. I then added all the edits from Hppavilion1. Thanks. — Preceding unsigned comment added by 132.204.243.88 (talk) 19:54, 12 March 2016 (UTC)


 * Suggestion for the template: Template talk:Intmath/doc. &mdash; Tentacles✉ mailto:Tentacles 22:53, 13 March 2016 (UTC)


 * Look at the beautiful integral symbols in font-family: 'Lucida Sans Unicode';! If only we could rely on the font being installed on the user's computer... &mdash; Tentacles✉ mailto:Tentacles 20:30, 15 March 2016 (UTC)

Cross and dot products in the "basic" section
While looking through the list I was surprised to see that the dot product is mentioned in the 'basic symbols' table grouped with other multiplication-related symbols. Why is the dot product mentioned here but the cross product is not? I would think that either the cross product should be included in this list, or the dot product should be moved to one of the non-basic sections below. Any thoughts? JCMPC (talk) 13:16, 11 May 2016 (UTC)

Matrix dimensions
Currently the section on symbols based on Latin letters includes × but fails to mention its use in matrix dimensions—e.g., a 3×5 matrix. Loraof (talk) 00:54, 22 June 2016 (UTC)

Number sets etc.
What about quadratic integers, quadratic numbers (real or not), algebraic integers etc.?

Sometimes 𝔸 is used for algebraic numbers according to

https://en.wikipedia.org/wiki/Latin_letters_used_in_mathematics

Likewise ℙ for prime numbers according to the source above. — Preceding unsigned comment added by 2001:6B0:E:4B42:0:0:0:206 (talk) 20:23, 30 June 2016 (UTC)

The symbols $$\ll$$ and $$\gg$$ in combinatorics
In combinatorics, writing $$f\ll g$$ usually means $$f=o(g)$$ (rather than $$f=O(g)$$). Similarly, $$f\gg g$$ usually means $$f=\omega(g)$$. See for one example by Andrzej Dudek, Alan Frieze, Po-Shen Loh and Shelley Speiss, or for another, more explicit example by Michael Krivelevich, Choongbum Lee and Benny Sudakov. Peleg (talk) 19:02, 16 July 2016 (UTC)

≍
What does this "≍" mean? Seen in pdf here: http://arxiv.org/abs/1412.5029 — Preceding unsigned comment added by 98.95.252.137 (talk) 08:21, 25 April 2015 (UTC)


 * This usually means "same order of magnitude. That is, $$f\asymp g$$ is a different way of writing $$f = \Theta(g)$$.  See Big O notation. Peleg (talk) 19:05, 16 July 2016 (UTC)

This article would be so much more useful if ...
... it actually showed how to write the symbols in html and in TeX, instead of just doing it and obliging the reader to use the "Edit" link to find out how. Like this:

If no-one objects, I'll volunteer to do the work myself. Maproom (talk) 21:18, 18 September 2016 (UTC)

Mayan Mathematics
Why are there so little glyphs to represent units? Do you expect people to memorize character after character without consciousness? This is why the Elite will destroy creations in the name of A.I. making people become useless. Why would the language of the universe (math) be without a proper system to represent perception of what reality has to offer and take? Most people see novelty in math (like finances): something akin to physics and astronomy 'being' only for academics locked away in labs and computer desks. It involves all life, where Force gives meaning to the Galactic Center. 216.223.90.33 (talk) 20:09, 17 October 2016 (UTC)

It's missing the ^ symbol
The carat (^) symbol for exponentiation is missing from the list. Can somebody add it? — Preceding unsigned comment added by 64.121.6.113 (talk) 05:03, 21 April 2017 (UTC)

*needs to also mention it's used for multiplication
I mean heck it's on the number pad, this is how you get it in excel, on the number pad, on my graphing calculator, within google's calculator. —Preceding unsigned comment added by 74.72.44.116 (talk) 18:58, 17 April 2010 (UTC)
 * Agreed. This should definitely be added. Adammanifold (talk) 04:47, 11 November 2010 (UTC)
 * Done. Alksentrs (talk) 16:27, 13 December 2010 (UTC)

Disagree. I disagree and think it should be removed; or if not removed at least have a note put with it. It is not a proper symbol for multiplication. Yes, we understand what is meant when we are in a calculator or computer context, but is is not correct mathematical grammar. It is a bastardization introduced by calculators and then computers due to special limitations of calculator displays and input in come computer languages. It only exist on a number pad because computer types who designed the number pads did not know any better. It is only that way in Excel because the designers of the program wanted to provide a quicker way to type in a multiplication from the keyboard than having to go find how to do a superscript over and over. It is similar to the ^ being used for raising to a power. 3^2 is not a proper way to write 3 squared. And 3E2 or 3EE2 are not proper mathematical grammar either. These were all bastardizations made back when calculator displays were primitive and the pixie-tubes and seven-segment displays could not display the proper symbols. Sure when we see it we know what it is; but we should not write it. Similar to when we hear aint, we know what the person means; but we still should not say or write it ourselves. At least but it at the bottom of the list with a note not to use it in formal maths. (Bob.A51 (talk) 08:11, 9 May 2014 (UTC))


 * I agree strongly that it should be removed. This is not a list of notations generally, it is a list of notations that would be suitable for general use in an encyclopaedia, and as used in Wikipedia. An article on a specific use (e.g. in a specific programming language) may mention it, but it is not a permitted notation in Wikipedia to denote multiplication generally. Not permitted: so it must be removed. Include it in this list, and we contribute to a degradation in notation in WP that the MOS seeks to prevent. —Quondum 13:52, 9 May 2014 (UTC)


 * How did you come to that conclusion? I did not see any statememt to that effect in the article. Nor is the article part of any categories that would suggest this. As far as I can tell it is simply a list of mathematical symbols, full stop. Not a "list of notations that would be suitable for general use in an encyclopedia, and as used in Wikipedia" as you claim 64.121.6.113 (talk) 05:28, 21 April 2017 (UTC)
 * As for the relevant section of the style manual, I think you are ignoring the spirit of it. It means not to use them in the text of articles, not pretend they don't exist. By analogy we're also supposed to use pinyin transliterations of chinese words, but that doesn't mean that we have to pretend that pinyin is the only romanization of chinese or even comparea word's pinyin transliteration to its wade-giles transliteration if it were for some reason relevant to an article. Similarly the section of the style guide about articles on Islam says not to follow the name of Muhammad with the invocation "peace be upon him" which, if we were to follow the manual of style as literally as you propose, would necessitate the removal of all the quotations in the article for the phrase Peace be upon him 64.121.6.113 (talk) 06:15, 21 April 2017 (UTC)

Better terminology for <= symbol
The symbol for greater than or equal to <= and the opposite is referred to as an "inequality". The symbol for not equal to /= is also referred to as an inequality. I suggest /= would be better termed an unequality. Krechmer (talk) 17:24, 18 August 2017 (UTC)

The "Basic symbols" table is broken
Just wanted to point out that the last row of the "Basic symbols" seems broken. The "QED" symbol is on the same row as the "Infinity" symbol. — Preceding unsigned comment added by 213.57.106.33 (talk) 08:55, 28 August 2017 (UTC)

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Directed join
In the Scott continuous article there is a red link to directed join: $$ \sqcup $$. Where might the symbol belong in this list? --Ancheta Wis   (talk  &#124; contribs) 09:14, 9 April 2018 (UTC)

f(x), evaluated from a to b and f(x), evaluated at a
I've had two mathematics teachers use this notation, to mean the f(x) evaluated from a to b, or f(b) - f(a). It looks like:
 * $$f(x)\Big|^b_a = f(b) - f(a)$$

And then I'm pretty sure when you use the single pipe symbol at the end of a polynomial, it means you're evaluating everything on that side of the equation. I find it ambiguous, though. One of my calculus teachers used it to mean just that term in the polynomial would be evaluated, and the other teacher just wrote the pipe bigger to mean the whole side of the equation. To disambiguate, you gotta write the end values a & b following brackets:
 * $$\Big[3x^2+2x+1\Big]^b_a = [3b^2+2b+1] - [3a^2+2a+1]$$

It can be combined with absolute value symbols:
 * $$\Big|(-13)x+4\Big|^b_a = \Big|(-13)b+4\Big| - \Big|(-13)a+4\Big|$$

My experience is seeing it used in calculus classes when evaluating definite integrals:
 * $$\int^b_a f(x) dx = F(x)\Big|^b_a = F(b) - F(a)$$

Oh yeah, and we're also missing $$f'(x)$$, the derivative of $$f(x)$$. And $$F(x)$$, the anti-derivative. And heck, there's also $$\frac{dy}{dx}, \frac{d}{dx}, dx$$, and all that fun calculus notation.

A similar notation, used to mean f(x) evalutated at a, is as follows:
 * $$f(x)\Big|_a = f(a)$$

~ JavaRogers (talk) 09:54, 24 May 2018 (UTC)

Several types/usages of arrows still missing
In particular, we are still missing entries for the use of the arrow for limits (the symbol is there, but not the particular usage), the double arrow for uniform limits, and the injection and surjection arrows, as well as the one specifically for inclusions/embeddings. 67.186.58.77 (talk) 16:03, 7 July 2018 (UTC) Alsosaid1987 (talk) 16:04, 7 July 2018 (UTC)

Compact embedding
Now I'm not the world's expert on compact embedding. But from what I know about the terms used in the definition, and the sets described in the example, something is wrong somewhere. When I read the definition "A ⋐ B means the closure of B is a compact subset of A.", I had a hunch it ought to be the other way around. But when I saw the example, "Q ∩ (0,1) ⋐ [0,5]", and applied the definition, there was no way it fit, For one thing, the set playing the role of B is already closed. And it is not even close to being a subset of A. But the other way around, yes. --Hccrle (talk) 22:40, 8 July 2018 (UTC)

Smash product
There is no mention of the smash product on the page, nor of the use of either ∧ or ⨳ as representing it. DinoD123 (talk) 00:24, 24 September 2018 (UTC)

Four dots
I'm sure I've seen four dots arranged in a square used to mark the end of a proof. I can't offhand find an example right now. Can anyone confirm that this is correct? SpinningSpark 18:04, 20 November 2018 (UTC)

modulo
Would it be worth noting % as the modulo operator used in comp sci? -Ravedave (talk) 17:16, 31 October 2008 (UTC)


 * Not really – that's a programming language operator used in C-like languages. Pascal-like languages use  instead (which is closer to how it's written in mathematics). Alksentrs (talk) 11:15, 1 November 2008 (UTC)


 * Speaking of % (the percent sign), it's not in the list at all, nor could I find any mention of it on this Talk page. Is it for some reason not considered a mathematical symbol, or it just hasn't been added yet? AVDLCZ (talk) 20:37, 23 April 2019 (UTC)


 * I don't consider it as a mathematical symbol, either as 1/100th or the modulus operator, and it's not listed in Mathematical operators and symbols in Unicode. &mdash; Charles Stewart (talk) 23:32, 23 April 2019 (UTC)

The One True list of missing symbols
There were (until I archived them) many requests for missing symbols above, so I'm grouping them all together here. Alksentrs (talk) 14:43, 11 May 2009 (UTC)

In complex analysis, the Omega constant, a solution of Lambert's W function A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral. In topos theory, the (codomain of the) subobject classifier of an elementary topos. In combinatory logic, the looping combinator, (λ x. x x) (λ x. x x) In group theory, the omega and agemo subgroups of a p-group, Ω(G) and ℧(G) In statistics, it is used as the symbol for the sample space, or total set of possible outcomes. In number theory, Ω(n) is the number of prime divisors of n.FreeFlow99 (talk) 09:58, 11 March 2013 (UTC)
 * complex infinity - the infinity symbol with a tilde above it — Preceding unsigned comment added by 66.41.43.172 (talk) 19:29, 20 July 2012 (UTC)
 * irrational numbers $$\mathbb{R}-\mathbb{Q}=\{p/q | p,q \in \mathbb{N}\}$$;
 * the forcing symbol $$\Vdash$$
 * differentiate d/dx $$\tfrac{d}{dx}$$
 * addition of vector spaces $$U + V := \{ u+v : u \in U, v \in V \}$$
 * identity permutation
 * concatenation? ||
 * multifunctions $$[\![$$ and $$]\!]$$
 * image of a path (suffix *)
 * division $\overline{)      }$
 * dual space $$\mathbb{X}^2; \mathbb{X} \subseteq \mathbb{F}^A $$. The equal sign should be placed above the inclusion sign, and not below it.
 * $$S^\circ$$ for the interior (topology) of the set $&#x2124;$. (It's just taken me nearly an hour to find out what that notation means…) Qwfp (talk) 21:47, 30 June 2010 (UTC)
 * Exponentiation is sometimes denoted using X^y or X**y rather than $$X^y$$.
 * Alternate symbols denoting the non-negative integers: $$\mathbb{J}$$, $$\mathbb{W}$$.
 * There should probably be more discussion of subscripts and superscripts for $$\mathbb{N}$$ & $$\mathbb{Z}$$. I have seen $$\mathbb{N}_0$$, $$\mathbb{N}^0$$, $$\mathbb{Z}^*$$, $$\mathbb{Z}$$≥, and $$\mathbb{Z}^+$$ to mean non-negative integers; $$\mathbb{Z}^+$$, $$\mathbb{Z}^{++}$$, $$\mathbb{Z}_+$$, $$\mathbb{Z}$$>, $$\mathbb{N}^*$$, $$\mathbb{N}^+$$, $$\mathbb{N}_1$$, and $$\mathbb{N}$$>0 to mean positive integers; $$\mathbb{Z}$$− and $$\mathbb{Z}$$< to mean the negative integers; $$\mathbb{Z}^*$$ and $$\mathbb{Z}$$≠ to mean the non-zero integers; and $$\mathbb{Z}^*$$ for $Z$.  (Obviously, there are many notational conflicts here.  It might be helpful to offer an opinion about conventional or preferred notation.) [Note problems with uniform wiki latex rendering of some of these super-/sub- scripts.]
 * I saw an X with sub and super-script that seemed to indicate a product of a sequence of matrices, similar to the E for addition and the capitol pi for multiplication, but I'm not sure -- does anyone know?
 * Omega (upper case) Ω is used to represent the last element of a list, presumably because it is the last letter in the greek alphabet.  See http://en.wikipedia.org/wiki/Omega: "Omega (the last letter of the Greek alphabet) is often used to denote the last, the end, or the ultimate limit of a set, in contrast to alpha, the first letter of the Greek alphabet." .   It is apparently also used for:
 * the gamma function 137.219.45.156 (talk) 02:46, 11 February 2011 (UTC)
 * the vector "harpoon" arrow
 * the colon used in ratios and odds
 * imaginary numbers $$\mathbb{I}$$ ?:: $$Im \{ \overrightarrow{z }\in \mathbb{C}\}=\{ \overrightarrow{z} = x + i \cdot y | y=0 \} $$; l.e. please read |x=0\}. Imaginary is Im(z)=0+i*y;
 * field $$\mathbb{F}$$
 * the delta as used in "change-in" Δ
 * path integral symbol ($$\textstyle \int$$)
 * multiplication star (* instead of ×)
 * almost/approximately equal: equals with dots centred on top and beneath (≑), or just on top (≐), or possibly offset from centre (≒ or ≓)
 * "a not-infinitesimally small" increment, in calculus derivations, δ
 * subgroup/subfield/subspace< > ≤ ≥ $$\subseteq \supseteq \supset$$
 * such/so that: | (or less commonly??) ϶
 * generic group theory operator
 * horseshoe commonly used for entailment
 * unit vector —Preceding unsigned comment added by Tracorn (talk contribs) 01:01, 25 May 2009 (UTC) : $$\hat{i}$$
 * Tensor operations, especially tensor product symbol and usage in tensor exponentiation. — Preceding unsigned comment added by Kikilamb (talk • contribs) 02:09, 6 September 2019 (UTC)

Possible to make a visual table/index
The page is long to scroll through in order for the reader to find the symbol they are after - is there any functionality in the wikipedia markup to make an m x n table with just the visual symbols that can then either jump to the appropriate section or bring up some type of disambiguation ? — Preceding unsigned comment added by 60.241.72.197 (talk) 04:04, 20 September 2019 (UTC)

Disjoint set
I was thinking of adding the following symbol, but would like others to review it first.


 * I strongly oppose to this inclusion. This symbol is absolutely non standard, and therefore it must not be used without being defined before. Moreover, the reference given is definitively not a reliable source for the symbol. On the contrary, they says that it is either ambiguous or an abuse of notation. Therefore, the symbol has no encyclopedic value, and is not notable enough for being included.
 * By the way, many entries of the list suffer of the same problem, and the article must be cleaned for distinguishing between standard symbols and non standard ones. Moreover, the non-standard symbols that are rarely used must be removed, and reliable references must be given for those that are kept. This is needed for complying with WP:Indiscriminate, WP:NOT, WP:Notability, and several other guidelines and policies. D.Lazard (talk) 09:15, 29 September 2019 (UTC)

Thank you for bringing this to the talk page for review. The citation is unsuitable. See Verifiability.

Wikipedia has an article disjoint union. The symbol $$\bigsqcup$$ (\bigsqcup) is presented as the standard symbol, but I do not know what that is based on. The symbols $$\biguplus$$, $$\ \cdot\!\!\!\!\!\bigcup$$, $$\bigcup\nolimits^{*}$$ are also mentioned. Wolfram uses $$\bigcup\nolimits^{*}$$.

Giorgio Levi's 1992 book mentions your symbol.

Perhaps we could use that citation. Richard-of-Earth (talk) 04:08, 30 September 2019 (UTC)

What is this K?
Not sure how to do the font, but in the sections on R (reals), Z (integers), etc., there is a K which is described as being the union of the reals and the complex numbers. Well excuse me but the set of complex numbers (C) is the union of the reals and the complex numbers. The real line is part of the complex plane and 3 (for example) is a complex number, 3 + 0i. Put simply, R is a subset of C!

I haven't heard of K before and I'm not necessarily disputing its existence but if it is a mathematical symbol then its definition/explanation is clearly wrong. Perhaps the person who wrote it in was confusing the complex numbers {a + bi | a, b real} with the imaginary numbers {ai | a real}? —Preceding unsigned comment added by 81.159.20.37 (talk) 16:04, 8 April 2009 (UTC)


 * I believe $$\mathbb{K}$$ is used in linear algebra to mean “either $$\mathbb{R}$$ or $$\mathbb{C}$$”. That is, if you make a statement about $$\mathbb{K}$$, then this statement is true if you substitute either $$\mathbb{R}$$ or $$\mathbb{C}$$ instead. Alksentrs (talk) 17:52, 8 April 2009 (UTC)


 * From my minor experience with algebraic geometry, the "field k" is often used. 67.158.43.41 (talk) 19:58, 4 November 2010 (UTC)


 * Yes, $$\mathbb{K}$$ stands for Körper, (German for field). Indeed K = R U C does not make sense, it should be K = R or C (or Q etc.) &mdash; MFH:Talk 13:29, 24 November 2019 (UTC)

Subset
In the two rows concerning subset ⊂ & superset ⊃, it is written that the correct symbol for these is ⊆ and ⊇, while ⊂ and ⊃ would mean proper sub/superset excluding equality. I think this is to the least obsolete, if not incorrect: today, ⊂ and ⊃ generally (in all reference texts and research papers I know and usually without any need for explanation) do mean the same as ⊆ and ⊇, and one uses \subsetneq, i.e., ⊊ or ⫋ in the rare cases where equality should be excluded. &mdash; MFH:Talk 14:12, 24 November 2019 (UTC)

New template:infobox symbol
I have created (well, ok, shamelessly copied Infobox currency sign created by u|DePiep and removed the currency-specific bits) a new Infobox symbol that can be used for non-alphanumeric signs and symbols that don't have a more appropriate infobox (such as we already have for punctuation and currency). Where a mathematical symbol has its own page, this seems a better solution than the punctuation sidebar currentky in use. Comments welcome at template talk:Infobox symbol. As 30 November, it is not yet in use anywhere but I have left a statement of intent to do so at talk:estimated sign and, unless anyone objects, will go ahead in the next few days. Other uses would require articles to host them. --John Maynard Friedman (talk) 11:38, 1 December 2019 (UTC)
 * The example here is to show capability. At present, Minus-or-plus redirects to Plus-minus so it is a trivial case. I could equally have put both glyphs in the display box and dropped the 'Different from' option.
 * Note also that there is a proposal at Template talk:Sidebar punctuation marks to discontinue support for mathematical symbols (as part of a plan to re-engineer the whole side-bar as an end-of-article nav-bar). --John Maynard Friedman (talk) 15:53, 1 December 2019 (UTC)

Quotient by a left action
Sometimes with groups, people distinguish quotient by a left action from quotient by a right action with G \ X vs X / G. --Arnaud Chéritat (talk) 18:59, 6 January 2020 (UTC)

"Lazy s"
...redirects here but is not mentioned or defined. 2A00:23C5:FE0B:700:D9F0:48B2:6393:972C (talk) 08:25, 18 January 2020 (UTC)

"Lazy S" listed at Redirects for discussion
An editor has asked for a discussion to address the redirect Lazy S. Please participate in the redirect discussion if you wish to do so. D.Lazard (talk) 11:29, 18 January 2020 (UTC)

Feature Request: Sketch Recognition Index
Searching for symbols by sketching them would be a nice feature. An example of such is Detexify — Preceding unsigned comment added by Andrew M. Cross (talk • contribs) 00:19, 29 January 2020 (UTC)

&#x2124;+ or &#x2124;> means {1, 2, 3, ...} : does it?
Doesn't &#x2124;+ mean {0, 1, 2, 3, ...} and &#x2124;- mean {0, -1, -2, -3, ...} : so both subsets should contain zero, doesn't it? Stephanvaningen (talk) 18:15, 3 March 2020 (UTC)
 * Addition: maybe my remark is not valid. I did find on the .nl-wikipedia, that the notation is different in Belgium compared to other countries :-/ very strange

Lowercase sigma σ for standard deviation.
Lower case sigma σ is also used for standard deviation. As far as I know this is widely accepted. APTRJ (talk) 13:35, 18 March 2020 (UTC)
 * You're correct, the letter s is also common for standard deviation with a slightly altered meaning so it would be benifical to add that in I think. Port u ghetti talk 17:01, 18 March 2020 (UTC)

Parallel symbol: || Use in electrical engineering
The expresson R1||R2 is used by electrical engineers (and some other engineers) as a binary mathematical operator meaning 1/[(1/R1) + (1/R2)], or the reciprocal of the sum of the reciprocals. ("Binary" in the sense that it operates on two elements of a field.) It is recognized as commuutative, associative, etc. similarly to other operators and has equal precidence as multiplication and division in an algebraic expression such as R1 + R2||R3. (Do the "in parallel" first, then the addition.) I've never seen this operator listed in mathematics oriented pages, but there is a page devoted to it on Wikipedia, a page that needs work. https://en.wikipedia.org/wiki/Parallel_(operator) Perhaps somebody can provide some expertise on why this use of the symbol is never recognized in mathematical circles. Electrical engineers find it very convenient. Would it cause confusion in other contexts where reciprocal and addition have definition? Doug iowa (talk) 02:48, 11 April 2019 (UTC)


 * This notation is used in mathematics to denote exact division. See [] (which is a duplicate of someone else asking about it) or [] . I'm sure it would be a great addition to a wikipedia page listing symbols in electrical engineering! Skeesix (talk) 20:20, 11 August 2020 (UTC)
 * I have moved your signature to the end of your post, and indented your post, as it is ususl in WP.
 * You are free to create the page List of symbols used in electrical engineering, but this not here (mathematical articles) that you have to ask for help.
 * About the use of the symbol in mathematic: This symbol is not commonly used in the meaning you are refering to, and the phrase "exactly divides" is generally understood as a synonymous of "evenly divides". The links that you provide are not WP:reliable sources. Your links define "$$a^n$$ exactly divides $b$" as "$n$ is the multiplicative order of $a$ modulo $b$. If the phrase "exactly divides" and its notation were common, they would appear in the linked article as well as in square-free integer and in all articles linked of multiplicative order. D.Lazard (talk) 09:21, 12 August 2020 (UTC)

Angle sign ∠
The angle sign (∠) is absent — Preceding unsigned comment added by 77.166.72.33 (talk) 20:19, 8 September 2020 (UTC)

∝ (Is Proportional to) Listed Twice
∝ (Tex: \propto) Is listed twice, under "Basic Symbols" and "Other non-letter symbols". I am of the opinion that it is a common enough symbol to apear on the "Basic Symbols" list, and think that it should be removed from the "other" section. I encountered it at least twice in my freshman year of college, and the similarity with handwritten lowercase alpha ( α )(used to represent various constants, as well as angular acceleration) was confusing.

--130.245.192.6 (talk) 07:09, 9 September 2020 (UTC)
 * Apparently, this symbol is commonly used only in US elementary courses. It is not used by mathematicans (during 40 years as a professional mathematician, I have never encountered it in mathematical texts. So its place is not in "Basic Symbols", but in "Other non-letter symbols". D.Lazard (talk) 09:31, 9 September 2020 (UTC)

Inconsistencies in the definition of the universal set
The comments under the universal set ($$\mathbb{U}$$ in TeX) are inconsistent with the definition of complex numbers given elsewhere in the article. That definition of complex numbers includes real numbers (by setting $$b = 0$$ in $$a+bi$$). Hence the note about U = (Z, C) not including π is false, and writing U = (R, C) is redundant. — Preceding unsigned comment added by 2804:14C:1A3:897C:7929:7C79:19FF:9DA7 (talk) 15:38, 8 October 2020 (UTC)
 * This is one of the multiple issues of the article. Even this single entry has multiple issues: the notation is not standard; the "set of all elements under consideration" is undefined and can lead to Russel's paradox (the set of all sets cannot exist); $$\{\mathbb R, \mathbb C\}$$ does not contains any number, as it is a set with only two elements, the set $$\mathbb R$$ and the set $$\mathbb C;$$ there are many things called numbers that do not belong to $$\mathbb C;$$ etc. D.Lazard (talk) 16:45, 8 October 2020 (UTC)

⨳ or ※ ?
Currently, lists the symbol ‘⨳’ (“smash product” U+2A33) and its TeX name “\smashtimes” in the first two columns, but the Examples column has ‘※’ (that is, the “reference mark” U+203B) instead. Is either correct or are both wrong for the use given in the Explanation column? The only reference mentioning usage for “contradiction” is to a chat, which can hardly be regarded a reliable source. ◅ Sebastian 12:53, 9 October 2020 (UTC)

WP:TNT must be applied to this article
One year ago, I have tagged this article with clean up with Since then, the tag has been changed into more specific tags, with the consequence that the detailed reason for tagging has been removed. Since then nothing has been done for fixing the issues. On the other hand some more issues has been revelead, including blatant errors (see the two preceding threads).

Here are some other issues
 * Large tables: The presentation as large tables makes the article difficult to read, even on the large screen of a laptop. Moreover using three indented lines for three different entries in a row make things ever worse. Bulleted lists or glossaries must be used
 * WP:verifiability: for most entries, no source is given. In most cases, the symbol is mentioned in the linked article, but this mention is generally not sourced. I believe that in some cases the notation appear in the linked article only because it appears here.
 * WP:DUE: Rarely used symbols and symbols used by a single author are not distinguished from the standard and commonly used symbols.
 * WP:SYNTHESIS: The classification of symbols seems original synthesis. For example, the dagger is presented as deriving from the letter T, while Dagger (typography) provides a totally different origin. Similarly $$\in$$ is presented as deriving from the the letter e, while Set membership says that it is a stylized version of the greek letter epsilon. Also $$\land$$ is presented as deriving from U. This may be explained (this is not done), but the explanation that I can provide is WP:OR. Similarly, $$\times$$ is probably not derived from X, but probably from a rotated $$+.$$
 * Confusing: Many symbols have several meanings, and it is not clearly said how to distinguish them (for common symbols this is usually done by the context, but for many other symbols a definition must appear in every text that use them)
 * Misleading: The above confusion may lead readers to use wrongly some symbols. I suspects that some notations appear in some articles only because the symbol has been inserted here as WP:OR

This list of issues is certainly not complete. IMO, the symbols must be classified into standard thorough all mathematics for symbols that may be used in any mathematical text without being defined (for example $$+$$ or $$\mathbb R$$), standard in a specific area of mathematics for symbols that do not need a definition in a specific area of mathematics, but requires a definition outside it (for example $$[L:K]$$ for the degree of a field extension), common but not standard, and uncommon. Also the symbols categorized as uncommon should be removed unless they must be kept for historical reasons.

With so many issues, it seems that WP:TNT is the only solution. Is someone willing to write from scratch a new version of the article? D.Lazard (talk) 14:04, 9 October 2020 (UTC)


 * , great work thus far. When I can find a suitable barnstar, it will be waiting for you. --John Maynard Friedman (talk) 13:44, 24 October 2020 (UTC)

Semi-protected edit request on 29 October 2020
List_of_mathematical_symbols Under Set Theory → ⊃,⊇,⊋ → There is a spelling mistake. Equivalent is misspelled as quivalent. (I think this is significant as it had me spending 10 minutes looking up what the 'quivalent' meant.) A Basil Biscuit (talk) 20:24, 29 October 2020 (UTC)

. Thanks for having pointed this typo. D.Lazard (talk) 20:29, 29 October 2020 (UTC)

Semi-protected edit request on 10 November 2020
In the "Operators acting on functions or sequences" section, at point 2 of the explanation of ∑ symbol, the converging infinite sum of x^i/i! results e^i instead of e^x. 151.49.175.109 (talk) 22:08, 10 November 2020 (UTC)
 * Thanks for pointing this typo. D.Lazard (talk) 10:08, 11 November 2020 (UTC)

Semi-protected edit request on 11 November 2020
Basic logic section: "∨ is often replaced by &" but the symbol | is usually used as replacement of OR operator (or the || in computer science). The & is used as replacement of ∧ (or && in computer science). 5.90.197.100 (talk) 17:21, 11 November 2020 (UTC)
 * . Thanks. D.Lazard (talk) 20:51, 11 November 2020 (UTC)

Semi-protected edit request on 12 November 2020
Please replace "1. Denotes the sum of a finite number of terms" with "1.  Sigma Notation. Denotes the sum of a finite number of terms". For people who are wanting to learn what these symbols mean, it is important to first find out what the symbols are called, but this list seems to omit many of the names of the symbols. CriscoCrusader (talk) 06:53, 12 November 2020 (UTC)
 * When a symbol has a name and a Wikipedia article, it is linked to this article. This is why many symbols appear in blue as headings for their entry. Here $$\sum$$ is linked to Sigma notation. D.Lazard (talk) 09:46, 12 November 2020 (UTC)

Uninformed edit request on 12 November 2020
At List of mathematical symbols, the first item in the HTML column is given as $S$. Should (could?) this be given as "a with macron", ā ( ? --John Maynard Friedman (talk) 20:01, 12 November 2020 (UTC)
 * It is the first time that I have heard the term of "macron" (except that it is the name of my President :-). This is an article on mathematical symbols. So we must use the names used in mathematics. For this, Unicode is not a reliable source, but LaTeX is a reliable source, since it has been designed by mathematicians for writing mathematics. The command \macron does not exist in LaTeX, and this symbol is called \overline. So, we must use "overline" with, possibly, a note saying that over a single chracter, it looks like a macron. However, I have not thought how I'll transform into a glossary the table of diacritics. D.Lazard (talk) 20:44, 12 November 2020 (UTC)


 * Thank you, that is why this angel feared to tread. (The "overline" diacritic, called a macron, is used in quite a few languages - see macron (diacritic)). Let it stand. --John Maynard Friedman (talk) 23:45, 12 November 2020 (UTC)

Semi-protected edit request on 25 November 2020
change: \mathbb {C} Denotes the set of complex numbers. It is often denoted also R. {\displaystyle \mathbf {R} .} to: \mathbb {C} Denotes the set of complex numbers. It is often denoted also C. {\displaystyle \mathbf {C} .} Mgjwblack (talk) 09:00, 25 November 2020 (UTC)
 * Pictogram voting wait.svg Already done by User:D.Lazard. Danski454 (talk) 19:34, 25 November 2020 (UTC)

^
The symbol ^ is used in this set-theory definition

Denotes set-theoretic union, that is, $A\cup B$ is the set formed by the elements of $A$ and $B$ together. That is, $A\cup B=\{x\mid (x\in A) \lor (x\in B)\}.$ but has not been defined. An oversight, still on the to-do list or defined elsewhere? -- John Maynard Friedman (talk) 13:45, 11 December 2020 (UTC)
 * See List of mathematical symbols and List of mathematical symbols. A question that is still open for me is whether it should be and entry for ^ as an alternate notation for exponentiation, and not to being confused with ∧. D.Lazard (talk) 13:54, 11 December 2020 (UTC)
 * Finally, I have added an item in . An advantage is that we have now an entry for Exponentiation, although it is normally denoted without any symbol. D.Lazard (talk) 15:20, 11 December 2020 (UTC)
 * D'oh!, I searched for ∧ by eye but must have seen ∧ as some kind of tent symbol (if I saw it at all) :-D ). Well at least my intervention was of some value. (I just hope I that there is a least one visitor somewhere in the world who didn't know that ${–1, 1}$ is shorthand for $\overline{a}$.) Thank you.--John Maynard Friedman (talk) 16:19, 11 December 2020 (UTC)