Talk:List of mathematical symbols

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One of the 500 most frequently viewed mathematics articles.


Switch TeX and HTML Columns[edit]

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, , quickly looking at the HTML column. It looks very much like other symbols, and not it all like it is usually represented in textbooks. (talk) 10:13, 28 December 2013 (UTC)


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

(capital E set)[edit]

I came across the symbol 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: (talk) 13:47, 9 April 2012 (UTC)

(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)

X bar[edit]

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 (talk) 13:05, 12 April 2011 (UTC)

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

Top versus transpose[edit]

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)


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

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)


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 mod instead (which is closer to how it's written in mathematics). Alksentrs (talk) 11:15, 1 November 2008 (UTC)


could someone please help me find the symbol for non-parallel, if there is one. —Preceding unsigned comment added by HawkE65 (talkcontribs) 10:19, 17 October 2009 (UTC)

"Not parallel" is probably something like (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)


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, ), which appears like this: ∘ (U+2218: Ring Operator, ). 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). (talk) 03:30, 12 October 2010 (UTC)

Euclidean Vector symbols[edit]

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"?

Notation for vectors in or out of a plane.svg
(...) 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#Representation of a 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?[edit]

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. (...)
The Monad was a symbol referred by the Greek philosophers as "The First," "The Seed," "The Essence," "The Builder," and "The Foundation"


Said that I noticed that there are astounding similarities with:

The sun symbol (Sun symbol.svg) 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)

What is this K?[edit]

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 (talk) 16:04, 8 April 2009 (UTC)

I believe is used in linear algebra to mean “either or ”. That is, if you make a statement about , then this statement is true if you substitute either or instead. Alksentrs (talk) 17:52, 8 April 2009 (UTC)
From my minor experience with algebraic geometry, the "field k" is often used. (talk) 19:58, 4 November 2010 (UTC)

The One True list of missing symbols[edit]

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)

  • complex infinity - the infinity symbol with a tilde above it — Preceding unsigned comment added by (talk) 19:29, 20 July 2012 (UTC)
  • the gamma function (talk) 02:46, 11 February 2011 (UTC)
  • the vector "harpoon" arrow
  • the colon used in ratios and odds
  • irrational numbers ?::;
  • imaginary numbers  ?:: ; l.e. please read |x=0\}. Imaginary is Im(z)=0+i*y;
  • field
  • the delta as used in "change-in" Δ
  • path integral symbol ()
  • the forcing symbol
  • 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 ≓)
  • differentiate d/dx
  • "a not-infinitesimally small" increment, in calculus derivations, δ
  • addition of vector spaces
  • identity permutation ()
  • concatenation? ||
  • subgroup/subfield/subspace < > ≤ ≥
  • such/so that: | (or less commonly??) ϶
  • multifunctions and
  • image of a path (suffix *)
  • generic group theory operator
  • horseshoe commonly used for entailment
  • division )       
  • dual space . The equal sign should be placed above the inclusion sign, and not below it.
  • unit vector —Preceding unsigned comment added by Tracorn (talk

contribs) 01:01, 25 May 2009 (UTC) :

I also couldn't find the usage of as the Laplace operator...? --Ichbinder (talk) 23:36, 11 October 2009 (UTC)
for the interior (topology) of the set S.(It's just taken me nearly an hour to find out what that notation means…) Qwfp (talk) 21:47, 30 June 2010 (UTC)
  • 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 "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:

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)

symbols used in early 20th century quantum mechanics[edit]

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)

Dirac notation[edit]

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. (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. 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 ( rather than < | >). I guess what I should have said is that I find this text a bit confusing:

There are many variants of the notation, such as 〈u | v〉 and (u | v), which are described below. The less-than and greater-than symbols are primarily from computer science; they are avoided in mathematical texts.

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"? (talk) 18:13, 4 August 2009 (UTC) Justin
I have removed < and > from the symbol column, and have changed the wording slightly:

As 〈 and 〉 can be hard to type, the more “keyboard friendly” forms < and > are sometimes seen. These are avoided in mathematical texts.

This should be better. Alksentrs (talk) 00:37, 6 August 2009 (UTC)

rowspan with template[edit]

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)

Irrational's symbol[edit]

so ya see wat is irrational's symbol —Preceding unsigned comment added by (talk) 22:59, 9 September 2009 (UTC)

There's no standard symbol for the set of irrational numbers. You could use , , or , but make sure you state which notation you are using. Or just use . Alksentrs (talk) 01:32, 28 September 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 , and , then . 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 [1] and [2]), 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[edit]

"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....???[edit]

Top half is omega and the bottom minus....???-- (talk) 01:35, 20 March 2010 (UTC)

If this convention is replaced by a new standard, please show the history of the edition-- (talk) 01:43, 20 March 2010 (UTC)

Its unicode U+224F ≏ 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)

*needs to also mention it's used for multiplication[edit]

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 (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)

!congruence not included[edit]

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

Add "action" to \cdot ?[edit]

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[edit]

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

ISO 31-11 standard[edit]

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[edit]

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 (talk) 22:37, 21 November 2010 (UTC)


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 (talkcontribs) 14:12, 11 January 2011 (UTC)

Linking to pages about the symbol?[edit]

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.

This is the wrong place, but[edit]

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)

Requested move[edit]

Table of mathematical symbolsList of mathematical symbols — Per Wikipedia:Manual of Style (stand-alone lists)#Naming conventions, 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)

  • 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)

Criteria for order[edit]

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

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

Deletion of DeTeXify link.[edit]

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. (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. -- (talk) 12:05, 1 June 2011 (UTC)


Shouldn't multiplication use ⋅ sdot instead of · 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 — Preceding unsigned comment added by (talk) 16:15, 7 June 2011 (UTC)

Links to LaTeX commands[edit]

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 (talk) 21:54, 30 July 2011 (UTC)

Tilde - please check on discussion on Tilde, Talk:Tilde pages[edit]

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[edit]

"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 (talkcontribs) 24 Nov 11

φ is the Greek letter phi. Alksentrs (talk) 15:20, 27 November 2011 (UTC)

Another use of the symbol #[edit]

See: . — Preceding unsigned comment added by Reddwarf2956 (talkcontribs) 14:44, 13 February 2012 (UTC)

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


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

⊕ Overriding union[edit]

Overriding union, mentioned in the article on Functions, is missing


Truth and Falsity symbols[edit]

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


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

Edit request on 21 March 2013[edit]

The question mark symbol is also used for IF following a logic statement and the first option is true, second is false... <Logic equation> ? <True>:<False> (talk) 18:00, 21 March 2013 (UTC)

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.[edit]

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. does give each symbol a specific name and use,[3] 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[edit]

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

Suggested addition[edit]

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:
AB if A−1B−1
is shorthand for the two statements:
  1. A < B if A−1 > B−1
  2. A > B if A−1 < B−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. or 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[edit]

I saw my math professor using this symbol for "such that": Link here — Preceding unsigned comment added by (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). -- (talk) 15:14, 10 November 2013 (UTC)

Logical Mirror Symbols[edit]

All directed logical symbols can also be used in their mirror form. It is not only allowed for arithmetic such as "1 < 2" and "2 > 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:

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.

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

↯ for "contradiction"[edit]

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#Notation.

Various internet discussions show that there is some preference for the use of ↯:

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

Incorrect / Superfluous use of := symbol?[edit]

In the section about summation symbol, the example is shown as equal by definition to . 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)


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:

  1. Basic math symbols
  2. Symmetric symbols
    1. Symbols based on equality "="
    2. Symbols based on arithmetic operators (+, -, X, /)
    3. Other symmetric symbols
  3. Asymmetric symbols
    1. Symbols that point left or right (<, >, etc.)
    2. Other asymmetric symbols
  4. Brackets ( [, ], etc.)
  5. Symbols based on letters
    1. Latin letter-like symbols (I would list e.g. dagger and the perp symbol under T)
    2. Hebrew and Greek letter-like symbols (e.g. co-product under Pi)
    3. Letter modifiers (a-bar, a-hat, etc.)

This in addition to translating the German by-subject list.--agr (talk) 22:22, 14 July 2014 (UTC)

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[edit]

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[edit]

Reading through a book and WTF do these symbols mean? Please add them to the article. — Preceding unsigned comment added by (talk) 02:01, 21 October 2014 (UTC)

I wonder whether such a symbol is even standardized. There is a Unicode symbol (⪋ U+2A8B LESS-THAN ABOVE DOUBLE-LINE EQUAL ABOVE GREATER-THAN) re is a similar Unicode symbol (⋚ 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 πij1/2 according as ViVi" 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)


Hi! Over on Wiktionary, we're trying to figure out if has ever actually been used as a symbol for the "fourth transfinite cardinal". (See wikt:WT:RFV#.E2.84.B8.) 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[edit]

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)


What does this "≍" mean? Seen in pdf here: — Preceding unsigned comment added by (talk) 08:21, 25 April 2015 (UTC)

This usually means "same order of magnitude. That is, is a different way of writing . See Big O notation. Peleg (talk) 19:05, 16 July 2016 (UTC)

Legendre/Jacobi symbol[edit]

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. (talk) 00:06, 21 September 2015 (UTC)

Update HTML Column[edit]

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

Symbol Symbol
in TeX
Name Explanation Examples
Read as
4 + 6 means the sum of 4 and 6. 2 + 7 = 9

Which looks like that to me --Physikerwelt (talk) 12:52, 8 November 2015 (UTC)

NTIME "k"[edit]

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


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
--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[edit]

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 {{math|...}} 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 (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. Mindmatrix 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 {{Intmath}} template: the only way to make the mathematics look sleek is to firstly (and consistently) use the {{math}} template (which should be used thoughout Wikipedia for all [inline] text style mathematics) and then to use a dollop of CSS in the {{Intmath}} template (which I was tentatively trying to figure out for the integrals on this page, before trying to improve the code of the {{Intmath}} 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 {{Intmath}} 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 {{math}} template throughout?— Preceding unsigned comment added by (talkcontribs)
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 {{Intmath}} template to make the integrals look nicer.) Thanks.— Preceding unsigned comment added by (talkcontribs)
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. Mindmatrix 20:43, 11 March 2016 (UTC)
You may want to review Wikipedia:Manual of Style/Mathematics#Typesetting of mathematical formulae, Wikipedia: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. Mindmatrix 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 (talk) 19:54, 12 March 2016 (UTC)
Suggestion for the {{intmath}} template: Template talk:Intmath/doc# Suggestion of new template code. — 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... — Tentacles mailto:Tentacles 20:30, 15 March 2016 (UTC)

Cross and dot products in the "basic" section[edit]

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[edit]

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.[edit]

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

Sometimes 𝔸 is used for algebraic numbers according to

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 and in combinatorics[edit]

In combinatorics, writing usually means (rather than ). Similarly, usually means . See [4] for one example by Andrzej Dudek, Alan Frieze, Po-Shen Loh and Shelley Speiss, or [5] for another, more explicit example by Michael Krivelevich, Choongbum Lee and Benny Sudakov. Peleg (talk) 19:02, 16 July 2016 (UTC)

This article would be so much more useful if ...[edit]

... 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:

in TeX
Name Explanation Examples
Read as


the (set of) integers
ℤ means {..., −3, −2, −1, 0, 1, 2, 3, ...}.

+ or ℤ> means {1, 2, 3, ...} .
* or ℤ means {0, 1, 2, 3, ...} .

ℤ = {p, −p : p ∈ ℕ ∪ {0}​}

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