# Talk:List of mathematical symbols

## 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, ${\displaystyle \prod }$, 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)

## 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)

## ${\displaystyle \mathbb {E} }$ (capital E set)

I came across the symbol ${\displaystyle \mathbb {E} [f(x)]}$ 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)

${\displaystyle \mathbb {E} }$ (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)

## 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)

## 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.

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)

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

## non-parallel

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 ${\displaystyle \not \ \!\parallel }$ (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)

## 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, ${\displaystyle \land }$), which appears like this: ∘ (U+2218: Ring Operator, ${\displaystyle {}^{^{\circ }}}$). 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)

## 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. (...)

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?

Hi Alksentrs!
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 () 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.
Maurice Carbonaro (talk) 11:09, 19 January 2009 (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 ${\displaystyle \mathbb {K} }$ is used in linear algebra to mean “either ${\displaystyle \mathbb {R} }$ or ${\displaystyle \mathbb {C} }$”. That is, if you make a statement about ${\displaystyle \mathbb {K} }$, then this statement is true if you substitute either ${\displaystyle \mathbb {R} }$ or ${\displaystyle \mathbb {C} }$ 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)

## 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)

contribs) 01:01, 25 May 2009 (UTC) : ${\displaystyle unit{k}}$

${\displaystyle {\hat {i}}}$ or ${\displaystyle }$
I also couldn't find the usage of ${\displaystyle \Delta }$ as the Laplace operator...? --Ichbinder (talk) 23:36, 11 October 2009 (UTC)
${\displaystyle S^{\circ }}$ 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 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:

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

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

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. ${\displaystyle \langle \ |\ \rangle }$ 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 (${\displaystyle \langle \ |\ \rangle }$ 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"? 71.236.215.87 (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

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

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 ${\displaystyle \mathbb {I} }$, ${\displaystyle \mathbb {J} }$, ${\displaystyle \mathbb {Q} '}$ or ${\displaystyle {\bar {\mathbb {Q} }}}$, but make sure you state which notation you are using. Or just use ${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$. 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 ${\displaystyle \phi \Rightarrow \psi }$, ${\displaystyle {\mathcal {M}}\models \phi }$ and ${\displaystyle {\mathcal {N}}\models \psi }$, then ${\displaystyle {\mathcal {M}}\supset {\mathcal {N}}}$. 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 [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

"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 ≏ 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

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)

## !congruence not included

negative of congruence is not included —Preceding unsigned comment added by Userdce (talkcontribs) 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)

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

=

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

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

Table of mathematical symbolsTemplate:No redirect — 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

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)

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 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

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

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 (talkcontribs) 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 (talkcontribs) 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)

## ⊕ Overriding union

Overriding union, mentioned in the article on Functions, is missing {{#invoke:main|main}}.

## 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

Template:Edit semi-protected 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> 70.39.231.44 (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)

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,[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

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)

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. ${\displaystyle \vartriangleleft \shortmid }$ or ${\displaystyle <\!\shortparallel .}$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)

## 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 < 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)