Talk:Glossary of mathematical symbols/Archive 1

What do you think?

This page is intended to make mathematical articles more readable for mathematical beginners. What do you Wikimaticians think about it? --Rade 20 Aug 2002

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This talk is all about visual appearances. I'm a non-mathematician attempting to create alt text for images of math formulae and need examples of how to verbalize or linearize them in natural language. The explanation column for each symbol in the table should include a natural language verbalization of the example in question, not just an explanation of it. How would one mathematician read the formula over the phone to another mathematician, perhaps a stranger, using best practice terminology, is what I'm after. For example, I'm having difficulty in trying to apply the "sum over ... from ... to ... of" given with the sigma/summation definition in the table to a very fancy-looking pair of formulae that place the symbol in different places, one covering an entire fraction, the other covering only the numerator part of a fraction.

Eamon

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John Knouse apparently has trouble seeing these symbols properly on Netscape 4.7, and I can't see them on IE 6.0. We really need to get some kind of help page for how to display math symbols, because neither of these browsers is all that old, and seeing math symbols shouldn't be a pain in the ass for wikipedians.

In my case right now, I think the trouble is that I don't have the right fonts installed. I tried to go to http://www.microsoft.com/typography//fontpack/default.htm to download the Microsoft "web fonts", which have resolved many of my past web font troubles, but they have discontinued the free downloads there.

Does anyone know where one can download the right fonts? I think it has to be a unicode font with symbols in the right range, but I don't off hand know what that range is, and my current connection is too slow to just try downloading things at random.

--Ryguasu

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It might be useful to add a column telling the reader how to produce these symbols. Eclecticology 08:32 Sep 4, 2002 (PDT)

Maybe, it is better to create a page in the Wikipedia name space for this purpose (if there isn't already one) and put a link in the article. --Rade

Yup: wikipedia:How does one edit a page contains a list of math symbols and their HTML entities. AxelBoldt

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Axel, what do you mean that the leftwards arrows aren't used? I see them all the time! Heck, I use them myself. — Toby 07:45 Sep 18, 2002 (UTC)

You mean for functions? f: X <- Y ? I have never seen that in my life. It certainly doesn't occur in Wikipedia anywhere. Or do you mean in logic? I would venture a guess that there are no left implication arrows in Wikipedia anywhere either. AxelBoldt

I have seen both of these, the function symbol often in literature related to category theory (and not just in commutative diagrams, but inline with the colon). An example where this is useful (in a variety of contexts) is

f: Y ← U ⊆ X

to indicate a partial function f from X to Y with domain U. This is clearer than either

f: U ⊆ X → Y or

f: X ⊇ U → Y,

at least in my opinion (and apparently in others'). That said, the question becomes whether we should document such usage if it's not used in Wikipedia. I think that we should, since it's easy to grasp and might end up being used in the future. However, I'm not 100% convinced of this.

— Toby 05:05 Sep 19, 2002 (UTC)

Well, since this page is directed at beginners, I think we should include only relevant symbols. People who read these category texts can probably figure out what the left arrows mean, for anybody else it's just information overload. AxelBoldt

All right, but you agree that the moment that it shows up in a basic Wikipedia article, then it shows up here. (And shows up fairly, of course; I won't stick an example in just to spite you ^_^.) — Toby 23:10 Sep 19, 2002 (UTC)

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The question of undisplayable characters in many popular browsers is, IMO, best addressed by creating graphics. A drawback is that it is too hard to make them in a variety of point sizes, so they must be made to fit the average context. I made such a character, "", and use it in several articles. David 22:12 Dec 27, 2002 (UTC)

IMO this question is not best addressed by creating graphics. Apart from the drawback you mentioned, the use of graphics is more complicated than the use of character entities. This reduces the ease of use which is a basic idea of Wikipedia. Another drawback is that in the mid-future all browser will display these characters and the re-substitution will be a lot of work. A better idea would be to suggest a software feature that translates the entities into graphics if the user sets their preferences so. In this way, proper character sizes could be chosen. --Rade

We now have TeX markup on Wikipedia: $\nabla$. problem solved -- it generates PNG images or HTML, depending on user prefs and complexity. In the future, as more browsers a re smarter, it will generate more HTML or MathML. -- Tarquin 19:37 Jan 6, 2003 (UTC)

Unfortunately, this solution does not work well. Look at the above paragraph with a browser and OS that do not support the "nabla" entity for "", and you will see problems: the background is white instead of transparent, and it is about 50% too large (at least, on my computer). It was a very good idea, though. David 21:36 Jan 7, 2003 (UTC)

Rejigging table

I would like to rejig the table, in part to get rid of those ridiculous H1 tags which someone has employed to make the left-hand column larger, and in part to make the layout more logical, giving more space to the larger items. How does the following look:

Symbol	Name	Explanation	Example
	Should be read as
	Category
+	addition	4 + 6 = 10 means: that if 4 is added to 6, the sum, or result, is 10.	43 + 65 = 108; 2 + 7 = 9
	plus
	arithmetic
−	subtraction	9 − 4 = 5 means: that if 4 is subtracted from 9, the result will be 5.	87 − 36 = 51
	minus
	arithmetic
	negative sign	−3 means: the negative of the number 3.	−(− 5) = 5
	negative
	arithmetic
	set theoretic complement	A − B means: the set that contains all those elements of A that are not in B	{1,2,3,4} − {3,4,5,6}  =  {1,2}
	minus; without
	set theory

Your version looks better to me. I always hated those extraneous lines in the "symbol" column. Some thoughts, you might want to consider adding some cellpadding, say cellpadding=3? Also It might be good to left align "name", center align "read as" and right align "category" to better distinguish these. Like so:

Symbol	Name	Explanation	Example
	Should be read as
	Category
+	addition	4 + 6 = 10 means: that if 4 is added to 6, the sum, or result, is 10.	43 + 65 = 108; 2 + 7 = 9
	plus
	arithmetic
−	subtraction	9 − 4 = 5 means: that if 4 is subtracted from 9, the result will be 5.	87 − 36 = 51
	minus
	arithmetic
	negative sign	−3 means: the negative of the number 3.	−(− 5) = 5
	negative
	arithmetic
	set theoretic complement	A − B means: the set that contains all those elements of A that are not in B	{1,2,3,4} − {3,4,5,6}  =  {1,2}
	minus; without
	set theory

Paul August 16:42, Oct 8, 2004 (UTC)

several omissions

This table does not do anything for dot or cross products of vectors, it lacks the superset symbol and doesn't do the funtion operators like composition. Where is the vector "harpoon" arrow or the colon used in ratios and odds? "Therefore" and "since" symbols are missing. The symbols for Irrational numbers, Imaginary numbers and Counting numbers (Ie natural numbers without 0) are not there. The article in general needs some serious cleanup too. I will do all this given time however, my times is quite limited. --metta, The Sunborn ☸ 21:26, 23 Nov 2004 (UTC)

It is also missing the delta as used in "change-in", the coproduct operator, the plus/minus operator and doesn't mention the circled plus as an operator for direct sum. This page needs some cleanup and expansion. ---The Sunborn

Also missing is the composition operator. ---The Sunborn

The bottom element of lattice theory is present but the top element is missing.

If we want a complete list, and we do, every unicode supported math symbol is available. It is a PDF so watch out.--metta, The Sunborn ☸ 19:22, 9 Dec 2004 (UTC)

The pdf is protected so if your thinking of copy and pasting the required symbol into a document, tough luck.--krackpipe

What about the path integral symbol? (\oint in wiki-markup) That's what I came here to look up. —The preceding unsigned comment was added by 216.165.132.250 (talk) 22:25, 7 December 2006 (UTC).

Printing

It would be incredibly useful for people to be able to print out this page. When I try to print this page I get muddled tables - pages break in the middle of cells, the top left edge of cells which occur at the top of a page is left out, some symbols don't show up.Is it possible (using CSS or some other method)to tell the printer that certain things (like table cells) are inviolable? Then you could set something up such that the whole table gets broken up into smaller tables (depending on where the end of a given page is, which I presume is variable across different platforms/setups) and the rule would be: divide table cells so that only the line between two large cells (i.e. the cells which contain the symbols, and which correspond to individual entries) may be interpreted as a breakable point in the table. With CSS I would think you could get the table to construct itself dynamically that way, assuming that CSS knows anything about or can account for the behavior of printers. As for some symbols not showing up in printing, I can't fathom why, it shows up fine in my browser, and the omitted symbols are not limited to symbols which occur at page breaks. Also, it only seems to affect the large symbols at the beginnings of each entry, so if anyone thinks they have an idea what this kind of problem sounds like, please fix. Note for testing purposes, I'm using Mozilla firefox. Things may (possibly) behave differently with different browsers. --Unknown

The table seems to print just fine using Internet Explorer 7.0 Beta, and most likely with the (stable) 6.0 release also. --User:ABelani 3:54, 9-Feb-2006 (UTC)

Inclusions

Does pi really belong here? It is the only constant in the table. If pi is here, why not 0?

Well for one, zero is number. But you have the right idea. There is at least one mathematically derived constant, e. So it would be interesting to know if pi would fit the bill of a mathematical symbol?--metta, The Sunborn ☥ 03:52, 25 Mar 2005 (UTC)

Template:MathSymbols - starting a quick reference template. -==SV 20:07, 25 Mar 2005 (UTC)

If Pi is in there, shouldn't the number "e" be in there as well? And perhaps (yet less relevant because less frequently used) Phi? I'd include them myself but as this is a rather essential article, and i'm rather clumsy :p Fisheke 02:37, 14 January 2006 (UTC)

Yeahhh hmmm well the letter "e" is a symbol-- not a constant. However, Euler's number, which is written using the letter "e" is a constant-- this is kind of a poor distinction, but it avoids having to put rather pointless descriptions for the numerals 1-9, which are symbols. With constant values. I think the worry lies in whether common variable names should go in there, too, because (using phi as an example) phi is commonly used as either an angle or as a pseudo-ratio (how precise is phi?). I think there should be a completely seperate table altogether for those, but linked obviously to this one, so the wikireader will think "oh, wait, maybe I'm looking for a CONSTANT (/variable), not a SYMBOL..." I'm also complaining quietly that we SHOULD have pictures (.png, .svg, whatever) because a lot of these are not in the "basic Unicode set" or whatever it's called, and (IMHO) unicode is so wierdly organized that it should be avoided (i.e. everything is scattered, e.g. the accented "e"'s are seperated (grave/otherwise)). Eh be sure to tell me if I'm being mean to unicode, though... I might be a little too critical, because I'm thinking that someday the unicode characters will be reordered and then replacing those numbers WILL be hard-- I've concluded that replacing pictures with their respective unicodes is probably an easier transition than making everybody download special character sets or using TeX (though TeX is kinda pretty and is a neat idea as far as I understand it). Nick 20:43, 26 April 2007 (UTC)

If we have pi we should also have e, phi, i, and any other symbols that are used to represent numbers. Personally I don't think any of them should be in there.

81.159.20.37 (talk) 16:15, 8 April 2009 (UTC)

"empty set" and "null set"

I reverted, a recent edit which changed the entry in the explanation column for the empty set from:

∅ means the set with no elements.

to:

∅ means the set with no elements, called a "null set".

This edit is problematic since although the empty set is sometimes also called the "null set" (there is only one empty set) the term "a null set" usually refers to a set with measure zero (see null set). In any case, the explanation column, is just to explain what the symbol means, not to give additional information.

Paul August ☎ 20:24, Jun 26, 2005 (UTC)

Editorial notes

The following two editorial notes were moved from the article to here

If some of these symbols are used in a Wikipedia article that is intended for beginners, it may be a good idea to include a statement like the following, (below the definition of the subject), in order to reach a broader audience:

''This article uses [[table of mathematical symbols|mathematical symbols]].''

The article wikipedia:How to edit a page contains information about how to produce these math symbols in Wikipedia articles.

—Preceding unsigned comment added by Paul August (talk • contribs) 30 Jun 2005

Some thoughts

• It might be worthwhile breaking the table up to make editing easier
• is the square-root sign also used more generally, to mean "if you do function B twice, then that's the same as doing function A once'?
• the "not" function is also used in boolean algebra, as well as propositional logic
• where's dot product and cross product? What about that wedge product thing, which I have never understood?
• there should be an entry for +/-
• there should be an entry for the delta symbol, meaning change in
• there should be an entry for the forcing symbol $\Vdash$

Physics quantities and symbols

This article is not really about symbols, it's more specific that this:

1. It's about mathematical symbols'
2. It's really about notation, nothing else. π doesn't belong here, for example..

So we have to move out the long new section on physics, but where should we put it? ❝Sverdrup❞ 00:45, 11 January 2006 (UTC)

I'll have a stab at merging Physics bit with Physical constant, which is where some of it should belong. Wish me luck! --H2g2bob 20:59, 12 January 2006 (UTC) -- Also created Variables commonly used in physics for most of it

I was going to make the same note: π does not belong here. Ulf Karlsson 10:33, 11 January 2007 (UTC)

Help!

Hi, I wasn't logged in, but I added the << and >> for "much less than and much greater than". I also added <> for inequality since it is commonly used in typing "non-strict" inequalities on a keyboard. However, there is a cell in the table now under "Inequalities" that says "everywhere" (meaning that the symbol is used everwhere). The problem is, I can't seem to get that word vertically centered in the cell. No idea why?? I tried valign, but it didn't seem to work. capitalist 11:28, 19 January 2006 (UTC)

Wrong Equation

$\{a:|a|\in \mathbb {N} \}=\mathbb {Z}$ is not always true, as $\{a:|a|\in \mathbb {N} \}=\mathbb {N}$ can be true also.

Instead the formula should be $\{a,-a:a\in \mathbb {N} \}=\mathbb {Z}$.

--dionyziz 16:48, 25 March 2006 (UTC).

If $\{a:|a|\in \mathbb {N} \}=\mathbb {Z}$ is not always true, then there must be a counterexample which shows that. However, I cannot see what value of "a" would provide that counterexample.

I'm also lost on how the fact that $\{a:|a|\in \mathbb {N} \}=\mathbb {N}$ leads to the conclusion that $\{a:|a|\in \mathbb {N} \}=\mathbb {Z}$ is not always true. capitalist 03:18, 26 March 2006 (UTC)

The statement $\{a:|a|\in \mathbb {N} \}=\mathbb {Z}$, is saying that the set $\{a:|a|\in \mathbb {N} \}$, that is the set of all numbers whose absolute value is a natural number $\mathbb {N}$ is equal to the set of all inegers $\mathbb {Z}$. Either those two sets are equal or not, it is not something which can be "not always true". In this case the two sets are equal. That is, every integer's absolute value is a natural number, and any number whose absolute value is a natural number is an integer. Paul August ☎ 03:56, 26 March 2006 (UTC)

Exactly, there's nothing wrong with the original equation. For a minute there I thought I was missing something. Thanks! capitalist 03:53, 27 March 2006 (UTC)

Is 3+4i an integer? Fredrik Johansson 07:27, 20 April 2006 (UTC)

It is true that the equation |a|∈N is true for all a∈Z. However, the main point is that, if we try to define Z using this equation, we do not know which values of 'a' to check, to see if they satisfy that equation.

Like Fredrik says, if we check a=3+4i to see if it satisfies the constraints, we have |3+4i| = sqrt(3^2+4^2) = sqrt(9+16) = sqrt(25) = 5. 5 is a member of N. Therefore |3+4i| is a member of N. Therefore 3+4i is a member of the given set.

In other words, the first definition is too vague. If we wanted to specify which values of a to check, we would have to mention Z or Q or R, which makes this definition much more clumsy.

The second definition is much better, since it directly specifies the set of values which a can take.

DonkeyKong the mathematician (in training) 14:47, 28 May 2006 (UTC)

That's the counterexample I was asking about. Makes sense to me now. Thanks! capitalist 02:34, 29 May 2006 (UTC)

The identity symbol

As a pedantic logician, I am unhappy with the explanation of the identity symbol given in the table. The formula '1+1=2' does not mean that 2 and 1+1 represent the same thing - it means that 2 and 1+1 ARE the same thing. The number two, after all, is not a symbol, and does not represent anything. Perhaps the writer intended ' 'x=y' means that 'x' and 'y' represent the same thing or quantity'. However, this is wrong too, for it fails to apply when 'x' and 'y' are being used as variables rather than proper names. I suggest: ' 'x=y' means that x and y are one and the same thing or quantity'.

Since the article is about symbols, wouldn't the statement in question refer to the 2 strings of SYMBOLS "1+1" and "2" as representing the same quantity when the symbol "=" is placed between them? Obviously the two strings are not the same; the first has 3 elements, "1", "+" and "1", while the other has only one element, "2". However, since the two strings are well-ordered, they each have the power to represent something in the real world. It so happens that they each represent the SAME thing, the quantity we humans know as "two". In order to communicate that relationship between these two VERY DIFFERENT STRINGS OF SYMBOLS, we use the symbol "=". capitalist 02:15, 19 April 2006 (UTC)

It is of course true that '1+1' and '2' have the same referent. However, one should not define identity by saying that 'x=y' is true iff 'x' and 'y' have the same referent. As I said, this definition fails when 'x' and 'y' are being used as variables rather than names. Consider for example the following statement of the 'symmetry of identity':

(for all x)(for all y)(If x=y then y=x)

Here 'x' and 'y' are not being used as names. They have no referents, and so the proposed definition fails to apply. The point is discussed in the opening of the third lecture of Kripke's Naming and Necessity.

I would have to disagree that "x" and "y" are not being used as names in the statement of identity. It's true that "x" and "y" are being used as variables in the two universal quantifiers at the beginning of the statement, but the statement would be meaningless if it did not imply the assignment of a specific value to the two variables in the conditional to which the quantifiers apply. When we say (If x=y then y=x), we are saying if effect, "Find the referent of "x". Do you have it? Good. Now find the referent of "y". OK, now that you have two individual, specific, constant(non-variable), very concrete real-world values in mind, tell me if the first is equal to the second. It is? Then according to this statement of identity, I can conclude that the second value is equal to the first as well." The purpose of a universally quantified statement is to say something general which can be applied to all possible SPECIFIC cases. The variable stops being a variable and starts being a name when you get past the quantifiers and into the propositional part of the statement itself.

Of course this is all a quibble on the underlying philosophy of logic. My view (which is probably in the minority) is that logic is not simply a word game or a self-consistent system of rules for the manipulation of symbols. Logic is a tool which allows real human beings to communicate in a more precise way about the real world in which they really live. Therefore, every term, variable, string, and symbol refers to something that really exists, or else it's meaningless. I'm not familiar with Kripke, but his view may differ.

At any rate, this Wikipedia article is like logic; it's meant to help people do something...not to confuse them. To change the statement about the equality symbol to "'x=y' means that 'x' and 'y' are the same thing" is not only meaningless and confusing, but demonstrably untrue. "x" and "y" are certainly not the same thing. They occupy two different locations in the alphabet and their ASCI codes are different. However, understood as SYMBOLS, "x" and "y" can certainly REPRESENT the same thing. That's what symbols do; they represent real things. But we shouldn't confuse them with the real things which they represent. capitalist 03:52, 20 April 2006 (UTC)

You have miscopied my proposed definition. You rightly criticise the proposed definition "'x=y' means that 'x' and 'y' are the same thing". However, this definition has inverted commas where mine had none. I doubt that the point is really important enough to merit much continued discussion. Either one of us is in error; perhaps a third person could spot the mistake!

Algebraic Multiplication

It is common for a dot or asterisk (*) to be used in place of the cross (X) in algebra due to X being the most common variable.

For example: 7*7=49

Sharp is a maths symbol

I saw in Schnirelmann density this # symbol and received this answer :

The symbol "#" is used in front of a set to indicate the number of elements in the set, so #{2,4,6,8} = 4. In the article, \#(A \cap \{1, 2, \ldots n\}) is the number of elements of A which are in the set {1, 2, 3, ..., n}. Hope that helps! Madmath789 21:00, 27 June 2006 (UTC)

I do not know how to enter "#" in the table, which looks quite complex. If it belongs there, please help. Thank you. --DLL 17:41, 28 June 2006 (UTC)

# has been added. Alksentrs (talk) 03:37, 22 November 2008 (UTC)

Cardinality is usually indicated by modulus signs, e.g. |{1, 2, 3, 7}| = 4. This should be added next to #. (Are we sure by the way that # is a mathematical symbol and not one from physics or computer science?)

81.159.20.37 (talk) 16:22, 8 April 2009 (UTC)

The |…| notation is already in the table. Alksentrs (talk) 17:52, 8 April 2009 (UTC)

< and > vs. << and >>

In the table, the symbols < and > and the symbols << and >> are not only placed under the same mathematical category, but are actually in the same "symbol section". These two symbols represent two very different ideas. < and > mean strictly less than or greater than, something purely algorithmic. A computer can analyse two numbers and determine if one is greater than the other. On the other hand, << and >> are "informal" symbols, they don't have a strict mathematical meaning. The property of x being much greater than y is a matter of opinion and has no algorithmic equivalent. I'm not denying that << and >> are useful symbols, they are used often in applied mathematics, but i feel that they should be put in their own section rather than with < and >. I mean, ≤ and ≥ have their own section, and they are way closer in meaning to < and > than << and >>.

By the way, after a bit of thought, the only place where I can think << and >> can be used algorithmically is if they are used to denote "much less/greater than" in transfinite set theory, as in $\aleph _{0}\ll \aleph _{1}$, but I have never seen it used that way so I highly doubt it. So dont mention it in the article because its just my idea ;). --AndreRD 11:57, 9 August 2006 (UTC)

I was the one that originally added the << and >> entries to the table. I put them in the same section as the other inequalities because they do in fact represent a subset of the notion of "inequality", albeit an informal one. The article will be used by casual readers as well as mathematicians, and the casual reader will not attach much significance to the distinction of "algorithmic vs. non-algorithmic" relationships. A casual user who is trying to find the "much greater than" symbol would tend to look for it in the area of the table that deals with equality and inequality, because those concepts are much more familiar to a wider audience. capitalist 02:42, 10 August 2006 (UTC)

Couldn't you have just made a new section, maybe called "strong inequality" or something like that as a seperate box next to the other one? --AndreRD 10:58, 10 August 2006 (UTC)

Sure, except that I had no inkling at the time that it would be an issue to put them in the same box. I would support that change though; sounds like a good idea! capitalist 02:59, 12 August 2006 (UTC)

not equals

I question whether "!=" and "<>" are mathematical symbols. I think they are only computer-language operator names. --Zero^talk 13:33, 27 August 2006 (UTC)

Since much of today's mathematical communication is now done via computer keyboard (in online forums, email and so forth), the table shows the "keyboard friendly" symbols as well as the standard ones. Maybe there should be some kind of distinction made within the table to show that, but I'm not sure how to do it without messing up the table structure. Any thoughts? capitalist 02:39, 28 August 2006 (UTC)

I agree that != and <> should not be part of the main table in this way. IMO you can't really claim that they are generalised 'computer science' terms, since their use is language dependent. 'Keyboard friendly' sounds sensible, but then they shouldn't appear in the HTML/Tex column. Sorry this is not more constructive, I'm not sure what the answer is, short of creating a whole new column which would only apply to one or two items. Could it perhaps be included in the description part instead? --Joff

other norms

Sometimes the "absolute value" symbol is used to mean the Euclidean distance (or with a subscript it could mean any of a class of norms). Many economics and calculus texts throw this at students without explination or the explination is in the little read appendix or chapter zero. I recieved some questions about this today, and thought that maybe adding in a note at least about euclidean distance to the absolute value symbol section would be good. I'm not sure about other norms, as they would usually be more advanced or well introduced near their first use. Smmurphy^(Talk) 20:54, 10 September 2006 (UTC)

Make easier to read

i am really interested in learning these things and i think you should make it eaiser to read or mabey it is i just don't get it so could someone please make this eaiser to read and understand Pineapple breath 02:26, 17 October 2006 (UTC)Pineapple breath

Split the table, maybe?

I've recently been studying set theory at great length, and had difficulty finding a "cheat sheet" of Set-builder notation, finding the wiki article on the subject useless. After 30 minutes wasted trawling wiki and Google for a guide, I finally found this page, and I'd love to link set-builder notation to this page, but jump to the appropriate symbols. For this reason I think the table should be split into sub-tables based on usage - one heading for symbols used everywhere, one heading for set theory, etc. I feel it'd not only make interwiki linking easier, but also improve readability. Unfortunately, I lack the ability to do this myself - wiki table markup makes my head spin. AKismet 08:10, 27 October 2006 (UTC)

I'd say that would be a good idea, especially as there's no real order in the table now. --h2g2bob 17:40, 27 October 2006 (UTC)

I've had a go at splitting a little of the table at User:H2g2bob/sandbox, just to get an idea of what it's like. This duplicates some of the symbols into different tables. But as I see it, the choice is between:

• Split the table, but have the same symbol mentioned in different tables
• Keep the table as one table, but explain everything so it is really long. As more and more symbols are added, the table might become almost unreadable.
• Remove all descriptions and have a very slimlined list, just pointing to other articles.

Not really sure which is best though. --h2g2bob 18:06, 28 October 2006 (UTC)

I'm in favour of repetition. That way, when searching for a symbol, the article related to that symbol can link to the appropriate section. If someone stumbles onto this table by themselves, looking for a symbol, they should at least know what field of mathematics they're working in. By the way, your table is broken... AKismet 19:36, 5 November 2006 (UTC)

Split the table--renewed proposal

This topic seems to have died out without a conclusion. I believe the table would be better if split into a small number (perhaps 3-5) sections. These sections might be Basic notation, Set theory, Logic, etc. The list would be nicer to look at, easier to read, easier to update. Symbols used in more than one category would be repeated but only an explanation and example relevant for each section would be given there. Then there could be a note to point readers to uses of the same symbol in other sections. Any objections to this? Hult041956 (talk) 18:10, 1 February 2008 (UTC)

I agree in principle, as long as repetition is minimised. —DIV (amended 128.250.80.15 (talk) 10:21, 22 April 2008 (UTC))

Universal Quantification

I think the description of this operator is incomplete. The article seems to describe the operator together with the colon, but how is it read when it appears without a colon, like here: http://en.wikipedia.org/wiki/Zermelo-Fraenkel_set_theory#The_axioms

Thanks! -- Matt24 14:40, 25 November 2006 (UTC)

Span

The notation <.....> can be used to represent the span of a vector space. For example R^2 = <(1,0),(0,1)>

83.10.14.253 20:22, 31 December 2006 (UTC) x
sign = does not mean, in my opinion, that x represents the same value or thing as it is written here. For emample

consider y= x * (y/x) ,is it true? You may say "no", but then you admit that "=" means the same as "≡". You may say "yes" and then you admit that "=" is not the same as "≡",
then to write an equation accurately we need to write:
y = x * (y/x) and x is not 0. (1)
You may also write: x * (y/x) = y and x is not 0. (2)
(1) and (2) differ. Why? Consider:
y <= x * (y/x) and x * (y/x) => y, while "=>" means "iff".

83.10.14.253 20:22, 31 December 2006 (UTC)

!

I read the discussion of != above for "not equal", and it's validity as a typeable equivalent to a mathematical symbol, thanks to use in programming languages and plaintext fora.

However, != is a specialization of the use of the general use of ! for "not" (e.g. (!(!A) ⇔ A) ≡ (¬(¬A) ⇔ A). Does the symbol require mention alongside the other "not" symbols due to its prevelance in plaintext environments? If so, what to do about the entry for "factorial"? Paul.w.bennett 19:47, 4 January 2007 (UTC)

I'm thinking the same thing, that the entry for "factorial" should contain the same subsection as "logical negation". Seeng as how other sections also duplicate subsections, I have made it so. --JanGB (talk) 11:12, 26 January 2009 (UTC)

≜

This is another symbol for "is defined by". It too is found in computing, but in mathematical descriptions in computer science of algorithms, data structures and so forth (rather than program source code). Is it worth including? Paul.w.bennett 19:47, 4 January 2007 (UTC)

It is already in the table, but I would like to comment anyway :-)

To me this symbol is obscure, compared the the triple-dash symbol (which I prefer). I've noticed that several WP articles use just "=" with "def" written above it (note: should not be italic). I have no idea where the latter came from, and am not fond of it at all because it introduces more letters, is more fiddly to 'type out' (in general!), and seems to be rather language-specific (unlike most other other mathematics notation). Still, it would be worth mentioning, too, in the table.

—DIV (128.250.80.15 (talk) 07:28, 22 June 2008 (UTC))

I agree that the symbol "=" with a "def" should be added, because other users have come here to determine its meaning, but it is missing. Wizard191 (talk) 02:36, 20 November 2008 (UTC)

${\overset {\underset {\mathrm {def} }{}}{=}}$ has been added. Alksentrs (talk) 03:25, 22 November 2008 (UTC)

For All

The inverted "A" symbol is denoted as meaning "for all" when I believe it only means "all". Often, the backwards "F" is used to mean "for" and hence the backwards "F" and inverted "A" are used together to mean "for all" Mingramh 15:44, 23 February 2007 (UTC)

Source? T.Stokke 17:10, 3 August 2007 (UTC)

Approximately Equal

Another sign I have seen for "Approximately Equal" is the equal sign with a dot above it. Mingramh 15:46, 23 February 2007 (UTC)

Factorials

Factorials are conventionally written in decreasing order of the factors NjtoTX 02:47, 8 March 2007 (UTC)

Does that mean 8! = 8x7x6x5x4x3x2x1? And does anyone bother writing out that last one, when expanind factorial? --pizza1512 ^{Talk Autograph} 11:06, 16 April 2007 (UTC)

That's how we teach it in middle school and high school math texts in the U.S. NjtoTX 01:41, 13 August 2007 (UTC)

important article

submitted as "good article" candidate 69.140.164.142 16:08, 31 March 2007 (UTC)

I have removed this article from the Good article candidates list because it is not an article, and therefore would have a hard time quantifying whether it fulfills the good article criteria. Please consider nominating this article for featured list status instead. Dr. Cash 03:45, 1 April 2007 (UTC)

Missing linear algebra

Just browsing through the list, it seems to be missing various parts of linear/matrix algebra: The perpendicular sign for vector spaces, the determinant operator, and the row equivalence operator are the only ones I can think of without looking at my textbook. If no one has any objections, I'm putting them in. IMacWin95 01:55, 25 April 2007 (UTC)

The Definition of Exclusive Union is Unclear

The definition presented:

(exclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, but not both. "A or B, but not both."

does not seem to make sense. In fact, it seems to be the opposite of the concept of union. Since exclusive union is not addressed on the page which defines union in set theory (Union (set theory)), it would be helpful if it were better clarified how a single symbol can seemingly represent two opposite concepts. --SLMarcus 17:07, 28 April 2007 (UTC)

I've removed the exclusive union (leaving just the “inclusive” union). Has anyone even heard of it before? Alksentrs (talk) 23:53, 13 October 2008 (UTC)

Missing d/dx and δ and Δ

d/dx is usually considered a "symbol" as far as I know. The symbol for partial differentiation IS included though without the /dx part - these should be consistent.

δ is often used in calculus derivations to mean "a not-infinitessimaly small" increment

Δ is generally used to mean "change in"

Dhollm 14:45, 7 May 2007 (UTC)

Missing symbol \mapsto

It would also be useful to add the 'arrow with vertical bar' as used in likelihood function:

"In statistics, a likelihood function is a conditional probability function considered as a function of its second argument with its first argument held fixed, thus:

$b\mapsto P(A\mid B=b),\!$"

Paul A Bristow 17:03, 10 May 2007 (UTC)

↦ has been added. Alksentrs (talk) 03:27, 22 November 2008 (UTC)

Can't see the Real or Complex Numbers symbol

There are 2 symbols in this table for Real or Complex Numbers. One is a bold K, and the other I can't see. I have tried installing some other unicode fonts, but I can't get it to display, and it is the only symbol on this page that won't display for me. I was wondering if anyone might know anything about what font I need to display this symbol. I am using Internet Explorer 7. MiNombreDeGuerra 04:02, 22 May 2007 (UTC)

Some extra symbols

Isn't ≅ also used for "isomorphic to" (group theory)?

Empty parentheses $(\ )$ can be used for the identity permutation.

It would be helpful if / "divide" was near / "quotient set".

+ (in linear algebra) can be used with subspaces: $U+V:=\{u+v|u\in U,v\in V\}$.

129.67.18.183 09:59, 22 May 2007 (UTC)

Second column too narrow

The second column of the table is too narrow. The text of the second column looks way too bunched up. I tried to set the second column to a fixed width, but I couldn't figure out how to do it. I tried the ways to set the width of a column that are given in m:Help:Table#Width, height, but none of them worked. Maybe someone else can figure out how to set the second column to a fixed width. MiNombreDeGuerra 19:01, 6 June 2007 (UTC)

Browser settings

To display all the mathematical symbols in UTF-8 using Internet Explorer one needs to set the font used to Arial Unicode MS or Lucida sans Unicode. If the Wikipedia articles appear to be missing characters, this might be a possible cause. --Jbergquist 09:38, 5 July 2007 (UTC)

||

The '||' symbol can be used to indicate concatenation. Is anyone able to have a go at including this in? fonetikli 02:58, 8 October 2007 (UTC)

What about $+\!\!+$ or ++ (Haskell), + (C++ and Java) and ~ (D)? 129.67.19.252 01:49, 26 October 2007 (UTC)

It also means "exactly divides", as in 2¹ | 24, 2² | 24 and 2³ | 24 are all true but only 2³ || 24. Richard Pinch (talk) 18:47, 7 July 2008 (UTC)

For Some

is the symbol for for some==for all?? I never knew that and wanted to know. —Preceding unsigned comment added by 67.85.160.89 (talk) 20:00, 13 October 2007 (UTC)

Missing symbols & Extra meanings

< > ≤ ≥ are also used for subgroup/subfield/subspace.

| and : can be used for such/so that.

The arrow $\mapsto$ can be used for mappings (different to $\to$).

$[\![$ and $]\!]$ for multifunctions.

Suffix * used for image of a path, generic group theory operator, and set-without-zero (i.e. $\mathbb {N} ^{*}=\{1,2,\ldots \}$).

[a,b], etc. for intervals; (a,b) for ordered pairs.

129.67.19.252 01:38, 26 October 2007 (UTC)

The horseshoe commonly used for entailment should be included. This article is worthless. —Preceding unsigned comment added by 132.235.73.24 (talk) 19:55, 21 May 2008 (UTC)

Dead Link

The following link is dead: Jeff Miller: Earliest Uses of Various Mathematical Symbols (http://members.aol.com/jeff570/mathsym.html) —Preceding unsigned comment added by 71.164.135.92 (talk) 06:37, 5 January 2008 (UTC)

Meaning of - sign

Would it be acceptable to mention that the - sign denotes "the opposite of" in many high-school applications?

For example, -6 denotes the opposite of 6, which would be -6, and -(-4) denotes the opposite of -4, which would be 4.

In this context "opposite" is roughly equivalent to "negative". The distinction is subtle, and I'm not interested in nitpicking the differences. I'd just like to see both words used to describe the symbol's meaning, for the benefit of users who may be familiar with one word or the other.

Source: The term "opposite" is used in McDougal-Littell textbooks and quite possibly others too (I just wouldn't know off the top of my head).

Anyone object to the inclusion? 68.29.78.17 (talk) 06:20, 15 January 2008 (UTC)

Whatever meaning you're looking to assign (which I won't comment on here), please be clear whether the symbol is a hyphen, a certain type of dash, a minus sign, or something else such as "¬" (Unicode Not Sign, U00AC). —DIV (128.250.80.15 (talk) 07:21, 22 June 2008 (UTC))

Inability to display symbols

I am one of those who has been frustrated by the inability to display the symbols on the "Table of mathematical symbols" page on one of my two almost identical computers. They both run Windows XP, SP2 but use two different versions of Microsoft Office. According to Microsoft the font MS Mincho (file msmincho.ttc, an 8.9 Megabyte file) should be included with XP, but it was not present in the faulty computer. I copied the file from the "good" computer (to the C:\WINDOWS\Fonts directory) to the "bad" computer and that fixed the problem. I do not fully understand the problem however, because the "Help:Displaying a Mathematical Formula" Wikipedia page displayed all the symbols perfectly on both computers from day one. James W. Overbeck (talk) 17:55, 29 February 2008 (UTC)

---

That's probably related to the version of windows you have installed. MS Mincho only installs itself on my machines if I setup the Asian Language support in the 'Regional and Language Options.'

I usually use it with the Japanese IME. Later versions of windows have come with it, but it's usually only if the machine needs to process non-standard English characters. Many English speaking users don't typically need that. —Preceding unsigned comment added by 74.74.226.44 (talk) 23:23, 13 March 2008 (UTC)

Definition for the ≐ symbol and related operators

What do these symbols mean? The general idea I get from a paper using them is that they are 'similar to'

The are scattered throughout Bouguet J.'s paper "Pyramidal Implementation of the Lucas Kanade Feature Tracker" —Preceding unsigned comment added by 74.74.226.44 (talk) 23:19, 13 March 2008 (UTC)

See above and below, but could have other meaning assigned. —DIV (128.250.80.15 (talk) 10:13, 22 April 2008 (UTC)) (Amended 128.250.80.15 (talk) 07:32, 22 June 2008 (UTC))

Symbols

It's sort of pointless to open a page and see a square box for some of the symbols.

I have tried &#8810; as Times New Roman, Tahoma, and Lucida Console - and it gives me a square on each. Obviously it works with some font, as it works on my vista machine.

Why not just use a gif instead? Isn't the goal to make sure a webpage is displayed correctly for everybody? —Preceding unsigned comment added by 24.234.227.109 (talk) 21:13, 28 March 2008 (UTC)
Answer -- We should not use images in place of symbols; symbol glyphs are much more versatile in terms of typefaces (granted, unless one is using a limited font which does not include them), but symbol glyphs also superior when it comes to scaling, screen readers, and just plainly for knowing which symbol to use in your own texts (assuming you don't want gifs in your math papers). --JanGB (talk) 11:14, 26 January 2009 (UTC)

Computer science

There has been brief discussion above (not_equals, !) of the merit of including the versions from computer science. Will I give away my bias if I call these "corruptions"? I have seen 37o instead of 37° (degrees), and even x_oo instead of x_∞ (infinity). Feel free to include these 'options' too ...but just not in the same field as the correct symbols.

Anyway, I think it would be better to split the leftmost column in two, using perhaps two different shades of green.
True mathematical symbols on the extreme left, then other 'options' beside them, not equally prominent. The columns to the right don't contain so much text, and can easily be squeezed. (And the notes about "computer science" can then be cut altogether, or relegated to a clarifying footnote.)
—DIV (128.250.80.15 (talk) 10:05, 22 April 2008 (UTC))

Almost equals

Synonyms, more-or-less, for ≈ are = with dots centred on top and beneath (≑), or just on top (≐), or possibly offset from centre (≒ or ≓). —DIV (amended 128.250.80.15 (talk) 10:16, 22 April 2008 (UTC))

Borders

I don't really know where to put this, but anyway, putting some borders around those TD's would be fantastic. This page is really hard to read. —Preceding unsigned comment added by 128.182.176.95 (talk) 15:16, 13 June 2008 (UTC)

Therefore

add this symbol? ∴ 194.81.36.61 (talk) 11:00, 4 July 2008 (UTC)

I agree; I was looking here for the name of therefore sign. My wiki skills aren't quite up to adding it (yet). Fourthark (talk) 23:36, 2 August 2008 (UTC)

∴ (and ∵) have been added. Alksentrs (talk) 03:29, 22 November 2008 (UTC)

Green

Why is the leftmost column green? It doesn't add anything and makes the TeX symbols ugly. Math notation is best expressed as plainly as possible; color isn't part of math. 192.249.47.9 (talk) 17:39, 6 August 2008 (UTC)

Division symbol

The )^----- one. Is it an oversight or intentional? Thanks. Saintrain (talk) 21:13, 18 September 2008 (UTC)