Talk:Table of mathematical symbols

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[edit] 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.

[edit] 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

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

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

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

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)

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)

[edit] 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)

[edit] 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).

[edit] 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)

[edit] 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. -==S V 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)

[edit] "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)

[edit] 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 $\Vdash$

[edit] Physics quantities and symbols

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

It's about mathematical symbols'
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

[edit] 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)

[edit] 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)

[edit] 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!

[edit] 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

[edit] 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)

[edit] < 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)

[edit] 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)

[edit] 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)

[edit] 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

[edit] 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)

[edit] 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)

[edit] Span

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

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