Wikipedia talk:WikiProject Mathematics

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Shapley–Folkman lemma at FAC

The article, initiated by David Eppstein, has received many helpful reviews from this project already. The FA project would benefit from mathematicians' insights, from simple support/oppose judgments, to short copy-editing volunteering, to more ambitious commenting/editing.

Best regards,  Kiefer.Wolfowitz 22:59, 27 September 2011 (UTC)

Vector measure: Product function

Is there a simpler discussion of product function, than the universal definition given in product (category theory)?

UPDATE  Kiefer.Wolfowitz 03:32, 1 October 2011 (UTC)

In advanced measure-theory, the Shapley–Folkman lemma has been used to prove Lyapunov's theorem, which states that the range of a vector measure is convex. Here, the traditional term "range" (alternatively, "image") is the set of values produced by the function. A vector measure is a vector-valued generalization of a measure; for example, if p₁ and p₂ are probability measures defined on the same measurable space, then the product function (p₁, p₂) is a vector measure, where (p₁, p₂) is defined for every event ω by

(p₁, p₂)(ω)=(p₁(ω), p₂(ω)).

Animation

Will anybody create an animation to illustrate the SF lemma?

• Mas-Colell, A. (1987). "Non-convexity". In Eatwell, John; Milgate, Murray; Newman, Peter (eds.). [[The New Palgrave Dictionary of Economics|The new Palgrave: A dictionary of economics]] (first ed.). Palgrave Macmillan. pp. 653–661. doi:10.1057/9780230226203.3173. (PDF file at Mas-Colell's homepage). {{cite book}}: Invalid |ref=harv (help); URL–wikilink conflict (help); Unknown parameter |newedition= ignored (help)

The best image would illustrate the set

S = 1/2 ( [0,1]×[0,2] ∪ [0,2]×[0,1] )

and then

$S_{N}={\frac {1}{2^{N}}}\sum _{1\leq n\leq 2^{N}}{S}\qquad (N\geq 2)$

for N = 0, 1, 2,3, ∞.

A translate of this set appears in Mas-Colell's article on non-convex sets (etc.).  Kiefer.Wolfowitz 18:58, 5 October 2011 (UTC)

FA review: Images and a Spot-check of references

Editor Ucucha asked for editors to examine the images of the article and to provide a spot-check of the references (which imho are very carefully done). Best regards,  Kiefer.Wolfowitz 18:45, 7 October 2011 (UTC)

Project members Geometry Guy and Ozob provided many helpful suggestions and well-documented criticisms of the article, which will take another week to address.

The image review has been passed, and David Eppstein's graphics received compliments on the relevant project's talk page (cited on FA nomination page).  Kiefer.Wolfowitz 20:15, 10 October 2011 (UTC)

Category:Mathematical function templates

Category:Mathematical function templates is undergoing a bit of a cleanup at the moment with quite a few of the templates there being sent to TfD. These include several templates for performing specific calculations: {{Oom}}, {{Absolute value}}, {{Sgn}}, {{Root}}, {{Addition}}, {{Add optional}}, {{Subtraction}}, {{Factorial}}, {{Rangemap}}. See the discussion at Category talk:Mathematical function templates.--Salix (talk): 06:28, 30 September 2011 (UTC)

The above category seems (to me) to contain three types of templates.

• templates which perform a function which, though possibly interesting, is not useful to the project
• templates whose function is so simple it's not worth enshrining in a template (a parser function will do) and finally
• templates which are actually useful

Come along an help out with the tidy up. JIMp _talk·cont 00:07, 9 October 2011 (UTC)

TeX not rendering

In Expectation–maximization algorithm, after the heading "Alternative description", the two lines of TeX after "expectation step" and "maximization step" are not getting rendered when I view them while logged in (and using MathJax. What's going on? Michael Hardy (talk) 19:50, 5 October 2011 (UTC)

It looks like the 'underset' command is causing the issues (just playing around with it a bit). I'm not an expert with TeX to know how to correct this appropriately without ruining the look. Anyone that knows this better can you please fix that.Zfeinst (talk) 19:58, 5 October 2011 (UTC)

There was no need for underset; I replaced it with \operatorname*{arg\,max}_q . Does this help Michael? The entire arg max article uses the underset command, it might be worth making the changes there, too. RobHar (talk) 20:30, 5 October 2011 (UTC)

I did manage to get it to display correctly by putting in another set of curly braces in each display. I'll take a look at later edits (if later edits are what you did). Michael Hardy (talk) 23:06, 5 October 2011 (UTC)

I see. Your way of doing it is also instructive. Michael Hardy (talk) 23:07, 5 October 2011 (UTC)

Just came across the same issue in Möbius transformation. Math like this not rendering

$\chi ({\hat {\mathbf {C} }})=2.$

adding extra braces fixed it.

$\chi ({\hat {\mathbf {C} }})=2.$

The problem was with both \hat and \widehat commands in about half a dozen formulae, so it looks like it's a more general problem with how the parser of these things works.--JohnBlackburne^words_deeds 21:58, 6 October 2011 (UTC)

See also Wikipedia:Village pump (technical)#Math/Latex --JohnBlackburne^words_deeds 22:36, 6 October 2011 (UTC)

and also Template:Bugzilla.--JohnBlackburne^words_deeds 16:02, 7 October 2011 (UTC)

Posted at the above bug you can search for all of these using Google, e.g [1]. I've fixed a few already but don't have time or the patience to do much more.--JohnBlackburne^words_deeds 16:01, 9 October 2011 (UTC)

Thanks for posting the google link, I'm going through a bunch of them now (starting at a random page in the results). Zfeinst (talk) 18:16, 9 October 2011 (UTC)

I believe I have fixed all the LaTeX parsing errors that I could find in articles. Zfeinst (talk) 20:01, 9 October 2011 (UTC)

Wishful thinking, not done yet: 1 2 3 4 5 6. It will take a while for Google to find them all. Dragons flight (talk) 20:52, 9 October 2011 (UTC)

Just keep sending them my way, I have a lot of free time today. Zfeinst (talk) 20:55, 9 October 2011 (UTC)

Thanks for doing all those, you clearly have more patience than me. And yes, it may be a time before they are picked up by Google, depending how often it checks pages. I wouldn't be surprised if we're still seeing them weeks from now, unless there's some way of doing it automatically using MediaWiki.--JohnBlackburne^words_deeds 21:00, 9 October 2011 (UTC)

If you know a specific chunk of code that generates errors, you can put that into the Wikipedia search engine to find all pages that use it, e.g. "\hat\mathbf". However, there is a delay with Wikipedia's index too, so you'll also see old results sometimes. And of course, the number of variations that could cause failures is quite large. Dragons flight (talk) 21:05, 9 October 2011 (UTC)

I went through the 6 that you posted. I'll now try my own searches, thanks. Zfeinst (talk) 21:21, 9 October 2011 (UTC)

In the german Wikipedia we have the same problem and I created a little Bash-script in order to find some still uncorrected errors. There is no guarantee that script will find every error, but it finds at least more errors than google.

#!/bin/sh

# No warranty, use at your own risk!

# As the first parameter you need a CatScan
# (http://toolserver.org/~magnus/catscan_rewrite.php?interface_language=en)
# with format "TSV" (with first two lines deleted)

if [ $# -ne 1 ]
then
  echo "Calling: $0 <CatScan>"
  exit
fi

if test -f $1
then

  if test -f $1.out
  then
    rm $1.out
  fi

  for i in `cut -f 1 $1`; do
    lynx -source http://en.wikipedia.org/wiki/$i | grep "Failed to parse" > /dev/null
    if [ $? = "0" ] ; then
      echo \* \[\[$i\]\] | tee -a $1.out
    fi
    sleep 0.2
  done

else
  echo "File $1 doesn't exist"
fi

I didn't tested it in WP-en, maybe there is still some localisation work to be done. --KMic (talk) 00:04, 12 October 2011 (UTC)

I've done a few more using Google to find them, but one was especially interesting: [2]. In it I fixed four lines even though only one was a 'Failed to parse' error. The others I found by finding '\dot\hat' in the edit window, after spotting two at once. The problem is it will happily render this, but incorrectly, e.g.

${\dot {\hat {\mathbf {x} }}}$, which should be ${\dot {\hat {\mathbf {x} }}}$

This was brought up in the VP thread but I didn't think through the implications. Neither ways of searching (the script or Google) will find these, and they're very difficult to spot (these are often very formula heavy pages). There's no easy way to search the wikisource that I know, and potentially a large number of patterns to match (many symbols, maybe spaced or with other things involved).--JohnBlackburne^words_deeds 00:43, 12 October 2011 (UTC)

I can at least explain what is going on, and if I am correct you can blame me for the bug. Texvc has a tendency to add extra braces to sanitize its input. It also adds lots of spaces. In combination these two things do not cause much harm together. Unfortunately this cause a small problem with code <math>\operatorname{sen}x</math> which would get parsed to something like $${\operatorname {sen}}x$$ which obliterates the point of \operatorname. To fixed this bug I removed some unneeded braces (uneeded from the latex point of view, clearly needed from the texvc point of view). Unfortunately there is lots of latex code which seems like it should compile under latex but doesn't. For example, at least on my systems $$\hat\mathbf{C}$$ fails to LaTeX, but the extra braces that texvc was putting in would sanitize this to something that would LaTeX. To complicate all of this some of it is system dependent. This seems system depedent. For example on my University's Unbuntu system $$\dot\hat {x}$$ simply doesn't compile under LaTeX, while under Mageia it does compile but offset as shown above, and in any case it should be sanitized as it used to be. I just had this bug called to my attention and I am working on it now. Thenub314 (talk) 23:02, 12 October 2011 (UTC)

I also found <math>\frac 1 \sqrt{2}</math> not working,

${\frac {1}{\sqrt {2}}}$

but <math>\frac 1 {\sqrt{2}}</math> does. (Note: I don't know whether this problem is due to MW 1.18, nor if it has already been fixed). --KMic (talk) 13:11, 16 October 2011 (UTC)

I don't know if it is trivial, but the new stricter parser would try to interpret this as \frac{1}{\sqrt} {2}, which won't work, whereas the previous version of the parser would somehow do look-ahead and some right-to-left parsing to get the intended meaning.

By-the-way, does that mean that texvc is now replaced by a true LaTeX-solution.--LutzL (talk) 15:13, 16 October 2011 (UTC)

Two archaic Greek letters are now available

We have long had the usual 24-letter Greek alphabet available in TeX on Wikipedia (since early 2003, I think):

$\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi \rho \sigma \tau \upsilon \varphi \chi \psi \omega .\,$

We now also have two archaic letters, koppa and stigma:

$\mathrm {\koppa} \mathrm {\stigma} \,$

I'm going to use these in some edits of Ptolemy's table of chords. They may also be useful in articles about traditional sexagesimal systems. Michael Hardy (talk) 23:10, 5 October 2011 (UTC)

PS: The way these appear if you're using MathJax may be different from the way they appear if you're not. Michael Hardy (talk) 23:11, 5 October 2011 (UTC)

There are also upper case versions

$\mathrm {\Koppa} \mathrm {\Stigma} \,\,$

and Unicode version of all four: ϘϙϚϛ.--RDBury (talk) 14:14, 6 October 2011 (UTC)

Why would you use them with something by Ptolemy, did he use them? I thought he was fairly late. Dmcq (talk) 14:43, 6 October 2011 (UTC)

He used them in the numeral system that he used, with a base of 60 and a subbase of 10. But I think the words he wrote were all in the usual 24-letter Greek alphabet. See the article I mentioned. Michael Hardy (talk) 22:47, 6 October 2011 (UTC)

Test:

$\alpha \beta \gamma \mathrm {\koppa} \mathrm {\stigma} \lambda \xi \,$

I'm wondering to what extent the appearance of these letters depends on the browser and its preferences. Michael Hardy (talk) 22:48, 6 October 2011 (UTC)

Thanks I'll be interested to see how he used them. I know the Greeks used some archaic letters in their numerals but not koppa, it's peculiar Ptolemy needed them for sexagesimal when that's positional. Dmcq (talk) 22:47, 7 October 2011 (UTC)

For the moment I'm working on properly understanding the table. I'll start doing some substantial editing when that's out of the way. Michael Hardy (talk) 00:39, 8 October 2011 (UTC)

Here is a complete list of symbols added when the ancient greek symbols were asked for: $\mathrm {\Coppa} \mathrm {\coppa} \mbox{\coppa} \mathrm {\Digamma} \mathrm {\Koppa} \mathrm {\koppa} \mathrm {\Sampi} \mathrm {\sampi} \mathrm {\Stigma} \mathrm {\stigma} \mathrm {\varstigma}$

The subsset that have Unicode HTML versions are $\mathrm {\Coppa} \mathrm {\coppa} \mbox{\coppa} \mathrm {\Digamma} \mathrm {\Koppa} \mathrm {\koppa} \mathrm {\sampi} \mathrm {\stigma}$

Some other bugs/features resolved include:

• Spanish speaking wiki's $\operatorname {sen} x\!$ is now recognized.
• In the same spirit \operatorname produces space as expected. Such as: $\operatorname {mysin} x$.
• For European's and currency enthusiasts math mode euro symbols are now supported, infact several of them: $\mathrm {\euro} \,\mathrm {\geneuro} \,\mathrm {\geneuronarrow} \,\mathrm {\geneurowide} \,\mathrm {\officialeuro}$

There were a few other small tweaks to html layout etc, but off the top of my head I do not remember which of my patches survived and which did not.Thenub314 (talk) 06:21, 14 October 2011 (UTC)

Mnemonic at Sieve of Eratosthenes‎

There's a minor dispute at Sieve of Eratosthenes‎ (yes, again) about whether a poem should be included in the article or not. Please comment at Talk:Sieve of Eratosthenes‎.

CRGreathouse (t | c) 18:50, 6 October 2011 (UTC)

I'd say in general mnemonics are an invitation for OR and rarely have much value, encyclopedic or otherwise. Most people of reasonable intelligence make up their own sentence whose acronym is SOHCAHTOA and many are tempted to add it to WP. You can remove them but it's the kind of thing that keeps popping up, for example there's an old AfD for trig mnemonics; the outcome was delete but we have a new version now with a slightly different name. It would be nice to have a guideline for when (not) include such things. I'm thinking at minimum it should appear in a reliable secondary source, meaning a source other than by the person who made it up, just as we require for poetry etc.--RDBury (talk) 00:34, 7 October 2011 (UTC)

Great, so first of all it does appear in reliable secondary source - no less than Clocksin and Mellish 1981 itself! Second, it is not a mnemonic per se but rather a folklore, long in use as evidenced by its archaic spelling used in that authoritative textbook, repeat, in 1981. In light of this, I'd expect anyone who were quick with their opinion, to rethink it and to recast their votes whether to delete it or not from the page - yes, we vote on the question whether to remove it or not, because its presence is in long-standing consensus. WillNess (talk) 18:20, 9 October 2011 (UTC)

To all participants - the matter is now reopen for new vote in light of reliable secondary source. Please cast your vote on Talk:Sieve of Eratosthenes. So far I count 2 votes TO KEEP. WillNess (talk) 18:33, 9 October 2011 (UTC)

Also please note, it is not a mnemonic but rather a folklore rhyme. Maybe the subsection name should be changed. WillNess (talk) 18:35, 9 October 2011 (UTC)

It doesn't matter to me whether you call it a poem, a mnemonic, folklore, a rhyme, or anything else. (Though in the case of "folklore" you should be careful lest it be misunderstood as Mathematical folklore.)

At the moment there's quite strong consensus that it be removed. But all of this should be discussed at the Talk page indicated, not here.

CRGreathouse (t | c) 18:39, 9 October 2011 (UTC)

"Quite strong" is currently 4 to 2, which is IMO not a large enough sample to call on. --Matt Westwood 19:11, 9 October 2011 (UTC)

The call for vote was put here, so the call for a REVOTE is put here as well. WillNess (talk) 19:45, 9 October 2011 (UTC)

PDE mathematicians

While looking at the new article Mark Vishik (mathematician) (which has a "no categ." tag) I have noticed that there is no category for mathematicians working in PDE. I guess the reason is that it is not clear how should it be called. Is there a standard noun for this? Sasha (talk) 02:47, 7 October 2011 (UTC)

The only word that comes to my mind is "analyst". But that appears to be used for many other things rather than for those who study mathematical analysis. JRSpriggs (talk) 04:43, 7 October 2011 (UTC)

I might go for "PDE theorist", but I don't know that that term is really used much. Of course, have you ever heard of a Monte Carlo methodologist‎? RobHar (talk) 05:32, 7 October 2011 (UTC)

Done: Category:PDE theorists. Sasha (talk) 15:17, 7 October 2011 (UTC)

Please help populate it.Sasha (talk) 16:27, 8 October 2011 (UTC)

Jacobson density theorem assist

Hello. I'm struggling to remember the following: let D be a division ring with discrete topology, and U be a D vector space with the product topology. Then the D linear transformations of U to U can use at least two topologies: the subspace topology inherited from U^U, or the compact-open topology. I rusty enough not to remember which is proper for Jacobson_density_theorem#Topological_characterization. Maybe they are the same in the case when D has the discrete topology? Thanks for the help. Rschwieb (talk) 19:47, 7 October 2011 (UTC)

If this is a question about math, the proper forum within Wikipedia is Wikipedia:Reference desk/Mathematics. This page is for discussion of how to edit Wikipedia's mathematics articles. Michael Hardy (talk) 06:25, 8 October 2011 (UTC)

Gallery of curves and Gallery of named graphs at AfD

Does WP:NOTGALLERY apply to Gallery of curves ? Discussion at Wikipedia:Articles for deletion/Gallery of curves (2nd nomination). Gandalf61 (talk) 20:11, 7 October 2011 (UTC)

See also Wikipedia:Articles for deletion/Gallery of named graphs - same nominator, same reason given for nomination. Gandalf61 (talk) 21:15, 7 October 2011 (UTC)

The same person nominated about a dozen such articles altogether; it's nothing aimed at a particular project though Wikipedia:WikiProject Heraldry and vexillology is being hit hard.--RDBury (talk) 04:09, 8 October 2011 (UTC)

I wouldn't call myself an inclusionist, but I've never seen such idiotic deletion nominations as in the past two weeks. Is it like this all the time, just that it doesn't effect us in mathematics? is it fish-slapping season? or what? Sławomir Biały (talk) 18:27, 9 October 2011 (UTC)

I don't know. I'm certainly not an inclusionist and yet I feel inclined to post 'procedural keep' !votes on all of these. CRGreathouse (t | c) 18:40, 9 October 2011 (UTC)

Wikipedia:Requests_for_comment/Kiefer.Wolfowitz

The community is invited to participate in a request for comment about my editing: WP:Requests_for_comment/Kiefer.Wolfowitz.  Kiefer.Wolfowitz 20:54, 8 October 2011 (UTC)

"any"

English-speaking mathematicians need to be very careful about the use of this word. At supremum I found this:

is the least element of T that is greater than or equal to any element of S.

I changed it to this:

is the least element of T that is greater than or equal to every element of S.

"any" is absolutely the worst possible word that could be used here. Reasonable readers could see "x is the least element that is is greater than or equal to any element of S" and think it means x is the least element for which there is any element of S that x is greater than or equal to. That is obviously not what is intended. Michael Hardy (talk) 16:00, 9 October 2011 (UTC)

Good point, Michael.

For some long time I have felt the lack of a clear explanation of what the quantifier words in English mean. That is, how does one translate a natural English sentence using "all", "every", "each", "any", or "some" into first-order logic? "All", "every", and "each" are universal quantifiers but they seem to imply something about the order of quantification. For example, "all" appears to be used when the universal quantifier is inside. "Some" is an existential quantifier. "Any" seems to be used as either universal or existential depending on the situation (what?). JRSpriggs (talk) 07:01, 10 October 2011 (UTC)

You also have to be careful about whether you assume the domain is always non-empty. When the domain may be empty the translation can get even more convoluted. Dmcq (talk) 07:46, 10 October 2011 (UTC)

I don't think the situation for "any" can be recoverd syntactically from English. For example, native speakers in a hurry might say both of the following:

If any element of A is less than or equal to x then x is an upper bound of A

If any two vectors in B are parallel then B is linearly dependent

You have to already know what is meant in order to read these correctly. I teach my students to just avoid the word "any" in mathematical writing. — Carl (CBM · talk) 11:22, 10 October 2011 (UTC)

I just did an informal survey of 10 "Mathematical Proofs" type texts sitting on my bookshelf. Of them 9 were mute on the subject and one definitely said that "any" is a universal quantifier without any discussion of the issue. IMO the meaning of "any" is contextually determined, and as such it should never appear in any(universal quantification) definition. To be on the safe side, I would agree with Carl and suggest that the word be avoided in mathematical writing.Bill Cherowitzo (talk) 19:29, 10 October 2011 (UTC)

Any seems unambiguous when it's paired with negation, as in "never any...". Sławomir Biały (talk) 22:28, 10 October 2011 (UTC)

I generally think that it depends on the context. For instance I have known of situations where the statement is along the lines of "for any x in X such that..." (trying to think of a page where that would be applicable right now). But in many cases the meaning would be "every" and that is certainly not wrong in the situation I give. Zfeinst (talk) 19:48, 10 October 2011 (UTC)

Free logic

Drmcq wrote, "You also have to be careful about whether you assume the domain is always non-empty. When the domain may be empty the translation can get even more convoluted. Dmcq (talk) 07:46, 10 October 2011 (UTC)"

Truly, the AMS and other authorities have cautioned mathematicians to avoid "any" because of its ambiguity.

However, "any" has a useful role (formalized in free logic) in allowing quantification without claiming existence. In particular, in lattice theory, the existence of a supremum (and infimum) in the base set characterizes complete lattices. Please double check the definition of complete lattice and see whether the original definition was correct in the real-number article, Michael.

Jaakko Hintikka has several discussions of free logic and particularly of the ordinary English uses of "any" in articles, often in Synthese, which have been republished in his books on game-theoretic semantics.  Kiefer.Wolfowitz 20:35, 10 October 2011 (UTC)

Our definition of a complete lattice does not use the word "any". If it did, we could replace the word with "all", "each", "every", "some", or similar while keeping the right meaning. — Carl (CBM · talk) 01:43, 11 October 2011 (UTC)

multimagic cube

Per my year-old request to merge bimagic cube, trimagic cube, and tetramagic cube into multimagic cube, and in the total absence of comment, I've done it. Please check to see if any of the references to the embedded stubs need to be changed. The only ones I can see are some of the semi-automated lists, and Book:Recreational mathematics. I don't understand Books....

I may also handle trimagic and tetramagic squares, per a request at the same time, but I haven't decided yet. — Arthur Rubin (talk) 23:39, 9 October 2011 (UTC)

Rename of There is no infinite-dimensional Lebesgue measure

There is no infinite-dimensional Lebesgue measure strikes me as one of the oddest titles that I've seen for an article, does anyone have any ideas on what to change it to?Naraht (talk) 14:16, 11 October 2011 (UTC)

How about 'No infinite-dimensional Lebesgue measure' or something of the like? Zfeinst (talk) 14:28, 11 October 2011 (UTC)

I think it should probably just be called infinite-dimensional Lebesgue measure. This requires some rewriting of the lede though.TR 14:36, 11 October 2011 (UTC)

Someone please tell me that an author refers to an infinite-dimensional Lebesgue measure as a "spoon" somewhere in the literature! Rschwieb (talk) 14:53, 11 October 2011 (UTC)

(ec)I'm thinking establish notability first and then worry about then name. The article only seems to list primary sources so step one isn't done yet. I think in mathematics the no neologisms rule needs to be applied more judiciously than in other subjects since authors in mathematics have a habit to refer to theorems by number instead of giving them a name, apparently a hold-over from Euclid. For example until about 1900 anyone with a background in mathematics would know what was meant by the fifth proposition of Euclid, but few would understand that phrase today so our article is called the Isosceles triangle theorem. In this particular case, even ignoring the no neologism rule the title does not conform to naming conventions. Perhaps a merge is in order, especially if notability can't be established, but I think a better solution is to call it 'Infinite-dimensional Lebesgue measure'. It meets the naming conventions and you can even argue that neologism rule is satisfied. Leave the fact that the subject does not exist in the article by analogy with fact we have an article called Unicorn and not one called 'Unicorns to not exist'.--RDBury (talk) 15:17, 11 October 2011 (UTC)

Thinking about it more, perhaps it would make sense to merge the page with the Lebesgue measure. Zfeinst (talk) 15:58, 11 October 2011 (UTC)

The current title seems just fine. It says exactly what the article is about. The claim that the sources are primary is mistaken. This is a well-known fact in functional analysis, and these can be used as secondary sources for the fact. Sławomir Biały (talk) 16:18, 11 October 2011 (UTC)

The title looks fine to me, I agree with Sławomir ... the one quibble I do have is: why do so many people insist on writing their mathematical proofs without any line breaks, all in one indigestible paragraph?

If it can be established that there is a secondary source which gives this result a name, then, as implicitly suggested by RDBury, we could call it by that name (but the implicitness in his argument is that he has been unable to fund such a name for it). I take the point about unicorns, but his argument is a bit straw-mannish, in that there is no fanciful literature or deep mythology in existence with names like "The Trapping of the Elusive Infinite-Dimensional Lebesgue Measure", with tales of wrapping a piece of cobweb round it by luring it with the tears of a virgin, or whatever the old claptrap ... Point is, unicorns exist in literature but I-DLMs don't. So discussing it as though it does have an existence (even though the entry states clearly that it does not) seems a bit silly. --Matt Westwood 20:57, 11 October 2011 (UTC)

I have to agree with Naraht that it's a strange-sounding title. Titles for WP articles should in almost all cases be nouns or noun phrases. The only time I could see admitting a complete sentence as a title is if the sentence itself is either the subject of the article, or the name of the subject of the article (an example of the latter case being The Sun Also Rises).

If a merge is not desired, I would suggest moving to nonexistence of infinite-dimensional Lebesgue measure, perhaps with an indefinite article or plural somewhere in there. --Trovatore (talk) 21:04, 11 October 2011 (UTC)

An example of a complete sentence that I would admit as a title, on the grounds that it's the actual subject of the article (as opposed to the sentence being the name of the subject of the article), is All your base are belong to us. --Trovatore (talk) 01:27, 12 October 2011 (UTC)

The title is currently a violation of WP:NOUN, so I've moved it to Infinite-dimensional Lebesgue measure. If someone prefers non-existence of infinite-dimensional Lebesgue measure then they can move it there; I wouldn't mind. Ozob (talk) 11:59, 12 October 2011 (UTC)

There are at least two good litmus tests for titles. One is that it accurately describes what the article is about, and the other is that it succeeds in leading people to the content they are looking for. I think "Infinite-dimensional Lebesgue measure" does the best at both tests, and the nonexistence bit will surely not go overlooked in the body. Rschwieb (talk) 14:11, 13 October 2011 (UTC)

Pythagorean triples grow on a tree

I finally got around to creating Tree of primitive Pythagorean triples. Probably more articles should link to it than currently do, and it needs other further work as well. Michael Hardy (talk) 21:16, 11 October 2011 (UTC)

There's some content from Pythagorean triples that should be reduced down and merged here. Sławomir Biały (talk) 10:42, 12 October 2011 (UTC)

So far only three articles link to the new article, if you don't count disambiguation pages and topics lists. Michael Hardy (talk) 15:17, 12 October 2011 (UTC)

Mathematical theorems category unwieldy

Category:Mathematical theorems currently has over a thousand articles and is pretty much useless for navigation. There a few subcategories by area but not enough to make a dent in main category. I'd like to propose splitting the category into subcategories by the list of areas we use in the 'maths rating' tag, specifically:

• Category:Theorems in analysis
• Category:Theorems in algebra
• Category:Theorems in geometry
• Theorems in applied mathematics
• Category:Theorems in number theory
• Category:Theorems in discrete mathematics
• Category:Theorems in the foundations of mathematics
• Theorems in mathematical physics
• Category:Theorems in topology

I'm leaving out probability and statistics since they are already covered, and the other areas because they're either not applicable for theorems or they aren't specific areas of mathematics. If no one has objections or a better idea I was going to get the process started by creating and populating 'Theorems in geometry'; I just spent an hour trying to locate articles on two theorems in geometry and in that time I could probably have gotten most of the possibles into a category so the next person will be able to do it more easily.--RDBury (talk) 05:44, 12 October 2011 (UTC)

Sounds like a good idea. I'm not clear on how subcategories work; is it possible for the same page to be listed in two or more different subcategories? Jowa fan (talk) 06:05, 12 October 2011 (UTC)

Any page can be listed in any categories whatever. —Mark Dominus (talk) 06:17, 12 October 2011 (UTC)

The categories in commons at commons:Mathematics are a bit of a mess too. For instance there's a mathematical theorems category at the top level but to get to mathematical proof you have to go through Subdivisions of mathematics to Discrete mathematics to Mathematical logic and then to Mathematical proof as far as I can see. Dmcq (talk) 09:14, 12 October 2011 (UTC)

Update: I wend ahead and created the geometry category and it now has 97 articles (and counting), check the link above. A hundred or more articles in a category is still pretty large so further division is possible but probably not a high priority. I also changed some of the maths rating tags for articles that where marked geometry but seemed like they were misplaced, see tomorrow's log if you want to check those changes.--RDBury (talk) 18:27, 12 October 2011 (UTC)

Since one might want to put a current article of the category "Mathematical theorems" in to several subcategories, would there be a way to first save a list of all the current articles in "Mathematical theorems"? This way one could go through that list in order to more properly diffuse "Mathematical theorems". RobHar (talk) 20:37, 12 October 2011 (UTC)

<mischief>What about setting up a page "List of Important Mathematical Theorems"?</mischief> (ducks) --Matt Westwood 21:25, 12 October 2011 (UTC)

But seriously folks ... I understand that what we're about in ProofWiki is completely different from what WikiPedia's about (for a start, their approach is insanely trivial detail, or detailed trivia, and tiny pages with just one thing on them ... but it might be worth exploring the category structure they have set up on there.

Another idea is to categorise them according to MSC 2010 (if not instead, then as well). --Matt Westwood 21:30, 12 October 2011 (UTC)

The reason I'm going with the maths rating tag is so I don't have to think too much about which article goes where. There are probably other ways of doing it but this should work as a first pass and it can always be refined later. We've had discussions here about whether the maths tag areas should be tweaked; there is a huge amount of inertia with what we have now so there would have to be some compelling reason to change. We've also talked about Areas of mathematics, Outline of mathematics, Portal:Mathematics/MathematicsTopics, etc. and how to make them consistent, but I doubt that that issue will be resolved any time soon and I think it's better to get something for theorems in place now even it it's imperfect. In other words I just want to be able to find Whosit's theorem on a triangle and a line without rethinking the categorization of every math article.

Btw, since you sort of suggested it, we do have a List of theorems. I'm not sure if it has any advantage over Category:Theorems though.--RDBury (talk) 23:13, 12 October 2011 (UTC)

One further point, to misquote a cliche: it will take a lot of effort to make it look effortlessly simple. Whatever you do, don't rush into it because it will all have to be redone when a better idea comes along. On the other hand, if we don't start experimenting with configuration, we won't know what works best. So I can see this being a long angst-filled process with lots of shouting. --Matt Westwood 05:20, 13 October 2011 (UTC)

Update: I created the analysis category and populated it with about 150 articles. That leaves less than 800 articles in the main category from over 1000 before I started.--RDBury (talk) 17:41, 13 October 2011 (UTC)

I have created the number theory categ. and moved a few articles there (and in the existing categ-s). Sasha (talk) 21:50, 13 October 2011 (UTC)

and also "theorems in topology", to which I have moved "compactness theorems" as a subcategory. Sasha (talk) 20:02, 14 October 2011 (UTC)

and also "theorems in algebra". Sasha (talk) 23:23, 14 October 2011 (UTC)

Thanks. I added some articles to number theory yesterday and will work on some of the others today. The current count on the main category is now less than half what it was, still too large but it's worth noting the milestone. It's probably not desirable to try get down to 0; I'm thinking finish doing the easy ones for now, then let the normal editing process take over and eventually the number will converge to a stable value of a couple hundred.--RDBury (talk) 17:12, 15 October 2011 (UTC)

Update: only 303 pages left. There is now a subcateg "functional analysis" of "analysis" (to which I have moved a few pages). Sasha (talk) 19:13, 16 October 2011 (UTC)

But is "Schröder–Bernstein theorem for measurable spaces‎" FA? Boris Tsirelson (talk) 20:13, 16 October 2011 (UTC)

perhaps not... I moved it back to "mathematical theorems" Sasha (talk) 20:19, 16 October 2011 (UTC)

It could be Category:Isomorphism theorems, but strangely this one is treated as a narrow class of algebraic theorems. Boris Tsirelson (talk) 21:52, 16 October 2011 (UTC)

If we are already cleaning the categories, I have suggested "Category:Mathematical theorems with German names" for deletion (there are 3 articles there). Sasha (talk) 22:39, 16 October 2011 (UTC)

MATLAB trashed

Happydaysarehere (talk · contribs) seems to have it in for MATLAB. He has removed at least four mentions of it from various articles. Since I am not familiar with MATLAB, I am asking you-all whether there is any basis for his actions or is this just vandalism/spite? JRSpriggs (talk) 08:24, 12 October 2011 (UTC)

I've just reverted all four edits. I can't see any justification for removing those mentions of Matlab. Jowa fan (talk) 09:13, 12 October 2011 (UTC)

Note N01b33tr (talk · contribs) is also removing mentions of MATHLAB because it's "proprietary". Paul August ☎ 22:54, 13 October 2011 (UTC)

Reverted three edits. MATLAB not MATHLAB (they're two different things). Is there a systematic way to check for this happening again by a different user? Ideally a list of all edits in the last 48 hours for which the diff includes the word "MATLAB", although I don't think such a thing is technically possible. Jowa fan (talk) 23:43, 13 October 2011 (UTC)

You could potentially request an Wikipedia:Edit filter which would flag all edits with the word MATLAB. The process seems a little complex though. A simpler method is to compare the what links here at two different dates and see if the number of links have decreased. I've made a page User:Salix alba/MATLAB which all the links as of 07:50, 14 October 2011‎, and this can be compared to a later version.--Salix (talk): 06:51, 14 October 2011 (UTC)

Other MATLAB removers: Susie8876 (talk · contribs) and Frogman10k (talk · contribs). Apparent sockpuppetry.  --Lambiam 01:14, 15 October 2011 (UTC)

XScreenSaver links

A user has added nearly 100 links to XScreenSaver in the 'See also' section of various math and computer articles. The only relation XScreenSaver has to these subjects is that there exist modules that convert something to do with the article into an animation, but you have to download the software and run in it in a compatible OS to actually see these animations. If there are no objections I'm going to start reverting these links based on they are not relevant to the subjects.--RDBury (talk) 05:22, 13 October 2011 (UTC)

Someone beat me to it so never mind.--RDBury (talk) 17:59, 13 October 2011 (UTC)

Vitez helix

Vitez helix is a new article on something in combinatorial mathematics that no other articles link to. I've done some cleanup on it, moving it closer to the norms of WP:MOS and WP:MOSMATH. If it's worth keeping then it needs more work, both within the article and in the form of links from other articles to it. Michael Hardy (talk) 17:14, 13 October 2011 (UTC)

The only source given seems to be a mirror of the article on a cooking website and there is nothing in GBooks. To me it's not worth keeping, but it's already survived a PROD.--RDBury (talk) 17:56, 13 October 2011 (UTC)

Is there any doubt that Purplepanda1458 is the Michael Vitez whose name appears in the article title? --Joel B. Lewis (talk) 21:33, 13 October 2011 (UTC)

Too bad. This article needs to disappear quietly. Is any admin willing to stretch a CSD (db-hoax, for instance)? Sławomir Biały (talk) 23:52, 13 October 2011 (UTC)

I've nominated the article for deletion. See Wikipedia:Articles for deletion/Vitez helix. Ozob (talk) 01:12, 14 October 2011 (UTC)

TeX issues

When I'm logged in, using MathJax, this table looks OK:

${\begin{array}{l||r|r|r||r|r|r}\hline \\\hline L'&\mathrm {O} &\lambda \alpha &\kappa \varepsilon &\mathrm {O} &\alpha &\beta &\nu \\\alpha &\alpha &\beta &\nu &\mathrm {O} &\alpha &\beta &\nu \\\alpha L'&\alpha &\lambda \delta &\iota \varepsilon &\mathrm {O} &\alpha &\beta &\nu \\\hline \\\beta &\beta &\varepsilon &\mu &\mathrm {O} &\alpha &\beta &\nu \\\beta L'&\beta &\lambda \zeta &\delta &\mathrm {O} &\alpha &\beta &\mu \eta \\\gamma &\gamma &\eta &\kappa \eta &\mathrm {O} &\alpha &\beta &\mu \eta \\\end{array}}$

While not logged in and viewing it, all I see is error messages saying something failed to parse. Why? It's at User:Michael Hardy/Greek.chord.table.

Notice the format of one line:

\begin{array}{l||r|r|r||r|r|r}

I had hoped that would result in two parallel vertical lines close together in two places. That actually works when LaTeX is used in a normal way on the Linux machine I'm typing this on. It doesn't work here. Is there some way to get that two work here, or, failing that, to get a thicker vertical line than in those places where one sees only a single vertical slash? Michael Hardy (talk) 23:48, 13 October 2011 (UTC)

Hi Michael, that code does work, I looked at your example, and it isn't the double lines that are the issue. You are trying to put 8 columns into an array that you only specify 7 columns for. Zfeinst (talk) 00:28, 14 October 2011 (UTC)

Well, in a future more just and humane society, there will be error messages that say something other than the something somewhere is wrong.

Thank you. Michael Hardy (talk) 02:35, 14 October 2011 (UTC)

TeX issues again

Here's something really weird: I type this table:

${\begin{array}{|rlr|rlr|rlr}\alpha &{\text{alpha}}&1&\iota &{\text{iota}}&10&\varrho &{\text{rho}}&100\\\beta &{\text{beta}}&2&\kappa &{\text{kappa}}&20\\\gamma &{\text{gamma}}&3&\lambda &{\text{lambda}}&30\\\delta &{\text{delta}}&4&\mu &{\text{mu}}&40\\\varepsilon &{\text{epsilon}}&5&\nu &{\text{nu}}&50\\\mathrm {\stigma} &{\text{stigma (archaic)}}&6&\xi &{\text{xi}}&60\\\zeta &{\text{zeta}}&7&\mathrm {o} &{\text{omicron}}&70\\\eta &{\text{eta}}&8&\pi &{\text{pi}}&80\\\vartheta &{\text{theta}}&9&\mathrm {\koppa} &{\text{koppa (archaic)}}&90\end{array}}$

When I view this while logged in (so I'm using MathJax), it looks exactly the way I intended: a column of Greek letters, followed by a column with their names written in Latin letters, followed by a Hindu-Arabic numeral.

But when I view this while I'm _not_ logged in, I see the names of the letters written in---of all things!--- Greek letters. And some of them are spelled wrong. The code looks like this:

\begin{array}{|rlr|rlr|rlr} \alpha & \text{alpha} & 1 & \iota & \text{iota} & 10 & \varrho & \text{rho} & 100 \\ \beta & \text{beta} & 2 & \kappa & \text{kappa} & 20 \\ \gamma & \text{gamma} & 3 & \lambda & \text{lambda} & 30 \\ \delta & \text{delta} & 4 & \mu & \text{mu} & 40 \\ \varepsilon & \text{epsilon} & 5 & \nu & \text{nu} & 50 \\ \stigma & \text{stigma (archaic)} & 6 & \xi & \text{xi} & 60 \\ \zeta & \text{zeta} & 7 & \omicron & \text{omicron} & 70 \\ \eta & \text{eta} & 8 & \pi & \text{pi} & 80 \\ \vartheta & \text{theta} & 9 & \koppa & \text{koppa (archaic)} & 90 \end{array}

Where it says \text{alpha}, I see $\alpha \lambda \pi \eta \alpha$. Why would I see Greek letters there? (And the correct spelling, if I'm not mistaken, should be $\alpha \lambda \varphi \alpha \,$). Michael Hardy (talk) 03:54, 14 October 2011 (UTC)

If you type in \text{alpha} then in the array it does what you show above but if you do \mathrm{alpha} (etc) instead then you get

${\begin{array}{|rlr|rlr|rlr}\alpha &\mathrm {alpha} &1&\iota &\mathrm {iota} &10&\varrho &\mathrm {rho} &100\\\beta &\mathrm {beta} &2&\kappa &\mathrm {kappa} &20\\\gamma &\mathrm {gamma} &3&\lambda &\mathrm {lambda} &30\\\delta &\mathrm {delta} &4&\mu &\mathrm {mu} &40\\\varepsilon &\mathrm {epsilon} &5&\nu &\mathrm {nu} &50\\\mathrm {\stigma} &\mathrm {stigma(archaic)} &6&\xi &\mathrm {xi} &60\\\zeta &\mathrm {zeta} &7&\mathrm {o} &\mathrm {omicron} &70\\\eta &\mathrm {eta} &8&\pi &\mathrm {pi} &80\\\vartheta &\mathrm {theta} &9&\mathrm {\koppa} &\mathrm {koppa(archaic)} &90\end{array}}$

which is what you want. Not sure why this is, but it is an easy solution. Zfeinst (talk) 04:40, 14 October 2011 (UTC)

I can at least explain why this is happening. In order to create the two archaic characters in the table, I had texvc needs to load the teubner which is an extension to the greek language babel package. This doesn't change much in math mode, but it changes the surrounding text mode to greek. \text{...} switches back to text mode. Notice \mathrm specifically sets the font to a roman one, that is why the two behave differently. This is unfortunately a side effect of my patch to add the two characters. This problem will only effect math tags if they have the archaic symbols loaded since that is the only time texvc will attempt to use the teubner package. I will have to think about how to fix this. Thenub314 (talk) 05:27, 14 October 2011 (UTC)

I have a patch worked out to prevent this in the future that I will commit to mediawiki in the next few days. But I am not sure when the next time the wikimedia people will update texvc. Thenub314 (talk) 06:22, 14 October 2011 (UTC)

Another difference: when I view it logged in and with MathJax, I see nice top and bottom lines on both versions of the table. But not-logged-in (under both Chrome and Safari on OS X) they are not there. —David Eppstein (talk) 05:28, 14 October 2011 (UTC)

I'm afraid that's a bug in MathJax. When a vertical or horizontal line is used in an array environment a solid frame gets added around the array/table. Border lines should only appear when said so via \hlines at top and bottom and enclosing pipe characters in the array command's argument. I have filed a bug report. Nageh (talk) 13:32, 14 October 2011 (UTC)

Thank you Thenub. Michael Hardy (talk) 13:28, 14 October 2011 (UTC)

---

Thanks are due to Zfeinst, Thenub, and Nageh.

I now have a section at Ptolemy's table of chords that includes what you see above and explains how to understand the base-10 and base-60 numerals that were used in the table. Michael Hardy (talk) 16:11, 18 October 2011 (UTC)

Nash

The article on Nash has changed a bit in the recent days; I am a bit critical (e.g. "visionary" links to "Defined broadly, a visionary, is one who can envision the future. For some groups this can involve the supernatural or drugs."; does this apply to Nash??) Sasha (talk) 15:31, 14 October 2011 (UTC)

What gets me is the word "apparent" before "struggle with paranoid schizophrenia", is someone suggesting he was faking it?--RDBury (talk) 15:48, 14 October 2011 (UTC)

Rename of The sum of the reciprocals of the primes diverges

Another maverick article name. I'm thinking change to 'Prime reciprocal series' but other possibilities are 'Series of reciprocal primes' and 'Prime harmonic series' (which already exists as a redirect). The French version of the article is "Série des inverses des nombres premiers" or "Series of inverses of prime numbers" if that helps. I'm looking for suggestions if you have a preference for the name or a better name to suggest, or do the move if you feel strongly enough.--RDBury (talk) 15:39, 14 October 2011 (UTC)

Right now the article is just a series of proofs, so it might be worth having the word proof in the title. One could turn this into an article about this series and have info on rates of convergence, and its history, etc. RobHar (talk) 16:17, 14 October 2011 (UTC)

I'm partial to Prime harmonic series but none of the suggestions are bad. CRGreathouse (t | c) 17:39, 14 October 2011 (UTC)

I've moved it to Divergence of the sum of the reciprocals of the primes. Michael Hardy (talk) 22:01, 14 October 2011 (UTC)

Inverse Laplace transform of derivatives

I stumbled on Inverse Laplace transform of derivatives while on new page patrol. As my mathematical skills are rather limited, I came here to ask if this article is viable stub, something that might merged or redirected or a completely trivial mathematical piece that does not belong in Wikipedia? MKFI (talk) 17:01, 14 October 2011 (UTC)

Not viable. All this already appears in Laplace transform, there is no need for a separate article. Sasha (talk) 19:26, 14 October 2011 (UTC)

Redirected. MKFI (talk) 21:04, 14 October 2011 (UTC)

I have changed the redirect to Laplace transform, since the inverse LT article does not contain this information. Sasha (talk) 21:45, 14 October 2011 (UTC)

RfC about \oiint

I was just reading the Help:Displaying a formula page, and I was surprised to see that people have been looking for a \oiint. I suppose I had a few comments and questions. First, in case you were wondering, archaic greek characters got supported before integrals simply because someone filed a bug report requesting archaic greek characters, but no bug reports mention \oiint. I can't fault anyone for not submitting bug reports because texvc has received little attention over the years. But bug reports are good things that do get noticed and eventually might make things happen.

As I looked at implementing something to enable this command, I checked the comprehensive symbols list, and immediately noticed it involves a) loading a new package, and b) several packages exist. The the question becomes, which \oiint should be implemented.

The following packages exist:

1. wasysym. - Care should be taken with this package. It changes the default \int command which means we will run into odd behavior of texvc. But can work around this by passing the package an option.
2. mathabx - Also redefines \int. Doesn't take an option to prevent it from doing so. Working around this to maintain backwards compatability would take a bit more work then wasysym. work around this
3. txfonts/pxfonts - defines many other potentially useful integrals, particularly clockwise vs counterclockwise variants but redefines some integrals currently used.
4. esint - same comments as txfonts/pxfonts with the exception of clockwise vs. counterclockwise.
5. MnSymbol
6. mathdesign

The question I am looking to answer is as follows. If I decide to implement a \oiint command, which package does the community prefer? My personal preference is towards txfonts/pxfonts. But to be honest I don't use these symbols much as it stands. Images of these fonts can be found in the "Comprehensive Symbol List" [3] on pages 29 to 33. Thenub314 (talk) 21:44, 14 October 2011 (UTC)

more TeXnicalities

${\begin{array}{ccc}\pi \varepsilon \varrho \iota \varphi \varepsilon \varrho \varepsilon \iota {\tilde {\omega }}\nu &\varepsilon {\overset {'}{\nu }}\vartheta \varepsilon \iota {\tilde {\omega }}\nu &{\overset {\text{`}}{\varepsilon }}\xi \eta \kappa \mathrm {o} \sigma \tau {\tilde {\omega }}\nu \\{\begin{array}{|l|}\hline {\mathsf {L}}'\\\alpha \\\alpha \;{\mathsf {L}}'\\\hline \beta \\\beta \;{\mathsf {L'}}\\\gamma \\\hline \gamma \;{\mathsf {L}}'\\\delta \\\delta \;{\mathsf {L}}'\\\hline \varepsilon \\\varepsilon \;{\mathsf {L}}'\\\mathrm {\stigma} \\\hline \mathrm {\stigma} \;{\mathsf {L}}'\\\zeta \\\zeta \;{\mathsf {L}}'\\\hline \end{array}}&{\begin{array}{|r|r|r|}\hline \circ &\lambda \alpha &\kappa \varepsilon \\\alpha &\beta &\nu \\\alpha &\lambda \delta &\iota \varepsilon \\\hline \beta &\varepsilon &\mu \\\beta &\lambda \zeta &\delta \\\gamma &\eta &\kappa \eta \\\hline \gamma &\lambda \vartheta &\nu \beta \\\delta &\iota \alpha &\iota \mathrm {\stigma} \\\delta &\mu \beta &\mu \\\hline \varepsilon &\iota \delta &\delta \\\varepsilon &\mu \varepsilon &\kappa \zeta \\\mathrm {\stigma} &\iota \mathrm {\stigma} &\mu \vartheta \\\hline \mathrm {\stigma} &\mu \eta &\iota \alpha \\\zeta &\iota \vartheta &\lambda \gamma \\\zeta &\nu &\nu \delta \\\hline \end{array}}&{\begin{array}{|r|r|r|r|}\hline \circ &\alpha &\beta &\nu \\\circ &\alpha &\beta &\nu \\\circ &\alpha &\beta &\nu \\\hline \circ &\alpha &\beta &\nu \\\circ &\alpha &\beta &\mu \eta \\\circ &\alpha &\beta &\mu \eta \\\hline \circ &\alpha &\beta &\mu \eta \\\circ &\alpha &\beta &\mu \zeta \\\circ &\alpha &\beta &\mu \zeta \\\hline \circ &\alpha &\beta &\mu \mathrm {\stigma} \\\circ &\alpha &\beta &\mu \varepsilon \\\circ &\alpha &\beta &\mu \delta \\\hline \circ &\alpha &\beta &\mu \gamma \\\circ &\alpha &\beta &\mu \beta \\\circ &\alpha &\beta &\mu \alpha \\\hline \end{array}}\end{array}}$

This looks very good when I'm not logged in, but when I'm logged in (and hence using mathJax), I get neither an error message nor the intended image; rather I just get TeX code, all on one long line, so that I have to scroll a long distance to the right to see the end of it. What's going on? Michael Hardy (talk) 23:39, 14 October 2011 (UTC)

Where should second order equation redirect to?

Currently, the second-order disambig page has a link to second order equation mentioning that it is for a second order differential equation. Yet, clicking on that link redirects you to quadratic equation. I looked for a better re-direct but was unable to find one. Maybe the best place to link it to is a section in differential equation but the section that deals with that isn't clear enough. Any help with this would be greatly appreciated. Thanks. TStein (talk) 02:04, 15 October 2011 (UTC)

I've added an example of a 2nd-order ODE at Differential equation#Nomenclature, with an anchor Differential equation#second-order differential equation (with a required hyphen). Perhaps the example helps to make things clear.  --Lambiam 03:14, 15 October 2011 (UTC)

I was hoping there was an article that I missed. That will have to do for now. I sent the link in the disambig page second-order to second-order differential equation which I redirected to your link. It isn't the best solution but it will have to do for now. TStein (talk) 05:26, 16 October 2011 (UTC)

My user page MfDed

My user page has been sent to MfD. If you have an opinion on this, you may express it at Wikipedia:Miscellany for deletion/User:JRSpriggs. JRSpriggs (talk) 12:54, 15 October 2011 (UTC)

I've just closed this discussion as speedy keep: nomination withdrawn. Jowa fan (talk) 00:48, 16 October 2011 (UTC)

Theorems in set theory

Is there, or will there be a new category for Theorems in set theory? If not, where's the best place for them? Thanks, Rschwieb (talk) 22:53, 15 October 2011 (UTC)

Perhaps, "Theorems in set theory and logic"? Sasha (talk) 23:37, 15 October 2011 (UTC)

I'd be happy having a category "Theorems in set theory" and a separate category "Theorems in logic". For example, Cantor–Bernstein–Schroeder theorem has nothing to do with logic, and while Gödel's incompleteness theorems apply to set theory, they are distinctly a result in logic. RobHar (talk) 04:39, 16 October 2011 (UTC)

Mathematical logic is sort of a term of art; it doesn't really imply that the material is about logic in the classical sense of the word. It refers to certain branches of mathematics that have historically had more to do with logic than other branches. The usual list is set theory, model theory, recursion theory (now often called computability theory), and proof theory. Personally I would add category theory and universal algebra, but for some reason that doesn't seem to be standard.

Of these, the only one that matches the sense of "logic" that I intuit you're using is proof theory (which is the branch the Goedel incompleteness theorems belong to). I don't think we should equate that with "logic" in our categories. It would better match the categories used by workers in the field to put an umbrella category "Theorems in mathematical logic", which could then be broken up into "Theorems in set theory", "Theorems in model theory", "Theorems in recursion (or perhaps computability) theory", "Theorems in proof theory".

I don't think we should have any category just called "Theorems in logic" without the word "mathematical" — within mathematics, it's common to refer to mathematical logic as just "logic" for short, but as the title of a category it's too ambiguous. --Trovatore (talk) 05:10, 16 October 2011 (UTC)

Sure, say "mathematical logic" instead of "logic". But I don't think it makes sense to include set theory inside logic. I mean this is not my area of expertise, but set theory is a separate thing. It's history and practice I'm sure is quite tangled up with that of (mathematical) logic, but it's still a distinct subject. Similarly, category theory and universal algebra are subjects in algebra. They have certainly been studied a lot by people interested in the foundations of mathematics, which are tangled up with mathematical logic, but they are also separate entities. To me things like model theory and proof theory are about what's true of "theories" in general, whereas set theory and category theory are specific theories (whose results are not about general theories). That's my point of view. RobHar (talk) 17:29, 16 October 2011 (UTC)

Set theory is not logic in the classical sense, but it is quite standard to include it as part of "mathematical logic". It's not up to us to invent new ways of categorizing mathematical thought. The resolution to the disconnect is not to say that set theory is not mathematical logic, but rather to say that mathematical logic is not logic. --Trovatore (talk) 20:26, 16 October 2011 (UTC)

Well, "theorems in set theory and mathematical logic" is reasonable, two separate categories could also be reasonable. Sasha (talk) 15:51, 16 October 2011 (UTC)

In this logic (I know it's pun), "theorems in analysis" is also not sufficiently disambiguous. -- Taku (talk) 16:09, 16 October 2011 (UTC)

Well, the only kind of analysis in which you have theorems is mathematical analysis. It's not clear that the only sort of logic in which you have theorems is mathematical logic. --Trovatore (talk) 04:18, 17 October 2011 (UTC)

...and probably more importantly, mathematical analysis is analysis, but mathematical logic is not logic. --Trovatore (talk) 04:30, 17 October 2011 (UTC)

I don't think mathematical analysis is analysis in the sense logical analysis is analysis. The former at heart is about the behavior of functions or (generalized functions). -- Taku (talk) 12:51, 21 October 2011 (UTC)

Please make the choice which is easiest to sort articles with :) Rschwieb (talk) 15:54, 16 October 2011 (UTC)

I think a joint category is as good (or as bad) as the existing "theorems in discrete mathematics". All the new categories are also too big, so if in the future someone moves most of the articles one level down to a subcategory, this will only make the tree easier to handle. Sasha (talk) 16:52, 16 October 2011 (UTC)

I was creating categories based on the subcategories of Category:WikiProject Mathematics articles. This was to minimize the decision making on my part since you can just look at the article talk page determine which articles belong where. Also, it's easy to do the sorting since you can just search for "theorem" in a page like Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Geometry/Mid and get a couple dozen articles that can be moved. The scheme wasn't really meant to be the final goal, just a step in the right direction, so if someone wants to make subcategories or move things around I'd encourage them to do so. As just general advice on categories, I'd suggest keeping the category sizes to between 10 and 100 articles; less than 10 means people trying to find an article will have to go too deep into the tree to find anything, and a list of more than 100 items is difficult for humans to scan. I'd also suggest finding a simple way of deciding what goes where so you can do most of the resorting "unencumbered by the thinking process" as the Car Talk guys say. Setting up criteria so WP's search engine does most of the decision making versus scanning the articles yourself is like driving versus walking. Some adjustments be needed after the fact but it's better to start from close to where you want to be.--RDBury (talk) 17:54, 16 October 2011 (UTC)

...and don't derive like my brother! Rschwieb (talk) 21:26, 16 October 2011 (UTC)

new section

I have just written this new section of Ptolemy's table of chords, which I could not write until we recently acquired the ability to include some archaic Greek letters in TeX.

Doubtless further work on that section could get done, and for the rest of the article, there is a "to do" list at talk:Ptolemy's table of chords. Michael Hardy (talk) 20:51, 16 October 2011 (UTC)

Table of functions

I was wondering whether others agree that there should be a page of tables of convex conjugates. Similarly for Laplace transforms (though such a table exists in the page itself). Mostly I'm wondering when such a table deserves its own page, if ever. Zfeinst (talk) 01:04, 17 October 2011 (UTC)

Sometimes an article gets unwieldy if a long table is included in it, so it becomes convenient to make that table a separate article. But I don't know of any explicitly stated criteria for deciding when to do that. Michael Hardy (talk) 01:38, 17 October 2011 (UTC)

Rewrite of proof at Intermediate value theorem

Would anyone care to review the rewrite of the Proof section at Intermediate value theorem by Toolnut (talk · contribs). I reverted their first rewrite because they did not use the property of continuity (see Talk:Intermediate value theorem#Error in proof?), but they have now done a second rewrite. Gandalf61 (talk) 09:48, 17 October 2011 (UTC)

The new proof seems to be original research. Some of Toolnut's other contributions are also worrying. For instance, this edit says that a function has a limit at a point if and only if the function is continuous there. I'm not sure if that's what he intended to say, but it's clearly wrong. Also, I remembered this ridiculous episode from last year. It's hard to find a basic mathematics edit in this user's history that isn't problematic. Sławomir Biały (talk) 11:10, 17 October 2011 (UTC)

But why is "this" episode so ridiculous? Rational numbers, but still, integer multiples... Boris Tsirelson (talk) 16:50, 17 October 2011 (UTC)

It's not in any of the standard sources. The user tried to reference a dictionary definition to support his novel definition of the LCM. Sławomir Biały (talk) 18:18, 17 October 2011 (UTC)

About the limit thing, I do have a source for that: any first-year calculus textbook would confirm the point that you can't have a limit if you don't have continuity (though continuity is not always implied, see below). It's a brief generalization of statements for one-sided and two-sided continuities (my reference to "neighborhood"); though I should have added that, to be continuous at an interior point of the domain of definition, the function at that limit must also have the same value as the two-sided limit, which I shall try to do, next, as succinctly as possible.Toolnut (talk) 17:38, 17 October 2011 (UTC)

It's true that you can't have a continuous function if the limit doesn't exist, but the converse is not true. It has nothing to do with one-sided limits. Sławomir Biały (talk) 18:27, 17 October 2011 (UTC)

According to my textbook: "The limit in the continuity test ... is the appropriate one-sided limit if c is an endpoint of the domain." This is a problem only with semantics. So I qualified my statement in the rewrite by adding "if that point is treated as an endpoint of the domain of definition," following it by an example of what I meant:

to find the limit at c, the function must be continuous in a neighborhood of c: (c-δ,c) or (c,c+δ), for some positive δ.Toolnut (talk) 18:52, 17 October 2011 (UTC)

Continuity at a point is (a) existence of the limit, (b) existence of the value, and (c) the equality of these. Boris Tsirelson (talk) 18:53, 17 October 2011 (UTC)

Continuity on a neighborhood is not necessary. For example, Dirichlet function multiplied by x is continuous at 0 only. Boris Tsirelson (talk) 18:57, 17 October 2011 (UTC)

But can you evaluate the limit of such a function using the definition of a limit, which requires that you work in the deleted neighborhood (which I specified above) of the point in question?Toolnut (talk) 19:19, 17 October 2011 (UTC)

Yes I can. Why not? Boris Tsirelson (talk) 19:31, 17 October 2011 (UTC)

Ok, I get what you're saying, but, based on my quote, standard textbooks do not acknowledge the existence of pathological functions.

Standard textbooks for mathematicians do. Boris Tsirelson (talk) 19:38, 17 October 2011 (UTC)

What quote? Thomas' calculus certainly doesn't support what you're adding to the article. Sławomir Biały (talk) 19:42, 17 October 2011 (UTC)

Look, you are wrong, wrong, wrong. You do not need one-sided continuity to evaluate a limit. Consider the function

$f(x)={\begin{cases}0&x\not =0\\1&x=0\end{cases}}$

discontinuous at the origin, but the limit exists (from both sides, in fact). Sławomir Biały (talk) 19:25, 17 October 2011 (UTC)

Your function, as defined, does not have a limit at x=0, but Boris' does. — Preceding unsigned comment added by Toolnut (talk • contribs)

Need I say more.... Sławomir Biały (talk) 19:47, 17 October 2011 (UTC)

Toolnut, this is a trivial example. I think if you are not understanding this perhaps you should not add your comments to pages on the subject until you understand the concepts more. If you have questions on ways to learn you can feel free to contact me on my talk page and I can attempt to help. Zfeinst (talk) 19:49, 17 October 2011 (UTC)

This is a sign that I'm getting tired of all this editing: yes it has a limit and it's 0. Your function is discontinuous if the point x=0 is treated as an internal point, but it can be viewed as continuous at x=0+, if the domain of definition is, say, (0,1). Boris' example was more relevant to the point I was making earlier, though.Toolnut (talk) 20:15, 17 October 2011 (UTC)

And this function is more relevant to my point. The limit exists at x=0, and interior point of the domain, and the function is discontinuous there. Hence it is false to say that existence of a limit implies continuity at an interior point of the domain. Sławomir Biały (talk) 07:52, 18 October 2011 (UTC)

In case there was any doubt before, I think this revert, where the user has once again inserted his totally false information into the lead, is a clear indication of the Dunning–Kruger effect. Sławomir Biały (talk) 19:29, 17 October 2011 (UTC)

Hmmm, I did not hear about Dunning–Kruger effect, but sometimes grading a completely nonsensical exam work I was unable to spot specific errors, and finally the student complained: "No errors, but no points; evident mistake?" Boris Tsirelson (talk) 19:36, 17 October 2011 (UTC)

I think I see what Toolnut is trying to say, but it is such a convoluted way of describing a limit in a single dimensional case that it is useless as is. For instance in the case where $f(x)={\begin{cases}0&x\not =0\\1&x=0\end{cases}}$ the f is continuous on $(0,\delta )$ for $\delta >0$ (with emphasis on open interval). I still do not think this should be included though. Zfeinst (talk) 19:40, 17 October 2011 (UTC)

Certainly the versions with 'limit iff continuous' can't stay. Requiring it to be left- and right- continuous isn't enough, of course, and it doesn't seem easier to repair this than to define the limit in the first place. CRGreathouse (t | c) 20:30, 17 October 2011 (UTC)

I went ahead and rved the last set of changes. Whether or not the new version is correct is beside the point imo, it was so obscured and obfuscated with abstract symbols that it was difficult to understand and verify, while the old version was in English and I could just read it to verify it. The idea is to write so that people will understand, not create abstract symbolism.--RDBury (talk) 21:44, 17 October 2011 (UTC)

The idea is to convince the informed reader, not to dumb it down. If you understood it so well, at least try to convince me: I'm reasonable; look at Boris, above, he was able to convince me that continuity in the neighborhood of a point does not have to exist for the limit to exist. (Come to think of it, Boris, your "pathological" example does not contradict my textbook, after all: your function is continuous at the limit, which exists, as proved by the one-sided limit test, though discontinuous everywhere else.) Try to address my concerns in this talk page.Toolnut (talk) 02:59, 18 October 2011 (UTC)

Evidence of reasonableness or well-informedness seems to be lacking. See Dunning-Kruger effect: the people least competent in a knowledge area tend to lack the metacognitive ability to assess their own ability accurately. In fact, both the discussion here and at the article resemble WP:CHEESE. Sławomir Biały (talk) 15:47, 18 October 2011 (UTC)

Who exactly are you? Is your sole job to criticize and taunt people on Wikipedia? I see that you don't reveal any of your credentials, as if you've got something to hide.Toolnut (talk) 17:54, 18 October 2011 (UTC)

Exactly what credentials do you believe are relevant to this discussion? That I have taught this material to thousands of American university students? That I have taught real analysis to hundreds of graduate students? That my students score consistently higher on departmental exams than average? I happen to feel that WP:RANDYs should be dealt with sharply. They and their enablers are the primary reason that Wikipedia's quality content gets eroded. They are a net drain on this project. Who, sir, are you? That doesn't know calculus, but is absolutely assured of your own correctness? Do us a favor and go back to Boise. Sławomir Biały (talk) 18:16, 18 October 2011 (UTC)

I'm certainly not your imagined Randy. If nothing else, I make contributors think twice about their articles and adjust them to expand their appeal as was just accomplished following my contributions and comments on both the LCM, Limits of functions, the missing citation in IVT's proof, and many more: that's what makes the Wikipedia Project work. If you don't like the idea then why contribute? If you were a college professor once, why don't you say so on your user page? Why not introduce yourself to the general public, so they know who they're dealing with. The fact of the matter is, this discussion would have been much shorter had you not commented on my comments at all, because you always failed to get the essence of my questions.Toolnut (talk) 19:13, 18 October 2011 (UTC)

When a reader fails to get the essence of something, it is very often the fault of the writer. —David Eppstein (talk) 19:17, 18 October 2011 (UTC)

To be sure, the proof could use some summarizing. But this remark misses the point. The editor in question has shown a systematic unwillingness to accept the principles of a quite standard epsilon-delta proof (e.g., instantiation of a universal quantifier as a valid logical inference), as well as similarly standard properties of limits and continuity (e.g., whether mere existence of a limit implies continuity at the limit point). He has repeatedly rejected counterexamples, and attempts to explain these issues to him. I believe that no matter how good the article, such a reader could not be served by it. (You can but only lead a horse to water.) A hypothetical reader wishing to learn about how to do epsilon-delta proofs doesn't go to an encyclopedia anyway. He acknowledges that he doesn't understand something and then refers to a textbook, maybe works on problems, takes classes, etc. Until he has some understanding of the subject, he especially shouldn't go to Wikipedia and try to rewrite portions of it. This is the WP:RANDY effect, and is positively destructive to our project. The lesson here for Toolnut is that if he wishes to contribute positively to these content areas, he should do so only after he has studied them much harder. Sławomir Biały (talk) 01:08, 19 October 2011 (UTC)

I think I understand your point very well, but I must mention one of the repeated criticisms on math articles is that they only make sense "after" you learned the material in the traditional way (i.e.,, reading/taking courses.) This is a problem since Wikipedia is meant to be a starting point; it should be read by those without prior training. (Some unrelated), isn't the intermediate theorem just a special case of connected sets go to connected sets under a continuous map? I think that's how the theorem was proven in W. Rudin's text, which is "the" standard for this sort of stuff. But again a reader shouldn't have to finish reading Rudin before reading Wikipedia. -- Taku (talk) 14:16, 19 October 2011 (UTC)

There are many proofs, probably some deserving of at least mention in the article. Bolzano's original proof uses the method of bisection. This proof is important in the modern world because it uses a procedure for solving the equation that can be implemented on a computer. The standard topological proof (a la Rudin) is also a nice proof because it validates our intuition about why the theorem is true. Sławomir Biały (talk) 14:28, 19 October 2011 (UTC)

About categories

Hi! In Marcinkiewicz–Zygmund inequality for example, one of the categories is a supercategory of the other two listed categories. Does it make sense to leave the supercategory tag in cases like this? I've also been passing over DAB pages with the Mathematical theorems category. Is there a rule of thumb about categorieson DAB pages? Thanks.Rschwieb (talk) 00:37, 18 October 2011 (UTC) Also, any input about the best subcategory for Category theory? Rschwieb (talk) 02:19, 18 October 2011 (UTC)

Proposal to change a section title

There's a proposal to adjust one of the main section titles used in "Wikipedia's contents", which will affect the order in which the section titles are presented. See Portal talk:Contents#Proposal for main section title adjustment. The Transhumanist 02:20, 18 October 2011 (UTC)

"Formal sciences"? I have never heard of that. RobHar (talk) 03:39, 18 October 2011 (UTC)

See Wikipedia talk:WikiProject Mathematics/Archive/2011/Jul#Formal sciences for an earlier discussion on formal science.--RDBury (talk) 06:41, 18 October 2011 (UTC)

Expert help requested, Coordinate space & Vector

We need math expert help at Coordinate space and Coordinate vector. Merge if warranted, otherwise delete the tags. Also, an ip commented that the page is confusing and non-standard. Fix that if needed. Thanks, D O N D E groovily Talk to me 04:47, 18 October 2011 (UTC)

Coordinate vectors come up often enough, but I think the phrase "coordinate space" is non-standard. I think it would make sense to merge coordinate space into coordinate vector (the opposite of what's being proposed). Jowa fan (talk) 05:47, 18 October 2011 (UTC)

I'm not sure about "coordinate space" being non-standard, but it certainly is less common than the term coordinate vector. I thus agree with Jowa fan that the current content of Coordinate space should be merged to Coordinate vector. The term "coordinate space" can actually refer to multiple concepts, one is the space of coordinate vectors as described in the current article, more commonly (judging from gbooks hits) it is used as a synonym of position space in classical mechanics. (i.e. the space of possible positions of an object, in contrast to momentum space. The Coordinate space should probably become a dab page.TR 09:48, 18 October 2011 (UTC)

Gröbner basis needs examples

The article on Gröbner bases has many definitions, listings of properties, characterizations, and so forth, but no examples. This makes it hard to understand even for someone like me who might be expected to understand it. I cannot fix this myself, and my request on the talk page has gone unanswered. Is there anyone here who would be interested in fleshing out this article? —Mark Dominus (talk) 14:18, 18 October 2011 (UTC)

The basic theory takes up 4-5 chapters with plenty of examples in Cox, Little, and O'Shea (or, in compressed form, in Rolf Froeberg's book). Perhaps an undergraduate honors or M.A./M. Ed. student in mathematics could write an expansion?  Kiefer.Wolfowitz 18:35, 18 October 2011 (UTC)

Math Études

The site Math Études has a collection of short movies on mathematical topics. I seem to be unable to play them in my browser though. If you have a moment, please try viewing one of the movies, if I'm the only one that's having the problem and the quality is decent it might be worthwhile putting some of them in the 'External links' section of the corresponding articles. If a special download is required to view them then I think WP:ELNO says they shouldn't be linked.--RDBury (talk) 14:55, 18 October 2011 (UTC)

It looks like a download rather than an in-browser thing to me too. —David Eppstein (talk) 15:28, 18 October 2011 (UTC)

Download links on a page with a wall of badly formatted text (at least the one I looked at) and they're DivX format so require a codec or player that many users won't have. So no, not a good target for external links I think.--JohnBlackburne^words_deeds 16:17, 18 October 2011 (UTC)

Thanks, I'll remove the link I found.--RDBury (talk) 16:57, 18 October 2011 (UTC)

I've just removed three more added by User:Mathetudes a short while ago, and added a second warning to their talk page. Whether or not the links are good ones going round adding them to web pages is clearly not appropriate behaviour.--JohnBlackburne^words_deeds 19:13, 20 October 2011 (UTC)

Does anyone want to use footnotes instead of inline links to link OEIS sequences?

A suggestion to change the template in that way has been made at Template talk:OEIS#This is an external link. Lipedia (talk) 15:59, 19 October 2011 (UTC)

Quasi-interior notability

The page on the quasi-interior seems very bare to me. And I'm not sure if it is notable since the only reference of the sort I can find is the reference provided. I would propose it for deletion except I: 1) wonder if anyone is more knowledgeable on this topic and can help with the page, and 2) don't know how to do that. Help in either direction would be appreciated. Zfeinst (talk) 00:55, 20 October 2011 (UTC)

I'm not as worried about notability as I am about the fact that there's nothing there but a definition. Perhaps merge to glossary of topology; it can always be undone if anyone can show that the notion is worth studying rather than just defining. --Trovatore (talk) 01:39, 20 October 2011 (UTC)

I think that a quasi-interior map is the same as a quasi-open map, see [4] and compare the defs. Quasi-open seems to be the more common term so I'd say is move is in order. Nouns should be used as article names so 'Quasi-open map' would probably be the best title.--RDBury (talk) 02:47, 20 October 2011 (UTC)

I am going through with the book to 'quasi-open map' and will add content now that I can find more sources on the topic. Thank you for your help. Zfeinst (talk) 15:23, 20 October 2011 (UTC)

Limits of functions

(I moved some of the discussion on limits of functions, which has gone off on a tangent and overcrowded the section on IVT proof, into this new section.)
@Toolnut: Derivatives are defined by certain limits:

$f'(x)=\lim _{\Delta x\to 0}{\frac {\Delta f(x)}{\Delta x}}.$

If this limit could not exist without the difference quotient being a continuous function of Δx at the point where Δx = 0, then there would be no point in taking a limit: one would simply plug in 0 in place of Δx and be done with it. If it were true that a function can have a limit at a point only if it's continuous at that point, then one could find all limits just be plugging in the point that is being approached. Then there would be no reason to have such a concept as limits. Michael Hardy (talk) 00:16, 18 October 2011 (UTC)

The just plugging-in-the-argument being easier is true of the Dirichlet function times its argument, x, at x=0, mentioned above. But the well-behaved functions do sometimes require finding their limits by, say, applying L'Hopital's rule. The exercise of finding the limits of well-behaved functions actually involves the same techniques as those used for evaluating derivatives (the numerator of the difference quotient is your ε, the denominator is the δ, and you need to show that ε/δ < a polynomial in ε), hence my propensity to think of limits as dealing mostly with functions, not only continuous in the neighborhood of the point, but also differentiable in that neighborhood.Toolnut (talk) 03:44, 18 October 2011 (UTC)

Michael Hardy is saying that: saying that f is continuous at a is equivalent to saying that to evaluate the limit as x goes to a of f you can just plug in a. I.e., the limit of a continuous function is the same notion as plugging in a value. Limits are only interesting when the function is not continuous at a point. When you look at sin(x)/x at x=0, it is not defined there, so it is not continuous there, and yet, using L'Hospital's rule if you wish, you can compute the limit as x goes to zero. RobHar (talk) 03:59, 18 October 2011 (UTC)

The "sinc" (sin x /x) function is actually continuous and infinitely differentiable at x=0, even though it evaluates to an indeterminate ratio, 0/0, when you simply plug in the point. That's what the limit derivation process shows. Just as proving the same with f(x)=x^2/x(=x) at x=0, involves a simple simplification.Toolnut (talk) 04:19, 18 October 2011 (UTC)

Erm... ${\frac {\sin x}{x}}\!$ is always undefined at zero. Sinc, properly defined is a piecewise defined function where you give the correct value at zero. But the domains of Sinc(x) and sin(x)/x are different, and so they are different functions. Similarly x^2/x is not, strictly speaking, the same function as x. Thenub314 (talk) 04:34, 18 October 2011 (UTC)

(edit conflict) You aren't understanding the point here, so let me spell it out. The functions sin(x) and x are continuous everywhere. But, the function f(x)=sin(x)/x is not defined at x=0 (and hence is not continuous there; it is indeed continuous everywhere else though). However, one can ask whether there is a way to "make sense of" f(0). The formal notion of "it makes sense to define this function to be 1 at 0" is exactly the notion that the limit as x approaches 0 is 1. Having computed that the limit of f(x) as x goes to 0 is 1, it then makes sense to define a new function

$\operatorname {sinc} (x)={\begin{cases}{\frac {\sin(x)}{x}}&x\neq 0\\1&x=0.\end{cases}}$

This new function sinc is continuous everywhere, but it is not equal to f(x) (they have different domains). This is an example of a removable discontinuity. Basically, it is not known a priori that it makes sense to "evaluate sin(x)/x at x=0", so you invent the notion of "limit of a function". You must be able to define the limit of a function that is not continuous at a point, so as to be able to "remove discontinuities" as above. RobHar (talk) 04:40, 18 October 2011 (UTC)

I stand corrected, but this is all a matter of semantics of how our forefathers have decided to define continuity and it does not affect continuity in the neighborhood of a point where a limit exists and which has been my main concern, as far as the limits of functions are concerned: I needed to see "continuity" mentioned in the introduction to the Wikipedia article on limits, as a founding concept, and I'm happy to see that some mention has finally been made where there was none before. Thanks.Toolnut (talk) 06:27, 18 October 2011 (UTC)

I'm surprised no one brought this up, but no continuity concerns exist in finding the limits of discrete functions, such as sequences and series, as the independent integer variable goes to ∞. The limit of a function article only briefly talks about sequential limit, but I think this should also be somehow touched upon in the introduction, don't you?Toolnut (talk) 20:56, 18 October 2011 (UTC)

I feel like you are making a bunch of comments without being very clear with what you are actually trying to say. In the above comment, do you want limits of sequences mentioned in the intro to limit of a function, or do you want sequential limits mentioned in that intro? These are two different things. And right above this, you say "I needed to see "continuity" mentioned in the introduction to the Wikipedia article on limits, as a founding concept"; that's not at all clear from any of the comments of yours that I've read. I think people are getting impatient with you because you are simply saying whatever comes to your mind and forcing everyone else to expend a lot of energy trying to figure out what you are saying. Look at the number of experienced users who have spent time trying to explain some basic calculus to you. This is not how the efforts of the wikipedia editors are supposed to be spent. You need to be expending some effort to understand what you are trying to say before saying it. That is what everyone else around here is doing. RobHar (talk) 15:43, 19 October 2011 (UTC)

Have you got a reliable source saying what you are saying? If not then it shouldn't go in. That's how things are done on Wikipedia. Dmcq (talk) 22:15, 18 October 2011 (UTC)

I think sequential limits are too peripheral to cram into the intro. Sequential limits are just a special case of "Limits involving infinity" for functions with domain N, so you might make some compelling addition to that section about sequential limits. Also, if I'm not gravely mistaken, if you want to look at N with the subspace topology inherited from R, then N has a discrete topology, and so all sequences (functions on N) are continuous functions. (Someone might have to jump in to correct me but I hope I'm not too far off.) Rschwieb (talk) 14:15, 19 October 2011 (UTC)

What I'm hoping to have gleaned from this discussion is that there are limits of three classes of functions: 1) differentiable functions with a finite number of discontinuities, 2) discrete functions at ∞, and (3) so-called pathological functions that are either nowhere-continuous or nowhere-differentiable, except at a finite number of points. Can you think of any other? The limits of each of these classes are clearly distinct in the tools needed to find them: the first class appears to be the hardest of the three.Toolnut (talk) 08:36, 20 October 2011 (UTC)

The maths reference desk is the place to ask questions about maths. This is a place to discuss improving the coverage of maths. The basic principle behind sticking things into Wikipedia is that they be already written down in some reliable source. So in this context you really need to be talking about established maths and about fixing up how it is shown in Wikipedia. A question like 'Can you think of any other?' in this context should only be for things like can you think of any other problems with using TeX for showing theorems in Category Theory? or can you think of any other criteria for listing a topic as being part of game theory? If you don't have a source about a subject and want to know more about it ask at the reference desk. If you don't know enough about a subject to even find something yourself about it you definitely shouldn't be making substantial changes to it Dmcq (talk) 09:04, 20 October 2011 (UTC)

I concur. To respond to Toolnut's gleanings, this is mistaken (like someone growing up in the far north concludes that there are two types of trees: pine and spruce). For instance, there exist functions having a limit at every point, but whose discontinuities are any prescribed first category $F_{\sigma }$ set (which is potentially uncountable). An example is the function $f(x)=0$ if x is irrational, and $f(x)=1/q$ if x is a rational number of the form p/q in lowest terms. This has limit zero approaching any point, is continuous at every irrational number, and yet is discontinuous at every rational number. (There exist functions discontinuous on any $F_{\sigma }$ set regardless of category, but we can't then ensure existence of the limit.) Sławomir Biały (talk) 10:27, 20 October 2011 (UTC)

+1 with Dmcq & Sławomir Biały--Kmhkmh (talk) 10:53, 20 October 2011 (UTC)

You are invited to continue the discussion of this thread at User_talk:Toolnut#Functions_and_their_LimitsToolnut (talk) 20:29, 20 October 2011 (UTC)

Roman arithmetic

The Roman arithmetic page really needs help. I think the Romans themselves didn't use them for math, but there's no decent sources in the article to suggest who, if anyone, ever did try to use them in that fashion. Is there anyone here who can help this poor thing out? Maybe it needs to be moved to Arithmetic using Roman numerals, or this article needs to explain how Romans did math, which it doesn't.--~TPW 16:25, 20 October 2011 (UTC)

They used counting boards with pebbles (calculi) to do arithmetic. I'm not sure why we would need an article on doing calculations in Roman numerals since it wasn't done historically and isn't really done now either. CRGreathouse (t | c) 16:43, 20 October 2011 (UTC)

I suspected as much, but didn't have the knowledge to back up the assertion. If anyone can prove a negative, it's mathematicians!--~TPW 16:54, 20 October 2011 (UTC)

I'm not sure that there's much salvageable from the article. The opening

In mathematics, Roman arithmetic is the use of arithmetical operations on Roman numerals.

is entirely wrong: it's much more classics than math, and no one uses that term to mean arithmetic on Roman numerals. The two paragraphs on performing arithmetic are unsourced and deal mostly with subtractive notation (a late invention!).

The idea of doing calculations on numerals themselves was so unheard-of that when it came into fashion (after Fibonacci's time) its practitioners even had a special name (algorists)...!

Frankly this falls much more into the domain of other WikiProjects than Math (Classics? Ancient Rome? History?).

CRGreathouse (t | c) 17:03, 20 October 2011 (UTC)

I do not know what the Romans actually did, but it is certainly not impossible to do simple arithmetic using Roman numerals. First, change all "IV" to "IIII", "IX" to "VIIII", "XL" to "XXXX", etc.. Then for addition, sort all the "I"s before the "V"s, etc.. Convert "IIIII" to "V", "VV" to "X", etc.. Then reverse the first step as appropriate. For multiplication, you have to know what the products of the letters are, e.g. V*L = CCL. JRSpriggs (talk) 17:31, 20 October 2011 (UTC)

It's certainly possible! I do it when I'm adding two numbers, the larger of which is a Roman numeral. It's just a matter of what was actually done by the Romans. CRGreathouse (t | c) 17:58, 20 October 2011 (UTC)

First, the Romans would not have used subtractive notation, so anything dealing with that in the article is OR and should go away. Smith's History of Mathematics has a short section on how the Romans might have done addition; it's fairly speculative but the gist is that it's hardly rocket science and they probably did not need anything like an abacus. I get the impression that little on that kind of thing was preserved. So if you keep to facts then there's probably not much you can put in an article like that.--RDBury (talk) 22:25, 20 October 2011 (UTC)

Certainly small sums would have been done mentally, just like today. Larger sums would have been done on an abacus. Only complicated calculations would require more (calculating board and/or cerae and stylus). There are surviving instruction manuals and even some calculations in progress (though mostly in later times, like the Vindolanda tablets). CRGreathouse (t | c) 01:53, 21 October 2011 (UTC)

It is a pretty ancient article but doesn't seem to have ever been prod'ed, I'll do that as I think i was just something made up by some editor. Dmcq (talk) 02:05, 21 October 2011 (UTC)

As to small sums judging from how the Japanese do things I'd guess they in effect used a mental abacus with stones if the problems were simple enough for mental arithmetic rather than representing the Roman numerals in their minds and calculating with them. Anyway my prod was removed so I'll give it a day and escalate to AfD as there aren't any citations supporting the topic. Dmcq (talk) 09:34, 21 October 2011 (UTC)

I originally created the article based on some notes from an old college handout but lost interested in it when 95% of my work was removed in 2007. I am against deletion - not because I created it - but that there is value from a history of Roman science and technology perspective. As pointed out here, very little is available to cite (as far as we know) but that makes it all the more important that is known is preserved. I advocate that the article get restarted with a better foundation of what is known about how the Roman's did math. Even if it is stub, it will still accurately what is currently known about that historical period. At present, there is a redirect to Roman Abacus, so there is need to rush to AfD. --D. Norris 10:53, 22 October 2011 (UTC) — Preceding unsigned comment added by Denorris (talk • contribs)

Changes to OEIS templates

User:Lipedia has changed about 30 articles using Template:OEIS2C to use Template:OEIS instead. The fact that there are two of these OEIS templates with difference usages was discussed last month. From the edits comments it appears that the editor does not understand that the templates are different, so it might be a good idea to review the changes to see if they're appropriate. In the mean time, this is the second time in a matter of a week or two that someone has made wholesale edits to math articles without bringing it up here first. I say next time it happens we break out the torches and pitchforks.--RDBury (talk) 23:05, 20 October 2011 (UTC)

Slight correction: The changes were to use a new template Template:oeis (note small letters) which is a copy of Template:OEIS2C. So now we have four versions of OEIS templates if you count Template:OEIS url. I know the situation with these templates is not perfect, but I don't think creating another version is the answer.--RDBury (talk) 23:52, 20 October 2011 (UTC)

So basically it's a copy-and-paste move? I don't really care for the name of OEIS2C, but I'm not convinced that's the right way to handle its bad name. —David Eppstein (talk) 00:11, 21 October 2011 (UTC)

On a related note, I thought we had already agreed that the icon in this templates is inappropriate, but yet it remains. Should someone remove it then? Sławomir Biały (talk) 10:27, 21 October 2011 (UTC)

Perhaps there should be separate copies of the various templates with and without the icon? ;-) Dmcq (talk) 10:36, 21 October 2011 (UTC)

Had we agreed on this? I didn't notice. CRGreathouse (t | c) 13:13, 21 October 2011 (UTC)

There was a discussion here several weeks ago. At any rate, WP:MOS#Avoid entering textual information as images seems quite clear on this. Sławomir Biały (talk) 14:13, 21 October 2011 (UTC)

I remember the discussion but not any kind of consensus against the icon. And I don't see the applicability of the link, since the comparison is with OEIS2C not OEIS which serve different purposes. CRGreathouse (t | c) 15:17, 21 October 2011 (UTC)

It's not as though the discussion was held in secret ;-). But obviously, consensus can change if there's further input. Generally speaking, we shouldn't use inline images at all, except in very limited circumstances. The old template was also clearer: Conveying textual information as text rather than a cryptic icon (that looks like an improperly rendered Unicode symbol). Sławomir Biały (talk) 15:53, 21 October 2011 (UTC)

Incidentally I should mention that I have no strong preferences. My initial reaction was negative, but I've come to like the icon somewhat. In any case I don't think I'd act to remove or re-add the icon. CRGreathouse (t | c) 18:55, 21 October 2011 (UTC)

Formerly the name OEIS2C (2C = 2nd citation) made sense, because only the long template linked to OEIS. At the moment the long and the short template are coequal ways to link sequences, because also the short template links to the article in the icon. So my intention was, to reflect this change in the character of the short template in it's name. "oeis" is easier to write and to remember than "OEIS2C", and I think it's quite logical that capital letters give the long and small letters give the short template. Sorry when I was too bold, but I didn't realize objection against the icon, so I came to the conclusion that the name change makes sense. Lipedia (talk) 13:09, 21 October 2011 (UTC)

{{OEIS}} and {{OEIS2C}} have different names to avoid confusion. You duplicated the latter at {{oeis}}. Writing a template with other capitalization in an article should normally not give another result. And template code should normally not be copied between two identical templates. Instead a template redirect can be made. It seems especially confusing that {{OEIS|A000001}} and {{oeis|A000001}} give different results when OEIS/oeis is an interwiki prefix and OEIS:A000001 and oeis:A000001 give the same result (interwiki prefixes are not case dependent). I think {{oeis}} should be deleted or redirected to {{OEIS}}, and all your changes from {{OEIS2C}} to {{oeis}} in articles should be reverted. You can propose a new name for {{OEIS2C}} if you want but I would oppose {{oeis}} when we already have a different template called {{OEIS}}. Difference in capitalization is not a good method to convey information. PrimeHunter (talk) 15:00, 21 October 2011 (UTC)

Lists and outlines again

Following on from Wikipedia talk:WikiProject Mathematics/Archive/2011/Sep#Undiscussed List -> Outline moves, people might like to follow the discussion at Talk:Outline of arithmetic#Outlines versus bare lists. This time round, only three pages are affected. They were originally called "Outline...", I renamed them to "List..." a few weeks ago for consistency with other lists, and they're now called "Outline..." again. Jowa fan (talk) 07:13, 21 October 2011 (UTC)

Wigner–Ville distributions?

See this edit.

One of the most absurd things I've seen in a while is that Wigner-Ville distribution, with a hyphen, and Wigner–Ville distribution, with an en-dash, redirected to two different articles. The now both redirect to the same target, but the question is whether it's the right target? Or maybe that other one is the right one? (Or even a third one?) Michael Hardy (talk) 22:43, 21 October 2011 (UTC)

I notice that the page to which it currently leads says nothing about Ville, whoever he/he is, so at the very least the page is insufficiently complete. It needs a section to which W-V distribution points so as to explain Ville's contribution. --Matt Westwood 05:21, 22 October 2011 (UTC)

Actually, having looked at it, the redirects from Wigner-Ville distribution and Wigner–Ville distribution should both be redirected to Wigner quasi-probability distribution as that says in the lede that this is what it is. I'll do that now, and then we can discuss what commonality these pages have with a view to tidying them up. --Matt Westwood 05:27, 22 October 2011 (UTC)

Converse links

We currently have a number of articles that use the word converse with a link. Many of these go, some via redirects, to Conversion (logic). The problem is that the target article seems to be written for someone with a degree in logic; it even assumes familiarity with the classical names of syllogisms. This makes it inappropriate for what we're using it for, namely a definition for people who are unfamiliar with a somewhat jargony term. In other words I think the links are intended to go to something like the version of Converse (logic) before it was changed to a redirect. Another issue is that converse and conversion are two different things, the former being the result of the latter. Perhaps a better target would be Converse (mathematics), though this is currently an unreferenced orphan and might be changed to a redirect any second. There is also an article called Converse implication, but it's about a binary operator in Boolean logic, and an article called Converse theorem but it's about something different altogether. What I'd like to do to replace all the links to 'Conversion (logic)' from math articles; right now I'm thinking the best replacement is to a suitable anchor point in Theorem#Terminology. Another viable option would be to merge 'Converse (mathematics)' into List of mathematical jargon and change the links to an anchor point there. Yet another would be to restore 'Converse (logic)', clean it up a bit and link to it. None of these options is perfect so it will be nice someone can come up with a better idea.--RDBury (talk) 06:24, 22 October 2011 (UTC)

More disturbingly, Conversion (logic) is either deceptively worded or wrong. At the very least, Converse (logic) should resurrected, adding an explanation of why P->Q does not imply Q->P, and perhaps listing a few famous converses (e.g. of the Four-vertex theorem). -- 202.124.73.223 (talk) 07:26, 22 October 2011 (UTC)

I'm with expanding Conversion (logic) and adding a section called "Converse" containing the information in the old page that got merged. --Matt Westwood 08:38, 22 October 2011 (UTC)

That won't quite work: there are two meanings of converse: (1) categorical (All X is Y vs All Y is X etc.) and implicational (X --> Y vs Y --> X). It would work if you split Conversion (logic) into those two parts. But you'd also need to clarify that "conversion" is not (in spite of the cited source) a type of inference: since it's not, in general, valid. Rather, "conversion" is just a traditional name for the process of swapping a statement around to produce its converse -- see e.g. Mahan (1857), The Science of Logic, p. 82: "The original proposition is called the exposita; when converted, it is denominated the converse. Conversion is valid when, and only when, nothing is asserted in the converse which is not affirmed or implied in the exposita." See also William Thomas Parry and Edward A. Hacker (1991), Aristotelian Logic for more details. Given that "converse" is used by mathematicians, but "conversion" is not, it would be better for converse (logic) to be the primary article, and "conversion (logic)" a redirect. -- 202.124.72.170 (talk) 11:03, 22 October 2011 (UTC)