Wikipedia talk:WikiProject Mathematics

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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)

I helped create Help:Cite errors, the associated help pages, templates and maintenance categories. We can create a template and apply it to the interface pages for each error message that will then put article pages into a maintenance category. If desired, we can create a help page for each error message. ---— Gadget850 (Ed) ^talk 18:00, 25 October 2011 (UTC)

Tried that ages ago. Math error message support only plain text, not wikitext, so you can't add categories or links to them. Dragons flight (talk) 18:03, 25 October 2011 (UTC)

How about now that Math is an extension, not core? ---— Gadget850 (Ed) ^talk 19:05, 25 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)

Thanks and closing time

Hi!

The RfC is about to close.

I'd like to thank the project members for supportive comments and helpful, thoughtful statements, from which I can learn.

Best regards,

 Kiefer.Wolfowitz 16:30, 23 October 2011 (UTC)

It's closed. Thanks again for the supporting words and indeed the helpful criticism. Now it's time to get the SF lemma through FA status.  Kiefer.Wolfowitz 19:39, 30 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)

My thanks to all who supported me at MfD, and especially to Polyamorph and Jowa fan. JRSpriggs (talk) 06:25, 27 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)

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)

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 [3] 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)

It seemed reasonable to me to redirect rather than remove as some people occasionally ask how the Romans calculated using their numerals. The answer seems to be they didn't, they used an abacus. Is that a whole separate article? Dmcq (talk) 14:19, 22 October 2011 (UTC)

I think that the the way the Romans calculated would be worth an article, yes. CRGreathouse (t | c) 14:28, 26 October 2011 (UTC)

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)

See Converse (logic) for an improved article covering both ideas. If the community likes it, Conversion (logic) could be redirected to it. -- 202.124.72.170 (talk) 12:10, 22 October 2011 (UTC)

That's really good. Yes, Conversion (logic) should be merged with it, and the existing material on Conversion can be included (with all that Aristotelian mediaeval stuff) in its own section on the Converse page as appropriate. Suggest a similar exercise can be done with Obverse (logic) next. --Matt Westwood 12:30, 22 October 2011 (UTC)

Thanks! The medieval stuff already is included, just in a more readable form. But I'll let someone else tackle Obverse (logic). -- 202.124.72.170 (talk) 12:33, 22 October 2011 (UTC)

The new version of 'Converse (logic)' is an improvement over 'Conversion (logic)' but it's still not what I had in mind. The target audience is a high school kid who needs to look up the word because it appears in Pythagorean theorem and I doubt the new article will be readable at that level. Actually the way Converse is used in mathematics is different than the way it's used in logic. For example the logical converse of the Pythagorean theorem is that a²+b²=c² implies a, b, and c are the sides of a triangle and that triangle has a right angle between sides sides a and b. In mathematics the custom is to take some of the assumptions of the theorem as context ("Given a triangle with sides a, b and c...") and then state the theorem and it's converse as implications within that context ("the angle between a and b is a right angle" implies or is implied by "a²+b²=c²").

Another possibility is to point the links to Wiktionary. That might get a bit confusing though since there are about a half dozen different meaning listed there.--RDBury (talk) 15:02, 22 October 2011 (UTC)

You make a very good point about the way Converse is used in mathematics: Basically the converse of "Given A, B implies C" is taken to be "Given A, C implies B." That should ideally be added to Converse (logic) at the point where converses of theorems are mentioned. What's the best example of the converse of a theorem to use? Pythagorean_theorem#Converse doesn't quite match what you said. -- 202.124.74.223 (talk) 15:14, 22 October 2011 (UTC)

Give them a link to this ultra-minimalist approach: http://www.proofwiki.org/wiki/Definition:Converse --Matt Westwood 16:10, 22 October 2011 (UTC)

I think the second version in Pythagorean theorem#Converse matches what I said pretty closely; there are three versions given. Note that Euclid doesn't call it a converse; apparently to him they're just two similar theorems that happen to be next to each other. Perhaps a better example would be the theorem on alternate interior angles: "Given a transversal of parallel lines, if a and b are alternate interior angles, then a is congruent to b." The logical converse would be "If a is congruent to b then a and b are alternate interior angles of a transversal of parallel lines." This isn't true even if you assume a and b are angles. The "converse" usually given is "Given a transversal of a pair of lines, if a pair of alternate interior angles are equal then the lines are parallel."

Proof Wiki is ultra-minimalist alright. I think they're assuming that everyone who reads it already knows what a converse is.

I don't see that. It defines what a "converse" is. What more do you need to know? Given a conditional statement (and if you don't know what one of those is, you can click on the link and it will tell you), the "converse" is described as what you get when you swap over the bits that are separated by the implies sign. What on earth more do you need? --Matt Westwood 21:43, 22 October 2011 (UTC)

The definition should not use any jargon at all, so the word "conditional" is out (at least as a noun) and the implies sign is out as well since it's just an arrow to the the average person. In other words the people who would understand the definition in Proof Wiki will probably already have seen enough math and/or logic to know what "converse" means already.--RDBury (talk) 23:30, 22 October 2011 (UTC)

That's what links are for - so as to be able to click on the link to find out what all those funny words and symbols means. --Matt Westwood 14:27, 23 October 2011 (UTC)

PS. Definition: A mathematician is a person who thinks the word Converse is a noun. A jock is a person who thinks Converse is a proper noun.--RDBury (talk) 18:47, 22 October 2011 (UTC)

A typical 21st-century chatterbox thinks Converse is a verb. --Matt Westwood 21:43, 22 October 2011 (UTC)

It's an initial-stress-derived noun. Michael Hardy (talk) 00:17, 23 October 2011 (UTC)

We call them "Chuck Taylors", bro. Sławomir Biały (talk) 19:08, 23 October 2011 (UTC)

So every jock is a mathematician? (I'm not actually sure, as there is an implicit blurring between "if" and "iff" in these statements. Oh dear.) Mgnbar (talk) 19:56, 23 October 2011 (UTC)

Fractions: introduction

Re: Fractions (talk). There has been a long ongoing discussion on the introduction to this article, and the use of technical terms. It would be help to have some input (on the Fractions talk page). --Iantresman (talk) 12:54, 23 October 2011 (UTC)

The "technical terms" that Iantresman objects to are "expression", "quotient", and "integer".Rick Norwood (talk) 14:03, 23 October 2011 (UTC)

Technical Terms

The question needs to be asked properly then.

It's a no-brainer that certain mathematical concepts can only be understood in context. That is, in terms of other, more basic mathematical concepts. Those, in turn, need to be explained in terms of other, yet simpler concepts, until we finally find the concepts can be explained in "plain english".

Now, to what extent do we have to explain the backstory for a higher-level concept? That is:

"A jolly-complicated-widget is a complicated-widget with a jolly-wobbler."

would be a self-contained definition.

If you are then going to make the jolly-complicated-widget page completely comprehensible to the idle browser who happens to come across it by pressing "Random page", you then have to explain (on the same page) what a complicated-widget and a jolly-wobbler are.

I suggest No: we just need to offer up a sentence saying: "For an explanation of complicated-widget click this link, and for an explanation of jolly-wobbler click this link."

Otherwise we are going to be filling the encyclopedia with colossal amounts of repetition, every time you need to explain a concept which uses another concept to explain it.

Examples from the "fraction" thread above: do we need to explain "integer", "expression" and what-all every time we use it? No, we just make "integer" a link and expect the mouth-breathing knuckle-dragger of a user to click on it to find out what it is.

Same applies to the "Converse" page - if the user needs to know what a "converse" is, then he/she is probably already doing an assignment requiring at least a basic understanding of a "conditional" and what the "implies" arrow is. So why do we have to retread every single concept on every single page? --Matt Westwood 14:37, 23 October 2011 (UTC)

The level of each article must be adjusted to suit the people who are likely to visit the page, the "target audience". So no one is expecting every term to be defined from scratch on every page, for example you can assume for example that the readers of Homology (mathematics) have some understanding of abstract algebra. But pages which are likely to be visited by a non-specialist should not make any assumptions about what the reader knows beyond general literacy (at least in the first few sections). That means avoiding jargon when possible, and linking to definitions when avoiding it is too cumbersome. It defeats the purpose to link to another article when the definition there has more jargon than the article it was linked from, and unfortunately this is the case with many such links.--RDBury (talk) 17:26, 23 October 2011 (UTC)

Updating OEIS Template

I'm going to go ahead an remove the icon from the OEIS template per the discussions above. An example using my test version is:

The first few amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368) .

The people who like the icon don't seem to be in the majority or feel that strongly about it. Plus, as mentioned above, putting in-line icons in text is contrary to the MOS. Another problem is that doing a text search for "OEIS" does not work when it's an icon. It's not a straight revert though since I left out the fullurl code; the only effects this seems to have is to add a link icon and remove the mouse-over text. I'll make the change tomorrow sometime unless there's a strong objection (e.g. someone says it will break hundreds of article pages). The issue of whether links to OEIS should be changed to references or moved the 'External links' section of an article is still being debated, and the discussion of what to do with redundant OEIS variants is still unresolved.--RDBury (talk) 15:52, 23 October 2011 (UTC)

I think what the icon was doing was flagging a certain kind of permitted inline link (much like interwiki links, ISBN links, links to texts in the Bible, and external links for standard sets of codes such as language codes or disease codes: ICD9 360.5). However, we don't normally do that with icons, and even the "link" icon is only sometimes used; what you have seems to be more in line with standard practice. However, I would strongly oppose changing OEIS links to references. -- 202.124.72.203 (talk) 06:14, 24 October 2011 (UTC)

Update: The change has been made. I also moved the documentation so all four templates use the same included page, this avoids having copies of the the same text in different pages and the associated version control issues. I also moved 'OEIS url' to 'OEIS link', changed it to an inter-wiki link and added it to the documentation page. It wasn't being used except in one article so this shouldn't be a problem; I'm hoping it will start to be used again now that the documentation defines a specific use for it. I'm still not sure what should be done with OEIS2C/oies since they seem to be used for different things in different articles. Maybe the best thing would be to go case by case.--RDBury (talk) 05:36, 25 October 2011 (UTC)

Progress in subcategories for Mathematical Theorems

Hello. It looks like the Mathematical theorems category is much improved, since the subcategories are all under 200 pages. I was wondering if there was any work still left, or if it is pretty much "mission accomplished" for now. Rschwieb (talk) 14:07, 26 October 2011 (UTC)

It's done for now as far as I'm concerned, though I'm certainly not going to try to stop someone from going forward if they want to put the effort into it. To me the high priority issue was that the Mathematical theorems category was too big to use, an issue that became apparent when I tried to use it to find an article, and that issue is now resolved, though there are probably still articles in the main category that should be resorted.--RDBury (talk) 17:02, 27 October 2011 (UTC)

Reference resources guidelines section

I took the liberty of creating a new section, Wikipedia:WikiProject Mathematics/Reference resources#Guidelines for selected websites in our Reference resources page. I believe this captures the outcomes of several discussions here on which math websites should be considered reliable sources. Discuss, revise or revert as you see fit.--RDBury (talk) 19:12, 27 October 2011 (UTC)

It looks good. I made some small changes to the wording, but it looks useful. CRGreathouse (t | c) 19:31, 27 October 2011 (UTC)

I like it so far. We should add a section of how to deal with arxiv papers. Another point would be some general advice regarding websites of math departments, institutes. lecturers and blogs of prominent mathematicians.

Another reliable source that might be useful to include here as well would be the the Stanford Encyclopedia of Philosophy.--Kmhkmh (talk) 01:24, 29 October 2011 (UTC)

An old issue?

I've recently rewritten the lead of Bijection, hopefully making it more accessible. Because the article is about bijections, I was able to define bijections first and only later bring up surjections and injections ... not the traditional way to broach the subject. What I've done is elementary, jargon-free and non-controversial, but if pressed I don't think that I could come up with a reference for this approach. The issue in my mind is whether or not this is considered to be OR. Let me point out that I would not have done this or anything similar in the body of the article – I would consider that OR. I am only talking about taking this kind of liberty in the lead, for the purpose of providing a gentler introduction to a topic. I am confident that this issue or something similar has been brought up before (in reference to math articles) and would appreciate any pointers to previous discussions. Bill Cherowitzo (talk) 21:28, 28 October 2011 (UTC)

I like this change. It's a good idea to avoid the technical terms injective and surjective in the very first sentence. I don't think it constitutes original research. I can imagine some wikilawyer pointing accusingly at WP:SYNTH, but I think people often misunderstand the difference between synthesis and compilation. What we have here is a collection of facts, for each of which a source could be provided if necessarily (although I'd hate to actually see a multitude of footnotes). "Original research" would be if you drew from those facts a conclusion that isn't in a reliable source. That's not the case here.

I don't recall any similar discussions in recent months, but it must surely have come up at some time. If anyone else can remember a similar discussion, I wouldn't mind seeing a link to it.

I do worry though that the new version is a little bit too long for a lead. What about just keeping the first sentence, then moving conditions (1)–(4) to a new section at the top of the article entitled "Formal definition" or similar?

Also, the discussion of bijections and relations has the potential to cause confusion. The phrase The process of "turning the arrows around" does not usually yield a function needs a caveat: in the context where this phrase appears, we're talking about bijections, so reversing the arrows does always yield a function (as you point out next). Currently it could seem that the one sentence asserts simultaneously that it's not always a a function and that it (the same thing) is a function. I know what you mean, but I can imagine it being unnecessarily difficult for someone new to this subject. Jowa fan (talk) 23:13, 28 October 2011 (UTC)

In general leads are supposed to summarize an article, so a cite shouldn't be needed for every statement if similar statements are in the body of the article and those have cites. Also, math articles tend to follow WP:Scientific citation guidelines which allow you to summarize sources rather than giving fact by fact footnotes.--RDBury (talk) 05:50, 29 October 2011 (UTC)

Somewhere in there you might want to say that property (1) is called "total" (the correlative of "onto") and property (2) is called "single-valued" (the correlative of "one-to-one"). JRSpriggs (talk) 18:08, 30 October 2011 (UTC)

Thanks for the comments. A section of Wikipedia:Scientific citation guidelines dealt directly with my concern, it seems that I was being a little too hawkish with my interpretation of NOR. I've re-edited the page, incorporating the suggestions made here and elsewhere, so again thanks. Bill Cherowitzo (talk) 03:12, 31 October 2011 (UTC)

Proposal/discussion of interest to this project

Here: Support check: a Wikipedia math naming principle?.--JohnBlackburne^words_deeds 15:19, 30 October 2011 (UTC)

Move request

I've asked to move the article Gauss–Codazzi equations around. Feel free to join the discussion. --The Evil IP address (talk) 10:45, 31 October 2011 (UTC)

Use the most common name, not the alphabetized name. JRSpriggs (talk) 12:56, 31 October 2011 (UTC)

Desargues' theorem

An image from Desargues' theorem is scheduled to become picture of the day this coming Wednesday, Nov. 2. So now would be a good time to look over the article and make sure it is as good as it could be for the readers who come to it from the front page. See the article and its talk page for details. —David Eppstein (talk) 21:19, 31 October 2011 (UTC)

The first thing I noticed is there are no inline cites, it's a problem but it's probably not the kind of thing that an be fixed in two days.--RDBury (talk) 01:27, 1 November 2011 (UTC)

Actually for the general audiences at least it might be useful to state an euclidean/affine version in terms of elemtary geometry.--Kmhkmh (talk) 01:42, 1 November 2011 (UTC)

Interesting. It says "A diagram of Desargues' theorem, created using Adobe Illustrator. Based on File:Desargues theorem.svg, created by User:DynaBlast." It's an improvement over the picture by DynaBlast in this respect: none of the three depicted lines meeting at the center of perspectivity is parallel to the axis of perspectivity. In DynaBlast's version, one of them is parallel. DynaBlast's version is metrically identical to my earlier version that it superseded; mine had no colors. Mine was based on another identical diagram I drew on graph paper in 1999. Wikipedia didn't exist until 2001, so I could not have imagined that my picture's grandchild would have this career. Michael Hardy (talk) 02:24, 1 November 2011 (UTC)

Recent MOS changes for transpose

Opinions on this? I found the code particularly helpful when it was in. Rschwieb (talk) 01:58, 1 November 2011 (UTC)

It was in for all of 11 days, with the editor removing what he had added previously. I don't think adding wikicode is necessary in that or other examples (and arguably if it's added to one it should be added to all). Editors can and are encouraged to look at the source of any formatting they don't know, which I'm sure is how most of us learn these things.--JohnBlackburne^words_deeds 02:21, 1 November 2011 (UTC)

bluetulip.org

This link was recently added to the Ellipse article. It generates simple problems in conic sections and checks the answer if you type one in. (A similar link is in Factorization.) This doesn't seem to be excluded by ELNO but I'm not sure you can call it a "unique resource" either since you can find similar exercises in any precalculus text. The general question is whether external links are appropriate if they only contain exorcises or drills with no factual information, assuming they are well intentioned. My feeling is no, WP is not a textbook so articles should not be offering a list of exercises at the end as if it were. But I can see how some people might consider such links useful so I'm looking for other opinions.--RDBury (talk) 12:10, 2 November 2011 (UTC)

I also vote no -- that's not the sort of resource one should go to an encyclopaedia to find. --Joel B. Lewis (talk) 13:56, 2 November 2011 (UTC)

I'm not sure of the exact guideline on this, but looking at the site, it had nil reference value, and does not seem to be related to the encyclopedic nature of Wikipedia. As I understand it, Wikipedia is not supposed to be pedagogical. I'm pretty sure that someone familiar with the policy will find a good reason to exclude it. Quondum^talk_contr 14:42, 2 November 2011 (UTC)

When are conjectures encyclopedic?

I just got a note questioning this edit. My reasoning is that conjectures are not facts and therefore the rules for verifiability do not apply. From what I can find though there seems to be little guidance from policies and guidelines as to what rules should be applied. My thinking is that the conjecture should meet some criteria for notability adapted from WP:N. Such as:

• If the conjecture is mentioned in a reliable secondary source.
• If the conjecture was made my a well-known mathematician (the celebrity factor).
• If the truth of the conjecture would aid in the solution of a notable unsolved problem.

This reminds me of the discussion on mnemonics here a while ago in that it's a question of when non-factual material should be included in Wikipedia. On the principle that (with apologies to T.H. White) "Everything not forbidden will eventually be added to Wikipedia," I think whether or not things like mnemonics, conjectures, unsolved problems, etc. are encyclopedic should be covered by guidelines more than it is.--RDBury (talk) 01:49, 3 November 2011 (UTC)

I don't see any problem with the guidelines here. "Simmons conjectures that..." is a fact that can be handled like any other fact. In wikipedia's thousands of articles about history, politics, literature and much more, facts of this nature need to be dealt with every day. Is it verifiable? Is it relevant to the article? I think it's OK for an encyclopedia to mention unsolved problems and conjectures, provided that there are sources to demonstrate that people are interested in such things. It's a matter of editors making judgements on what should be included; it's right and proper that the guidelines leave some room for judgement and consensus-building. Jowa fan (talk) 02:08, 3 November 2011 (UTC)

What Jowa fan said. If you discriminate against conjectures as a blanket rule, then that's Riemann out of the window, which would be absurd.

In general I think the Wikipedian community in general is getting just a little bit hung up on what is or what is not allowed as content, based upon a set of more-or-less arbitrary rules for inclusion that are being Pharisaically interpreted, honed, filed down, chopped up, squeezed out and then slapped over every single entry, at the expense of the overall philosophy of an encyclopedia, that is: to inform and educate. And if you don't agree that this is what an encyclopedia is for, then I'm afraid I have to disagree in the strongest terms. --Matt Westwood 06:38, 3 November 2011 (UTC)

To me a conjecture is notable if it has been noted in reliable sources, no different from lots of other things. Its unprovenness does not give it any special status that prevents us from writing about it, nor does it excuse us from finding adequate sources. In particular, re the original poster's assertion "conjectures are not facts and therefore the rules for verifiability do not apply": no, whether someone has made a conjecture or not is definitely a fact and should be verifiable. For instance, when one goes back to the original sources, one often finds things that later authors say are conjectures but which the original author stated less strongly. In the edits in question, two questions were stated as conjectures in an unverifiable form, with no references and without even enough information to reliably identify the mathematicians in question. Their removal, until sources could be added, was appropriate. —David Eppstein (talk) 07:07, 3 November 2011 (UTC)

Actually the person the person who added the conjectures stated they came from OEIS, which I believe the consensus is that it is reliable. My point is that not every conjecture in a research paper somewhere should be mentioned in a Wikipedia article. Research papers and sites like OEIS are reliable sources of fact, but I don't think the fact that "Relatively obscure mathematician X made a conjecture about even more obscure sequence Y" is encyclopedic even if it is verifiable.

@Matt Westwood, please read what I'm proposing before dismissing it. You're claiming I'm trying to remove Riemann from WP which is ridiculous. Riemann would pass all three of the criteria I gave and I'm only suggesting that a conjecture pass at least one before it's included. If you don't like the idea then give a valid reason, don't use some silly strawman argument. I understand that many Wikipedians get frustrated with all the guidelines and policies, but I disagree that they are arbitrary and in general unhelpful. Guidelines are very helpful when removing something that does not belong on Wikipedia, otherwise the reason you have is give is that you don't like it. The person who added the material obviously did think it was appropriate and without some kind of guidelines on what should be included and what shouldn't it's a matter of one person wanting it and the other not wanting it with no rational way to decide between them. The guidelines and policies are not always states as clearly as they should be, and I believe in IAR as much as the next person, but Wikipedia houses a huge amount of useless cruft and getting rid of it is hard enough; having guidelines helps the process by by keeping it from appearing arbitrary and helping to stave off edit wars.--RDBury (talk) 08:06, 3 November 2011 (UTC)

No I am not. I'm complaining about the fact that there is a culture developing of deletion-uber-alles. I was setting up an extreme case (which some would call a "straw man") pointing out the foolishness of deleting conjectures purely because they are conjectures and therefore not truths. You go away again and read exactly what I said. And I stand by it 100%. I utterly, utterly despise deletionism.

My approach, rather than just complacently delete the statements in question out of hand would have been to add a tag "requires sources" or whatever. Then at least the OP would have a nudge to go back and see whether the problem can be fixed. --Matt Westwood 08:28, 3 November 2011 (UTC)

I don't understand why this is worth making a fuss about. Someone added a statement to an article, someone else deleted it, and now it's being discussed. This is normal process: the system seems to be working as it should. There's no need for additional guidelines to cover this situation. In fact, I think it would undesirable to have a guideline that stifled discussion in cases like this. Is this an isolated incident, or can anyone point to more edits showing that the handling of conjectures is a problem that needs solving? Jowa fan (talk) 09:42, 3 November 2011 (UTC)

The statement "Fred Bloggs conjectures that XYZ" needs a reliable source like any other statement. The problem appears to be the use of OEIS as a source in this case: I think we all accept it as a reliable source for sequence properties, but some editors seem to object to leaning too heavily on comments by OEIS editors. Notability and reliability would certainly be more obvious if one could find a journal article by Bloggs. In the specific case here, the Simmons conjecture does appear to be notable, listed here and in some Martin Gardener columns. -- 202.124.72.1 (talk) 14:33, 3 November 2011 (UTC)