Wikipedia talk:WikiProject Mathematics/Archive/2011/Mar

Anti-geometric mean and anti-harmonic mean needs rescuing

The new article Anti geometric mean and anti harmonic mean has been proposed for deletion for a lack of sources. This article needs rescuing. These two means are legitimate: one of them is the same as the contraharmonic mean. Sławomir Biały (talk) 14:02, 28 February 2011 (UTC)

They may be means within the meaning of that word, but are they notable? Also the article should explain how to generalize them to three or more inputs. JRSpriggs (talk) 15:20, 28 February 2011 (UTC)

At least the contraharmonic mean/antiharmonic mean is notable (there are many google scholar and google books hits for both of these terms). Perhaps an alternative to deletion is to redirect to the contraharmonic mean article. Sławomir Biały (talk) 15:34, 28 February 2011 (UTC)

The means may be legitimate, but the notability, names, and the connection between them don't seem to be. They appear to be taken from http://aweeklyriddle.blogspot.com/2010/10/anti-geometric-mean-and-anti-harmonic.html , the October 16 entry in a "riddle" blog.

The anti-geometric mean is a mean, as it's

$\operatorname {not} {{\frac {x^{3/2}-y^{3/2}}{x^{1/2}-y^{1/2}}}={\frac {\int _{x}^{y}t\,dF(t)}{\int _{x}^{y}\,dF(t)}}}$ (oops, how do you strikeout within a formula}

for an appropriate value of F. — Arthur Rubin (talk) 15:50, 28 February 2011 (UTC)

${\frac {x^{3/2}+y^{3/2}}{x^{1/2}+y^{1/2}}}$

which is the Lehmer mean with p=3/2. — Arthur Rubin (talk) 15:58, 28 February 2011 (UTC)

The article is fairly clearly OR; note where it says "copyright shrenuj 2010" in the title of the blog entry that Arthur linked to, and see the username of the Wikipedia article creator. Having said that, "anti-harmonic mean" seems to be used elsewhere as a synonym for the contraharmonic mean, so this term (on its own) could merit a redirect. Gandalf61 (talk) 15:55, 28 February 2011 (UTC)

As an aside, should we make a note as to the generalized Lehmer mean,

$\left({\frac {x^{p+q}+y^{p+q}}{x^{p}+y^{p}}}\right)^{1/q}$

— Arthur Rubin (talk) 16:56, 28 February 2011 (UTC)

I've fixed the punctuation in the article's title. Michael Hardy (talk) 23:21, 1 March 2011 (UTC)

Multilinear subspace learning

Someone has been adding sections on and links to something called multilinear subspace learning to a variety of articles on linear algebra and multilinear algebra. I have removed one such section from the tensor article since it obviously didn't belong where it was. I'm wondering whether the rest of the added content is worth keeping though. There seem to have been only a handful of papers] published (in fairly obscure places) on this topic, most of them in the past few years and mostly by the same group of authors. What should we do about this, if anything? Sławomir Biały (talk) 11:53, 1 March 2011 (UTC)

Proposing deletion, and tagging, although I believe the SIAM journal to be legitimate. I believe most of the references should be weeded out, but I suspect that, as long as the article is here, it should be linked somewhere in multilinear algebra. — Arthur Rubin (talk) 16:14, 1 March 2011 (UTC)

Perfect number articles

Jurvetson2 (talk · contribs) has created articles 33550336 and 8589869056. As far as I can see, the only interesting property of these numbers is that they are perfect numbers, so I don't think they meet the criteria for notability of specific individual numbers at WP:NUMBER. Speedy deletion was proposed for one article, but declined. I have noted my concerns on Jurvetson2's talk page. Should we take these articles to AfD ? Gandalf61 (talk) 09:32, 1 March 2011 (UTC)

I think they should be deleted. — Arthur Rubin (talk) 10:11, 1 March 2011 (UTC)

Yes I feel like imitating the Cybermen and saying to the article 'You are deficient, you will be deleted. deleted'. I seem to be wanting to delete things quite often nowadays even though I try to find something useful about them and leave them time to grow. Dmcq (talk) 11:44, 1 March 2011 (UTC)

Both articles now taken to AfD - thank you, Arthur. Discussion is at Wikipedia:Articles for deletion/33550336. Gandalf61 (talk) 09:03, 2 March 2011 (UTC)

@Gandalf61: Thanks. It wasn't easy to do the AfD multi.

@Dmcq: They're not deficient, they're perfect. LOL — Arthur Rubin (talk) 09:12, 2 March 2011 (UTC)

Aargh! I am deficient. If I were a Cyberman my head would explode! :) Dmcq (talk) 13:05, 2 March 2011 (UTC)

k-Poincaré disambiguation

I've just saved the Kappa-Poincaré page from speedy deletion for the time being, but it definitely needs to be changed into something else, either be deleted (Wikipedia's search does seem to find all the k- K- and κ- variations already) or converted into a disambiguation page or a redirect. I'm not conversant in math issues, so I need to ask a question: Is there some particular reason that both the K-Poincaré algebra and K-Poincaré_group articles shouldn't be merged into subsections of the Poincaré group article followed by the creation of redirects for the various k- kappa- κ- -algebra -group variant names to that article? Alternatively, how about an article for k-Poincaré with the -algebra and -group versions as subsections. Because I don't understand the math or the significance of the math, I'm clueless but I'm sure one of you do. Best regards, TRANSPORTERMAN (TALK) 16:38, 1 March 2011 (UTC)

K-Poincaré algebra and K-Poincaré_group can probably be safely merged, since they are basically two sides of the same coin. Explaining what these objects are may in fact be easier if they are in the same article. However, I don't it such a good idea to merge with Poincaré group, which a much simpler and widely known object, that needs an accessible article. (The Poincaré group article should however mention at some point that it can be deformed into the K-Poincaré_group.)TR 14:41, 2 March 2011 (UTC)

Chain rule

The article titled chain rule currently says:

The chain rule is frequently expressed in Leibniz notation. Suppose that u = g(x) and y = f(u). Then the chain rule is

$\left.{\frac {dy}{dx}}\right|_{x=c}=\left.{\frac {dy}{du}}\right|_{u=g(c)}\cdot \left.{\frac {du}{dx}}\right|_{x=c}.\,$

This is often abbreviated as

${\frac {dy}{dx}}={\frac {dy}{du}}\cdot {\frac {du}{dx}}.$

However, this formula does not specify where each of these derivatives is to be evaluated, which is necessary to make a complete and correct statement of the theorem.

Does this last form really fail to "specify where each of these derivatives is to be evaluated"? It seems to me that the first form above clutters things in such a way as to interfere with understanding, and that the second, read correctly, doesn't really fail to do anything that should be done.

Opinions? Michael Hardy (talk) 23:04, 1 March 2011 (UTC)

I'm with you on this one. The sentence isn't really Wikipedia-appropriate, anyway -- at best that's textbook language. CRGreathouse (t | c) 01:47, 2 March 2011 (UTC)

Well, since I'm the one who wrote that sentence, I think I should defend it. But I'm going to do so on Talk:Chain rule, not here. Ozob (talk) 01:49, 2 March 2011 (UTC)

Just out of interest why is chain rule marked as "mid priority"?TR 09:20, 2 March 2011 (UTC)

Help needed

There appear to be a series of disputes with Optimering (talk · contribs). One is listed at Talk:Algorithm. Another is at WP:COIN#Optimering and is mostly about an edit war at Luus–Jaakola. The assumption is that the user is the person whose work the user keeps citing, thus making WP:SELFCITE relevant. As Optimering has announced a preference to deal only with people who are also mathematical experts, I was hoping that some of you would please look at these disputes and see if you can help resolve them. WhatamIdoing (talk) 17:02, 28 February 2011 (UTC)

@WhatamIdoing, your suggested reading for Optimering seems to have been read as an endorsement of his behavior, rather than a spur to reflection (on the WP dynamics of expert editing).  Kiefer.Wolfowitz  (Discussion) 03:26, 4 March 2011 (UTC)

Also see the threads at my talk. So far I've only seen this editor write in a neutral way. He is obviously watched with some scepticism. By some in a healthy way, but by others in a fashion that borders on harassment. It would be a pity if an editor capable of writing is a niche area got scared away. —Ruud 00:52, 1 March 2011 (UTC)

Alas, Optimering's use of sources and apparent OR (in ... trying ... to document notability of the thesis) is far from neutral. Lately, Ruud has insulted MrOllie on his talk page, and similar insults to Mr Ollie by Optimering appear on the article talk page.  Kiefer.Wolfowitz  (Discussion) 03:23, 4 March 2011 (UTC)

G. J. Toomer

I just created a new article titled G. J. Toomer. Quite a large number of articles link to it, but it's very stubby. Do what you can to improve it. Michael Hardy (talk) 00:22, 4 March 2011 (UTC)

C*-algebra

Hello, I saw on the discussion page of C*-algebra that this WikiProject supports the page. Is there anyone here who knows of references to support the statements found in the "Some history: B*-algebras and C*-algebras" section (that I have recently added 'fact' tags to)? Any help would be appreciated. 121.216.130.64 (talk) 11:45, 28 February 2011 (UTC)

I've added cites (with links) to a supporting reference to the the article. Paul August ☎ 12:25, 28 February 2011 (UTC)

On a maybe related note, that page could use some attention from the C*-folks here. Mct mht (talk) 11:15, 5 March 2011 (UTC)

Archimedean property

Should Archimedean property and non-Archimedean ordered field get merged? Michael Hardy (talk) 21:42, 5 March 2011 (UTC)

Merge Archimedean with non-Archimedean? Cute, let's merge p-adic numbers with ordered field at next step. Incnis Mrsi (talk) 22:04, 5 March 2011 (UTC)

Very funny. Archimedean property is about a property; it needs to give both examples of cases where the property holds and examples of cases where it fails. Michael Hardy (talk) 23:14, 5 March 2011 (UTC)

More seriously. There are many non-Archimedean fields, some of which are ordered, but so notable as p-adic numbers are not. Imagine a redirect from "non-Archimedean ordered field" to a mess of examples and counterexamples resulting in all 4 possible flavours (because there are also Archimedean normed, but unordered, fields such as complex numbers). Incnis Mrsi (talk) 23:25, 5 March 2011 (UTC)

Non-Archimedean ordered field could be enriched by some history, which is certainly rich. Tkuvho (talk) 07:43, 6 March 2011 (UTC)

No free lunch theorem, help from probability & algorithmic analysts

This article needs scrutiny:

"no free lunch theorems... 'state[s] that any two optimization algorithms are equivalent when their performance is averaged across all possible problems.'" (The probability measure on all possible problems would be an interesting object, I assume.)

There is a related article,No free lunch in search and optimization, which cites an article by the well-known computer scientist Wegener, which probably can be salvaged.  Kiefer.Wolfowitz  (Discussion) 14:04, 5 March 2011 (UTC)

There is nothing problematic about considering probability measures an all possible problems of a fixed size. And "any two optimization algorithms are equivalent" is too strong a statement — one algorithm might perform redundant work compared to another — but I think it's safe to say that in this problem setting no algorithm is better than a brute force search. —David Eppstein (talk) 17:06, 5 March 2011 (UTC)

The statement seems completely reasonable in the context of No free lunch in search and optimization. The two articles have a lot of overlap, and it might be better to merge them. Ozob (talk) 18:40, 5 March 2011 (UTC)

Whether an algorithm is optimizing (or not) depends (in part) on which probability measure one uses on the space of possible problems. No algorithm is optimizing for all such measures. That is the point. JRSpriggs (talk) 20:40, 6 March 2011 (UTC)

Axiom

I'm not sure it's the right board to post it on, but the article axiom caught my eye. AFAIK the notion of axiom being self-evident truth is very outdated: even when talking about logical axioms as described in the article, we cannot treat them as 'self-evident truths', if only because there are several logics (e.g. classical, intuitionist) that use different axioms, so calling them self-evident seems moot.

Is there anything that can be done to improve the article? I'm a complete layman in logic, so I didn't edit it myself. — Kallikanzarid^talk —Preceding undated comment added 13:13, 6 March 2011 (UTC).

I don't see the problem. It distinguishes between the traditional use and the current use in mathematics quite clearly in the lead as far as I can see. Dmcq (talk) 15:20, 6 March 2011 (UTC)

The "traditional" sense of the word makes sense in certain contexts other than mathematics. For example, in epistemology. To say it's outdated is to limit one's world-view to mathematics and forget that other subjects exist. Michael Hardy (talk) 19:26, 6 March 2011 (UTC)

This began with Euclid's Elements which distinguishes between axioms (obvious and general premises) and postulates (premises which are specific to geometry and not quite so obvious). Most of us use those two words as synonyms today. JRSpriggs (talk) 20:54, 6 March 2011 (UTC)

"Number theory"?

Our article titled Basel problem currently begins like this:

The Basel problem is a famous problem in number theory, first posed by Pietro Mengoli in 1644, and solved by Leonhard Euler in 1735.

[snip snip......]

The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:

$\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}=\lim _{n\to +\infty }\left({\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+\cdots +{\frac {1}{n^{2}}}\right).$

Should we change "number theory" to "analysis", or to something else, or should we just delete it? Or let it stand? Michael Hardy (talk) 19:24, 6 March 2011 (UTC)

I WP:BOLDly changed it to mathematical analysis, but if someone else wants to change it again I won't object. We shouldn't just delete it because we need some context to tell readers it's about mathematics. —David Eppstein (talk) 19:30, 6 March 2011 (UTC)

Is it worth mentioning in that article that the reciprocal of that sum is the asymptotic probability that a pair of integers, selected at random, are relatively prime? (As with any special value of the Riemann zeta function.) From this perspective, number theory seems like the right categorization. Sławomir Biały (talk) 19:42, 6 March 2011 (UTC)

Certainly that's worth mentioning in the article. Michael Hardy (talk) 04:24, 7 March 2011 (UTC)

Does anyone have any idea how Mengoli and Euler thought of this problem? Tkuvho (talk) 20:16, 6 March 2011 (UTC)

Simple solution: Put both. I left analysis first as it has claim to be 'senior' here. CRGreathouse (t | c) 18:43, 8 March 2011 (UTC)

I've changed it to read thus:

The Basel problem is a famous problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644, and solved by Leonhard Euler in 1735.

Michael Hardy (talk) 03:49, 10 March 2011 (UTC)

Citation templates now support more identifiers

Recent changes were made to citations templates (such as {{citation}}, {{cite journal}}, {{cite web}}...). In addition to what was previously supported (bibcode, doi, jstor, isbn, ...), templates now support arXiv, ASIN, JFM, LCCN, MR, OL, OSTI, RFC, SSRN and Zbl. Before, you needed to place |id={{arxiv|0123.4567}} (or worse |url=http://arxiv.org/abs/0123.4567), now you can simply use |arxiv=0123.4567, likewise for |id={{JSTOR|0123456789}} and |url=http://www.jstor.org/stable/0123456789 → |jstor=0123456789.

The full list of supported identifiers is given here (with dummy values):

• {{cite journal |author=John Smith |year=2000 |title=How to Put Things into Other Things |journal=Journal of Foobar |volume=1 |issue=2 |pages=3–4 |arxiv=0123456789 |asin=0123456789 |bibcode=0123456789 |doi=0123456789 |jfm=0123456789 |jstor=0123456789 |lccn=0123456789 |isbn=0123456789 |issn=0123456789 |mr=0123456789 |oclc=0123456789 |ol=0123456789 |osti=0123456789 |rfc=0123456789 |pmc=0123456789 |pmid=0123456789 |ssrn=0123456789 |zbl=0123456789 |id={{para|id|____}} }}

Obviously not all citations needs all parameters, but this streamlines the most popular ones and gives both better metadata and better appearances when printed. Headbomb {talk / contribs / physics / books} 03:05, 8 March 2011 (UTC)

GREAT! This update shall increase the consistency of citations, e.g. the ordering of JSTOR and MR.

It seems that if I want to have two ISBNs, I can use "isbn= " for one (e.g., 13-digit), and then use "id=ISBN 0123456789" for the second. Unfortunately, math-reviews can then split the isbns: For example

Molchanov, Ilya (2005). Theory of random sets. Probability and its applications. Springer-Verlag London Ltd. pp. 194–240. doi:10.1007/1-84628-150-4. ISBN 978-185223-892-3. MR 2132405. ISBN 1-85233-892-X. {{cite book}}: Check |isbn= value: checksum (help); Invalid |ref=harv (help); Unknown parameter |address= ignored (|location= suggested) (help)

I would prefer to be able to use 1-3 isbns: isbn=,isbn-10=, isbn-13=, simultaneously. Thanks!  Kiefer.Wolfowitz  (Discussion) 18:15, 8 March 2011 (UTC)

With ISBNs, there's actually a trick (it only works for ISBNs however), |isbn=0123456789 translate into a raw "ISBN 0123456789", which is linked via the software rather than being linked through the template. So this means you can use |isbn=0123456789, ISBN 0987654321, ISBN 1029384756 and it will be converted to Bob's Book. ISBN [[Special:BookSources/0123456789, ISBN 0987654321, ISBN 1029384756|0123456789, '"`UNIQ--templatestyles-00000017-QINU`"'[[ISBN (identifier)|ISBN]]&nbsp;[[Special:BookSources/0987654321 |0987654321]]<span class="error" style="font-size:100%">&nbsp;Parameter error in {{[[Template:ISBN|ISBN]]}}:&nbsp;checksum</span>, '"`UNIQ--templatestyles-00000018-QINU`"'[[ISBN (identifier)|ISBN]]&nbsp;[[Special:BookSources/1029384756 |1029384756]]<span class="error" style="font-size:100%">&nbsp;Parameter error in {{[[Template:ISBN|ISBN]]}}:&nbsp;checksum</span>]]. {{cite book}}: Check |isbn= value: invalid character (help); templatestyles stripmarker in |isbn= at position 13 (help). Headbomb {talk / contribs / physics / books} 18:41, 8 March 2011 (UTC)

I tried this technique but the ISBNs have disappeared:  Kiefer.Wolfowitz  (Discussion) 19:32, 8 March 2011 (UTC)

Molchanov, Ilya (2005). Theory of random sets. Probability and its applications. Springer-Verlag London Ltd. doi:10.1007/1-84628-150-4. MR 2132405. {{cite book}}: Invalid |ref=harv (help); Text "|isbn=9781852238923, ISBN 185233892X" ignored (help)

Try not using the span; that was just to show you what the wikiformatting should look like. Without the span, it's: Molchanov, Ilya (2005). Theory of random sets. Probability and its applications. Springer-Verlag London Ltd. doi:10.1007/1-84628-150-4. ISBN [[Special:BookSources/9781852238923, ISBN 185233892X|9781852238923, '"`UNIQ--templatestyles-0000001C-QINU`"'[[ISBN (identifier)|ISBN]]&nbsp;[[Special:BookSources/185233892X |185233892X]]]]. MR 2132405. {{cite book}}: Check |isbn= value: invalid character (help); Invalid |ref=harv (help); Unknown parameter |address= ignored (|location= suggested) (help); templatestyles stripmarker in |isbn= at position 16 (help) —David Eppstein (talk) 20:57, 8 March 2011 (UTC)

Semper Benignus! THANKS!

That was much easier Kiefer.Wolfowitz  (Discussion) 21:25, 8 March 2011 (UTC)

Wikipedia:Articles for deletion/Timelike topological feature

This pretends to be a piece of theory of Lorentzian manifolds, but… it is a theory of doubtful notability. Incnis Mrsi (talk) 09:18, 9 March 2011 (UTC)

Ptolemy's table of chords

I've created Ptolemy's table of chords, in its present form an imperfect article. Work on it! Michael Hardy (talk) 23:12, 10 March 2011 (UTC)

At Talk:Ptolemy's table of chords, I've created a "to do" list of work that should get done on this article. I'll probably get to most or all of it eventually unless others get there first. Michael Hardy (talk) 00:09, 12 March 2011 (UTC)

Here's the list:

Work that needs to be done on this article:

• Further inline citations, including:

• It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy
• (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of 7½°).
• Several centuries passed before more extensive trigonometric tables were created.
• Page numbers in Glowatzki and Göttsche?
• The parts about the three distinct methods of computing chords.

• More on the geometric theorems: Their precise statements, how they are proved, how they are used in deriving trigonometric identities, how those identities are used in computing chords.
• History of editions of the book including those in Arabic.
• When did more extensive tables supersede this one? Which century?
• How did the table influence later work?

• And probably other things.........

Michael Hardy (talk) 00:16, 12 March 2011 (UTC)

Please review seriousness v. proposed deletion as parody of new article Names of small numbers at Wikipedia:Articles for deletion/Names of small numbers

Mathematics WikiProject members, please, this is being discussed at:

Wikipedia:Articles for deletion/Names of small numbers http://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Names_of_small_numbers#Names_of_small_numbers

Thank you. Pandelver (talk) 00:05, 12 March 2011 (UTC)

May be of remote interest

There's a math-related arbcom case in which someone has proposed something along the lines that discussing math on talk pages without references or (lord forbid) pointing out an error in a WP:RS is a blockable offense (after warning, of course). Linky here. Tijfo098 (talk) 07:22, 12 March 2011 (UTC)

Is not this absurdity restricted to Talk:Monty Hall problem? JRSpriggs (talk) 10:06, 12 March 2011 (UTC)

Invitation to comment on RFC regarding the stubbing (deletion) of the Mathematics in medieval Islam article

You are invited to comment on the content dispute regarding the stubbing of the Mathematics in medieval Islam article Thank You -Aquib (talk) 04:11, 14 March 2011 (UTC)

Whew! I've certainly had problems with some rather industrious people making unjustified claims about Islamic maths with citations that don't quite back them up and bending things like turning Persian into Islamic. This seems a very drastic step though and rather a pity. I hope it all gets fixed up soon again but my experience does indicate that all claims will need to have the citations examined. Dmcq (talk) 13:25, 14 March 2011 (UTC)

Numerical approximations of π -> Approximations of π

Please see Talk:Numerical_approximations_of_π#Requested_move. Cheers, Ben (talk) 11:52, 16 March 2011 (UTC).

Template:Pi

The usage of {{pi}} is under discussion, see Template talk: pi . 65.95.13.139 (talk) 13:40, 18 March 2011 (UTC)

Quarter squares

Another editor is insisting on adding their bit on calculating quarter squares to Multiplication algorithm and I'm failing to get them to desist, latest round at Talk:Multiplication_algorithm#Construction_of_tables. ANyone like to have a look at it thanks? Dmcq (talk) 13:11, 20 March 2011 (UTC)

Cardinals

There are many used notations for cardinal numbers and cardinality. In all (advanced) mathematical articles which use them, we need to clarify whether the axiom of choice is assumed, and whether the von Neumann cardinal assignment and/or the assumption that cn(cn(X))=cn(X) (i.e. that "the" cardinal number of a set has the same cardinality as the set) is made. The "Union" of cardinal numbers requires some assumption similar to the von Neumann cardinal assignment, and the Sum or Product of an infinite set of cardinal numbers requires some version of the Axiom of Choice to define.

I would like to have a centralized discussion on this, putting pointers on all the articles which refer to "cardinality". I was also thinking that merging initial ordinal with aleph number might be a good start. The constructions are the same, but the assumptions are different. — Arthur Rubin (talk) 23:20, 20 March 2011 (UTC)

Unfortunately, my reference library is not available (i.e., I didn't keep it from my last move), so I would be forced to reference the material to my and my parents' books and papers. This is generally considered improper. Any ideas? — Arthur Rubin (talk) 23:21, 20 March 2011 (UTC)

I would not merge those two, no. I think aleph number is an appropriate title for a brief, and not extremely mathematical, article of fairly limited scope, namely just to tell people what these funny $\aleph _{0}$, $\aleph _{17}$, $\aleph _{\omega }$ thingies that they may have seen somewhere are. For deeper information, readers should be directed to articles like cardinality. --Trovatore (talk) 00:00, 21 March 2011 (UTC)

I can see your point. In that interpretation, I couldn't help rewrite aleph number, but much of the material now in aleph number is in initial ordinal and should not remain in aleph number.

I wonder if someone can describe the difference between cardinality and cardinal number, also. Should those be divided in a similar way, with cardinality being non-mathematical, and cardinal number being more mathematical? — Arthur Rubin (talk) 00:18, 21 March 2011 (UTC)

At first thought it seems plausible to me to merge cardinal number into cardinality. I suppose cardinal number could be used as meaning "some complete invariant for cardinality, with the exact invariant depending on what scheme you have in mind" but I don't know that that is particularly standard. --Trovatore (talk) 00:25, 21 March 2011 (UTC)

@Arthur: Personally, I am not very worried about the (potential) conflict of interest. The articles we are talking about are on completely established subjects, and the books by H. and J. Rubin are mainstream, not fringe sources in any way. There are plenty of other editors who watch the articles and can edit them to add other references. Your identity is known, and you are a long-time contributor to the project. Given those facts I think you should not be too worried about editing the articles, and I will say that again if anyone raises the issue. — Carl (CBM · talk) 00:29, 21 March 2011 (UTC)

Square bracket in a link

I was thinking about puttting in a link to interval (mathematics) for things like (−π, π] because people keep 'correcting' it to two round brackets. However there is a little problem in that one then gets three right square brackets or else one has to put in a space or the right bracket is black as in (−π, π]. Any ideas on a good way of getting it looking right thanks? Dmcq (talk)

Create a set of templates {{left half-open interval}}, {{right half-open interval}}, etc. Makes it more difficult to "correct" them (and more obvious why they shouldn't be). —Ruud 16:07, 14 March 2011 (UTC)

well you could always use $(-\pi ,\pi ]$ as long as you're not to picking about Latex within a text block.--Kmhkmh (talk) 16:10, 14 March 2011 (UTC)

Use <nowiki> tags, or any other delimiters: (−π, π] Nageh (talk) 16:20, 14 March 2011 (UTC)

Thanks everybody. I think I'll go with the nowiki or perhaps nobreak so I don't even need the &nbsp; Dmcq (talk) 16:41, 14 March 2011 (UTC)

Just been thinking about the templates left half-open interval etc. It does have the advantage it can be used for later instances that shouldn't be linked. Dmcq (talk) 17:18, 14 March 2011 (UTC)

We had this discussion a while ago (in 2003 or so?) and one of the things that got decided was that the brackets in asymmetric intervals should be enclosed within "nowiki" tags. Has that been neglected lately? Michael Hardy (talk) 17:22, 14 March 2011 (UTC)

I'm afraid so. I have difficulty with last week never mind eight years ago :) Anyway I just set up {{open-closed}} and {{closed-open}} - my first foray into creating templates! I guess I should stick something about it in a math help with formatting page if people like them else just the <nowiki> method. Dmcq (talk) 18:40, 14 March 2011 (UTC)

And I've tried them out on atan2. I've used {{math}} to format the contents rather than just {{nowrap}} as I think π looks better than π. Dmcq (talk) 22:10, 14 March 2011 (UTC)

A similar problem occurs when one tries to put a link to one of our articles into the comment part of an external link. See this edit to Monetary policy where Mattdarst tried to insert a link to Credit Channel into the comment field of an external link where the comment read ""THE STOCK OF CLOSED BANK DEPOSITS, DURATION OF CREDIT CHANNEL EFFECTS, AND THE PERSISTENCE OF THE U.S. GREAT DEPRESSION"". It caused the external link to terminate prematurely. JRSpriggs (talk) 01:27, 15 March 2011 (UTC)

I've seen bots "correct" semi-open intervals and similar mathematical notations. I'm aware of the nowiki solution, but seem to recall that this doesn't always discourage the more vigilant bots. A template solution seems best. Sławomir Biały (talk) 12:35, 15 March 2011 (UTC)

Which bots? Michael Hardy (talk) 18:04, 17 March 2011 (UTC)

Unfortunately, I no longer remember. I also don't know if this issue has since been fixed. It was a few years back that I noticed that some bots would sometimes parse mathematical markup incorrectly, and attempt to "correct" the problem. Sławomir Biały (talk) 18:33, 17 March 2011 (UTC)

I've set up {{open-open}} and {{closed-closed}} as well to complete the set. I hadn't thought about it before but they must be doing some special work to stop things like [1, 2] causing trouble. Anyway I use &#91; and &#93; instead in the templates. Dmcq (talk) 13:36, 15 March 2011 (UTC)

As an example {{open-closed|−π, π}} produces (−π, π] and the eventual code sent out to do this is <span class="texhtml" style="white-space: nowrap;">(−π, π]</span> Dmcq (talk) 14:07, 15 March 2011 (UTC)

I have formatted the argument (complex analysis) article using math type formatting for any inline mathematics throughout. I also set up a {{mvar}} template to do individual variables easily. Any comments gratefully received. Dmcq (talk) 15:14, 21 March 2011 (UTC)

Florentin Smarandache

The article Florentin Smarandache has been nominated for deletion for a 2nd time (AfD here); members of this project may be interested in commenting. Mlm42 (talk) 18:35, 17 March 2011 (UTC)

At least one editor there seems to be laboring under the impression that the subject of that article is a very influential mathematician. It is very frustrating arguing with this person. Sławomir Biały (talk) 01:31, 22 March 2011 (UTC)

Logarithm is up for FAC

Opine here. Jakob.scholbach (talk) 17:59, 21 March 2011 (UTC)

Probability notations

On the suggestion of one of the editors interested in the arbitration on Monty Hall problem, I started a little essay on mathematical notation in probability theory and its applications. First draft is at essay on probability notation; you can talk about it at: probability notation essay-talk. Comments are welcome! Especially if you can tell me that this is all superfluous because it's been done, and done better, before. Richard Gill (talk) 18:21, 21 March 2011 (UTC)

Duffin–Schaeffer conjecture

I've put an "orphan" tag on Duffin–Schaeffer conjecture, so get busy and think of a few (dozen) articles that should link to it. Michael Hardy (talk) 02:49, 22 March 2011 (UTC)

DYK: Criss-cross algorithm for linear optimization

A new article on the Criss-cross algorithm for linear optimization has been nominated for Did You Know?:

• ... that, while the criss-cross algorithm visits all 8 corners of a cube when started at a worst corner, it visits only 3 more corners when started at a random corner?

Corrections and comments are especially welcome. Best regards,  Kiefer.Wolfowitz  (Discussion) 03:48, 22 March 2011 (UTC)

Normal numbers page is broken

I was looking at Normal number and there seems to have been an edit by a well-meaning anonymous user which broke the markup. I would revert his edits, but I don't know enough about the subject to know if he was correcting an error in the article and made a mistake. Could someone with some more math skills than I take at look at the last two edits? Thanks.

DavidSol (talk) 01:34, 22 March 2011 (UTC)

I just noticed that Lindelof space was broken in much the same way for no apparent reason. It appeared to be caused by an edit adding a Korean interwiki, but now I wonder instead if it's a software problem. Sławomir Biały (talk) 01:43, 22 March 2011 (UTC)

Please note: Lindelöf space and Lindeloef are essentially identical spellings, whereas Lindelof is different (and incorrect). So if you can't type the umlaut, then write Lindeloef. Michael Hardy (talk) 02:51, 22 March 2011 (UTC)

At the time I was more concerned with having a link to the right place than valid typography, Michael. And yes, I can't type an umlaut at the moment. Sławomir Biały (talk) 10:46, 22 March 2011 (UTC)

I think it's just the wiki software getting confused. The anon at normal number undid his/her own change. The article got better after I tried purging it. I've seen similar issues with other unrelated pages today as well. —David Eppstein (talk) 01:45, 22 March 2011 (UTC)

Article should be in mathematics project?

Pick's theorem seems pretty applicable to your project. You might want to examine it and tag it if appropriate. Cliff (talk) 05:50, 22 March 2011 (UTC)

I added the project rating to the discussion page. Sławomir Biały (talk) 11:12, 22 March 2011 (UTC)

The article was already on List of mathematics articles, as well. That is the master list of articles in the project. — Carl (CBM · talk) 11:18, 22 March 2011 (UTC)

Arbcom decision on MHP: OR vs exposition in mathematics

The arbitration of the Monty Hall problem is nearing its decision phase.

Two proposals for the arbitration committee's decision concern Wikipedia policy on mathematical articles, especially original research versus secondary sources. Both proposals endorse editors' use of "arithmetic operations". This language could be of great concern to this project, and deserves your attention. Sincerely,  Kiefer.Wolfowitz  (Discussion) 23:47, 13 March 2011 (UTC)

Yes, it's of real importance to our project, and there are important nuances that neither version captures. But I thought we weren't supposed to edit Arb proposals?

CRGreathouse (t | c) 00:19, 14 March 2011 (UTC)

Editors may comment on proposals on the appropriate talk page. (I can strongly recommend against editing the arbcom pages that have warnings against civilian editing!)

I have asked two wise editors to watch the proceedings and this language, and I am sure that another wise editor already there can also comment effectively. (I commented informally on one arbcom member's talk page, and raised my concerns.) I believe that the most experienced editors should be trusted to advise ArbCom.  Kiefer.Wolfowitz  (Discussion) 00:44, 14 March 2011 (UTC)

Most worrying. Either version appears to make original research out of even routine examples. Sławomir Biały (talk) 01:19, 14 March 2011 (UTC)

Examples make or break articles, on WP and elsewhere. IMHO, we have to have the ability to make simple examples to interest readers, who would never be able to read research or even junior-senior math.

They should not issue any ruling on mathematics exposition. The social problems sufficed to make the MPH talk page a horror. If a mathematics article appears at ArbCom without social disorder on the talk page, then it may be reasonable for ArbCom to invent new principles to guide mathematics exposition. with apologies for being opinionated,  Kiefer.Wolfowitz  (Discussion) 01:33, 14 March 2011 (UTC)

I don't see how the proposed principles interfere with the presentation of routine examples, being routine they will undoubtably be able to be sourced. Paul August ☎ 02:01, 14 March 2011 (UTC)

Having looked closer at this I now have concerns about the proposed language. Paul August ☎ 12:55, 14 March 2011 (UTC)

Copying examples from reliable sources is generally not possible, due to copyright. While it is true that I've often seen people introduce errors into examples, there's not really a great alternative. Dcoetzee 02:27, 14 March 2011 (UTC)

Our examples are often similar to, but not identical with, those in other sources. The proposed mandate would in principle require that we copy sources step for step. Otherwise, it us generally not possible to find sources for each and every particular detail, even if the general principles are well-known. For instance, even simplifying a polynomial at the end of a longer example now requires sources in which the very same polynomial is simplified, which seems to be straightjacketing. Sławomir Biały (talk) 02:43, 14 March 2011 (UTC)

I think that the OR rule together with the Copyright law make coverage of mathematics (or any other subject) impossible. You have to think (commit 'original research') to do mathematics. The only alternative is to blindly copy from 'reliable' sources which violates copyright. Of course, such copying and the verification that the source is indeed reliable also require thought (OR). So the rule against OR is an absurdity which should be repealed.

The reason we have a rule against OR is to try to avoid disputes about what is correct reasoning by appealing to an outside source. Notice that in mathematics, this is usually only necessary when one or more of the disputing parties is a crank or troll. However, refusing to allow an edit on grounds that it is OR is ultimately just an excuse for rejecting what we think is false without having to get the agreement of a crank or troll. JRSpriggs (talk) 03:05, 14 March 2011 (UTC)

This one is fairly complicated. I don't think it true that, outside of mathematics, OR and copyright makes coverage impossible. The problem is that an allowable rephrasing in most fields becomes OR in mathematics, as even a change in notation does not fall in the "routine arithmetic calculation" exemption in Principles 11. However, an expert mathematician's edits may qualify as allowable per se under WP:SPS, but may fail WP:COI. This might lead to weird results as using the diff adding the material as a reference, but it seems to satisfy the rules. I'll comment there if I can think of anything sensible to say. — Arthur Rubin (talk) 04:33, 14 March 2011 (UTC)

To be more precise, if I make an edit to an article on (say) the Axiom of Choice which I consider obvious, and it's reverted as OR, another editor can restore it sourcing it to the diff. — Arthur Rubin (talk) 04:42, 14 March 2011 (UTC)

After David Eppstein and Geometry Guy have alerted ArbCom of concerns about unintended consequences of the proposed wording(s), some ArbCom members have declared that they need some time to think about this issue.

I have followed only a couple of the ArbCom proceedings, but reading those few proceedings, I have impressed with the conscientiousness and intelligence of its members --- it is like a committee made up of Geometry Guys who actually read and think before writing!

Mathematicians should not cluck like a brood of chicken littles on the ArbCom pages. Let us leave our most experienced and articulate volunteers, whose work on WP is known to and respected by some ArbCom members, to discuss calmly the proposals with them. As the original chicken little,  Kiefer.Wolfowitz  (Discussion) 08:49, 14 March 2011 (UTC)

JRSpriggs's comment describes my experience. The WP community is able to control tendentious editing by agreeing that some edits represent OR (often OR by synthesis).

I am worried that the proposed language may influence featured-article and good-article criteria, rendering mathematical articles ineligible if they include examples for lay readers or explain concepts using consensus explanations that cannot be sourced: for the latter, see the example on my talk page, which could be challenged as OR by synthesis, I fear.  Kiefer.Wolfowitz  (Discussion) 09:12, 14 March 2011 (UTC)

Alternative wording suggested by Kiefer.Wolfowitz

I (K.W.) suggest the following changes:

1. Change "arithmetic" to "mathematical".
2. Add "providing context using standard mathematical results or providing elementary examples" to the list of accepted editing activities.
3. Add the following: "Explanations, which use routine mathematical results or reasoning, are not considered "original research by synthesis", even if such routine mathematics are not referenced specifically for the application discussed: The mathematical results should be capable of routine referencing (easily referenced if challenged) and the article's editing should display an overwhelming agreement both that such derivations are routine (rather than original research) and that (to avoid simple OR proofs of important results) the result is unsurprising."

I would suggest that we strive for consensus language here, and then ask our leaders to communicate consensus suggestions to the ArbCom page.  Kiefer.Wolfowitz  (Discussion) 11:34, 14 March 2011 (UTC)

Elen asks for alternative wording

If you guys can get together a variant form of words quickly, and post it on the proposed decision talkpage, it can be put in as an alternative.

Providing examples is not a problem - slotting in different variables to a sourced method is not OR, nor is it really deriving from first principles. Glossing should not be a problem if you have some referencing to show the general applicability of the gloss. I do have concerns with the example Kiefer gave on his talkpage [1], but I'd have more problems with the old version that the new, assuming that somewhere in the sources cited are the two equations, the definition of limits, and the information about strictness in relation to Minkowski sum. It is the old example which seems to have lots of derivations without referencing. --Elen of the Roads (talk) 14:20, 14 March 2011 (UTC)

I refactored and emboldened Elen's request for help, which is most important!  Kiefer.Wolfowitz  (Discussion) 15:12, 14 March 2011 (UTC)

@Elen, I updated the references in the example. For sequential convergence, the most elementary exposition is John Fridy's Analysis:The Theory of Calculus, and I am sure that the results are available in the Green & Heller reference (and probably Arrow & Hahn, Mas-Colell, etc.: I am away from my references this week). Certainly the strictness of the Minkowski sum is covered by Rockafellar (pages given) and also Schneider: I believe that Rockafellar has a sequential discussion of limits, also. The equation (inclusion) appears in Ekeland (pages given).  Kiefer.Wolfowitz  (Discussion) 14:42, 14 March 2011 (UTC)

I made this proposal. It would be best for others to strive for a consensus statement, following Elen's very kind and thoughtful statement of interest.  Kiefer.Wolfowitz  (Discussion) 14:46, 14 March 2011 (UTC)

I've only had a chance to skim most of the Arbcom case, but it seems like the main issue is the detailed derivations from first principles. The language used should more closely reflect the actual problem, rather than casting an overly broad net against anything that could possibly be construed as original research.Sławomir Biały (talk) 16:10, 14 March 2011 (UTC)

I have posted an alternative wording on the workshop page. Geometry guy 22:10, 14 March 2011 (UTC)

Teaching and OR

I don't have much to say about the MHP apart from thanking the people who have commented on the arbcom page. I did want to say something related. Lately, after discussion at WT:TECHNICAL and WT:NOR, and looking at WP:NOT, I have been thinking about the underlying issues that lead to these disagreements. I'm only thinking about articles at the advanced undergrad level and beyond here; articles on basic topics are less problematic because there are plenty of low-level references. But there are few references on advanced topics that are accessible to an untrained reader.

Three points:

• There's a tension between making "reference" articles that are primarily useful for people who already know the topic, and making "didactic" articles that help people who don't know the topic learn it. When WP:NOR is interpreted more strictly, that leads us to favor specialists over learners. WP:TECHNICAL, on the other hand, asks us to lean more towards learners, by explaining things in our own words, using analogies, and giving examples. These two policies are naturally opposed to each other.

• WP:NOT has the same opposition inside it, saying both that articles should not be written for specialists and that articles should not be written to teach people about the topic at hand. For example, it says both "A Wikipedia article should not be presented on the assumption that the reader is well versed in the topic's field." and "The purpose of Wikipedia is to present facts, not to teach subject matter.".

• These disagreements go back all the way to the founding of Wikipedia. There was never a time when all the articles "followed policy" after which time the articles began to "violate policy". Instead, the articles have always been in a state of flux, and the policies have never perfectly captured the balance between the goal to be a reference work and the goal to present material to students who are learning it for the first time.

I think that we do a reasonable job at balancing these things in our articles, both overall and in mathematics. My main point is that if we realize that Wikipedia's goals are sometimes in conflict with each other, it can help us find a middle ground. — Carl (CBM · talk) 13:43, 14 March 2011 (UTC)

Let's not forget IAR

Seems to me we are in danger of becoming too rule-obsessed, hierarchical and obsequious over this. If Arbcom produces a ruling which appears to prohibit simple explanatory examples in mathematics articles, then common sense tells us this cannot be what was intended - either Arbcom have mis-worded their statement or we have mis-interpreted it. As explanatory examples obviously improve the encyclopedia, IAR tells us we can use them anyway. At the same time, we can either ask Arbcom to clarify their ruling, or simply drop them a hint by awarding them a trout. Gandalf61 (talk) 15:50, 14 March 2011 (UTC)

This ruling, percolating through WP like phosphorous from a lava chamber (! ;) !), may make it impossible to get articles approved for feature article status, although it probably would have no effect on most articles.  Kiefer.Wolfowitz  (Discussion) 16:00, 14 March 2011 (UTC)

Personally, I don't think it's worth focusing on featured article status anyway. The goals of the FA wikiproject are not necessarily aligned with our goals, but that's OK. Wikipedia can accomodate both. — Carl (CBM · talk) 16:31, 14 March 2011 (UTC)

New wording

In response to comments made by editors from this WikiProject, Arbitrator Elen of the Roads has proposed an alternative wording of the principle, which caused concern here, for other arbitrators to consider and vote upon. You can comment on the proposed principles at Wikipedia_talk:Arbitration/Requests/Case/Monty_Hall_problem/Proposed_decision. Geometry guy 23:42, 14 March 2011 (UTC)

Thanks again for working with this. — Carl (CBM · talk)

The links being said to show Original Research

Regardless of the OR statement of principle that ArbCom may or may not adopt, I am concerned by what the examples of what they are claiming is OR in their statement of facts -- specifically the three claimed examples cited at Wikipedia:Arbitration/Requests/Case/Monty_Hall_problem/Proposed_decision#Article_has_been_subject_of_original_research Article has been subject of original research.

As far as I can see (more detail on the decision talk page here, here, and here), none of these three examples properly constitute original research.

It seems to me that this is no small issue, because the examples Arbcom cite are going to be the most direct operational indication of what they consider to be OR, and how they mean whatever principles they adopt to be interpreted.

I'd welcome second and further opinions on these examples, and whether we think they are OR or not, because the Arbcom members are refusing to engage on the merits of these links; yet are still happily voting for the proposition. Jheald (talk) 09:55, 15 March 2011 (UTC)

This is extremely concerning for me as well. There are thousands of words on that talk page detailing how horrible these words are, and no one except Elen (which is epically wrong bout what is OR and what isn't) seems to bother reading these concerns. Perhaps we should write message on the arbitrator's talk page to address the concerns raised on the talk page about how the all the proposed wordings are utterly horrible. Headbomb {talk / contribs / physics / books} 21:53, 16 March 2011 (UTC)

WP:CALC seems open to improvement

Even some ArbCom members refused to vote on using its exact current wording in their principles (which they are still struggling to formulate in that respect). So, clearly WP:CALC is deficient. I suggest you guys take this opportunity to improve the wording in the policy, so you won't have to put out this kind of fire in the future. All the best, Tijfo098 (talk) 18:27, 16 March 2011 (UTC)

I don't think wp:calc was ever meant to be used as a guideline for quantitative disciplines, rather the sort of routine calculations that one does in history and biography articles for instance. It's obviously insufficient to cover more mathematical articles, but I don't know if it's worth emending the policy, or just clarifying its intended scope: it doesn't exclude things that aren't just pure arithmetic from the more quantitative articles, provided no original research is committed. Sławomir Biały (talk) 19:00, 16 March 2011 (UTC)

Clarifying its scope would be my choice too. We don't want editors to start making inferences in other article claiming that "A implies B" from RS1 "B implies C" from RS2 therefore ... because in social science in particular B from RS1 is often not quite the same as B from RS2. Yes, math and a few closely related formal sciences are an epistemic exception, where inferences like the above are possible without much "OR". But I'm not sure how to say that without being too pretentious or too insulting. The current arbcom wording, something along the lines of: it's fine if it has consensus and nobody asks for citation, seems better, and has the elephant standing for it. -) Tijfo098 (talk) 23:29, 16 March 2011 (UTC)

Latest proposal

There is a new proposed wording. It works for me. Does anyone else have any thoughts about it? Sławomir Biały (talk) 14:11, 17 March 2011 (UTC)

It leaves matrix calculus as a dead article, but that may be for the best. The only sourced notation so far provided is misleading, and (IMHO) unusable for real mathematics. — Arthur Rubin (talk) 15:00, 17 March 2011 (UTC)

The essential thing I think that WP:CALC is missing is a reiteration that the methods must not be novel and it must not support a novel conclusion. Basically it shouldn't support original research. An example illustrating a method or a straightforward indication of how a result is obtained is okay. Saying "it is okay because I have only used standard methods to derive it, it is straightforward mathematics" is an immediate red flag. Dmcq (talk) 15:10, 17 March 2011 (UTC)

I see WP:CALC as a separate entity from original research in mathematics. That's meant to cover routine "everyday" calculations (like in a biography or history article), rather than derivations in quantitative articles. I think the Arbitration Committee has, with this last proposal, finally realized that WP:CALC is ill-suited as a criteria for original research in mathematics. There seems to be some support here for clarifying the intended scope of WP:CALC. Sławomir Biały (talk) 15:17, 17 March 2011 (UTC)

Decision

The decision has been publicized.  Kiefer.Wolfowitz  (Discussion) 00:44, 25 March 2011 (UTC)

MathJax update

Just to let you know, I have updated my mathJax user script to recent version 1.1 of MathJax. Notable change is the support for webfonts via CDN (i.e., no local font installation requirements). Details at the user script documentation page. Feedback welcome. Nageh (talk) 21:37, 23 March 2011 (UTC)

Currently on the Main Page ...

... is John Milnor, who has been awarded the Abel Prize. The article is OK as such, but could obviously be expanded quite a bit. Charles Matthews (talk) 09:43, 25 March 2011 (UTC)

Drinker's paradox

There seems to be a bit of hostility to the newly-listed article Drinker's paradox on the article's discussion page. Various editors are grumbling about deletion, original research, etc. I thought perhaps someone in the project should investigate. Sławomir Biały (talk) 12:16, 25 March 2011 (UTC)

You mean Drinker paradox, right? Most of the opposition seems to be about the title; it is argued that it is not a "paradox". Which, as far as it goes, I would agree with, but it can still be an interesting and possibly notable illustration of some tension between the mathematical tradition of using English to express logical formulae, and what English sentences usually mean in an everyday setting. –Henning Makholm (talk) 12:31, 25 March 2011 (UTC)

This sort of thing is covered by WP:COMMONNAME. This is clearly the common name as it is found in a number of books, which by the way also means it will not be deleted. Whether it is actually a paradox or not is only slightly relevant and certainly would not trump the common name criterion in this case. Lots of people have this funny idea that a title is the article whereas it is simply a way to find the article which is what common name is all about. Dmcq (talk) 13:00, 25 March 2011 (UTC)

Could you add references to some of that number of books to the article? I found it strange that the only source it gives is to Smullyan's book, which according to the article itself called it the "drinking principle" rather than the "drinker paradox". So the title is currently unsourced, which is not good when it has been seen to cause contention. –Henning Makholm (talk) 13:31, 25 March 2011 (UTC)

maybe make a redirect from "drinker principle" too? regards "difference between [propositional logic] and what English sentences usually mean": no. there is no difference there. the grammar, syntax,, AND semantics is exactly the same; it is a perfectly ordinary sentence and the meaning of it is no different whether you address it with formal logic or with "ordinary interpretation". the difference lies in what happens after the sentence has been linguistically parsed and what not converted into formal relations. up to that point nothing has diverged, and at that point you will have the same thing in either case. once in the form of formal relations, however, differences of two types are introduced: 1.) implicit assumptions, and 2.) rules of logical manipulation. regarding 2.), a person untrained in logic is more likely to use the rules given to them by instinct, which are incorrect. well, in a certain sense. they are not designed to be correct, they are designed to be quick, and to be decent approximations, and to the end they serve well. but, fundamentally, there are incorrect. regarding 1.) the sentence as is gives incomplete information, from a logical point of view, eve. do you mean just right now? this round? ever? here logic differs from conventional usage, in filling in this missing information: logic always refers to the instant, unless otherwise explicitly noted. whereas conventionally we fill in this missing information with "...ever...". and this is how one gets to the difference in conclusions. they are both actually correct, it is simply a matter of how you fill in the missing information. Kevin Baas^talk 13:40, 25 March 2011 (UTC)

I suppose in that sense it is a "paradox", because most (if not all) so-called "paradoxes" really just appear as such because there was a missing piece of information that we didn't realize was missing. really when you include the missing information you see that there is no paradox at all. nature simply does not do "paradoxes". Kevin Baas^talk 13:43, 25 March 2011 (UTC)

I just tried out "Drinker paradox" | "Drinker principle" in Google books and scholar and there's two pages of references, some to principle, some to paradox and various ones having a 's after the first word! At least there's paradox ones predating the article, I keep worrying that somebody will stick a wrong title in and that takes over from what people were actually using :) Dmcq (talk) 14:14, 25 March 2011 (UTC)

A paradox is an *apparent* nonsensical or *apparently* false statement, which on careful consideration can be seen to be correct after all. So it seems to me that the drinker paradox is a paradox indeed! Or: it shows that ordinary logic is maybe not so appropriate to logical reasoning in everyday life, as most of us thought. Quite a few paradoxes in mathematics can be seen as symptomatic of inadequacies of the "usual axioms* of present day mathematics. But either way, this is the sort of thing that is usually called a paradox, so I see no problem at all with the nomenclature. Richard Gill (talk) 16:07, 25 March 2011 (UTC)

The term paradox is fairly informal. Any puzzling statement may be called a paradox. Paradoxes are not a big deal, because they can be resolved. A paradox that is a big deal, and that cannot be resolved (easily) is called an antinomy. In order to resolve an antinomy, one has to forsake an important part of one's intellectual heritage. The Barber paradox is resolved by accepting that, well, there just isn't such a village with such a barber. In order to resolve an antinomy, one may have to reject long standing accepted fundamental principles. Over the course of history antinomies eventually become mere paradoxes because our knowledge and language catches up with them.Greg Bard (talk) 16:37, 25 March 2011 (UTC)

Tai's method

Apparently someone rediscovered the trapezoidal rule and managed to get it published. See Tai's method. Just an article about the trapezoidal rule under another name? Or an article about how something weird like that can happen? Either way, is the article in some way worth keeping? Michael Hardy (talk) 03:49, 26 March 2011 (UTC)

It is claimed that more than 100 works cite the article. Michael Hardy (talk) 03:53, 26 March 2011 (UTC)

If the claimed citations do check out, I'd say it is ok to keep it. Also imho this is partially not a math issue, but a question for the applied field/domain in which the "discovery" was made (here biology, medicine I guess). Many apllied sciences have there own names and versions of math theorems and though I can't think of another example on top of my head, I'm pretty sure there is quite a number of such cases. If the name/method in question is well known/established enough (not among the math community but in the domain in which it originated), WP should provide an article or a redirect. Which of the 2 options is better needs to be judged on a case by case basis.--Kmhkmh (talk) 13:21, 26 March 2011 (UTC)

Use of maths symbols in html

The 'Math and logic' symbols in the editor include a load of special symbols. Is it okay to use all these in maths articles? For instance can I say ℝ rather than $\mathbb {R}$ in inline maths? And by the way I don't believe I should bold that as in ℝ, would that be right too? Dmcq (talk) 12:56, 26 March 2011 (UTC)

The WP:MOSMATH, which can always be revisited, recommends the ordinary boldface R to the blackboard bold ℝ, due to the latter being potentially unsupported in some browser configurations. I agree that ℝ is wrong (in fact, I don't think this can be typeset in LaTeX easily either). I really don't like the way inline PNG looks in the middle of running text, so I would avoid using the <math> form in any case. Sławomir Biały (talk) 13:41, 26 March 2011 (UTC)

Well I guess I better raise something at MOSMATH then because it seems silly to have them prompted in the editor and then deprecate them. I think I'd prefer to have the text and the stand along formulae match up better and having those symbols available would help greatly with that but it really needs to be checked. Dmcq (talk) 15:49, 26 March 2011 (UTC)

"Inline" as opposed to "displayed" use of TeX within Wikipedia has always been problematic. Things like the following can happen:

blah blah blah $e^{x^{3}}\,$ blah blah blah.

Obviously the e should be at the same level as the surrounding text and the x³ should be in superscript, but that's not what happens. Also on some browsers, the part in math tags looks comically gigantic. You can also get siuations like this:

There are examples (such as $\int {\frac {\sin x}{x}}\,dx$

) in which etc. etc. etc.

The right parenthesis is on the next line! It also happens with periods, commas, etc. "Displayed" TeX, on the other hand, generally looks quite good:

$\int _{0}^{x}{\frac {\sin u}{u}}\,du.$

So I generally prefer non-TeX notation in an "inline" setting. Michael Hardy (talk) 00:54, 27 March 2011 (UTC)

N-dimensional space

Over at Talk:N-dimensional space we're having a traditional merging discussion. The issue is that these articles (and probably others) all contain redundant material: Space (mathematics), Vector space, Dimension, Dimension (vector space), Basis (linear algebra), Euclidean space, Manifold (mathematics), N-dimensional space. So I thought I'd bring it up here.

My opinion: Each kind of space (vector, Euclidean, manifold, etc.) obviously deserves its own article. Additionally the Space (mathematics) and Dimension articles seem useful as catalogues/overviews. But Dimension (vector space) could be merged into Basis (linear algebra) and/or Vector space, and N-dimensional space could be merged into Space (mathematics) and/or Dimension.

Any comments? Mgnbar (talk) 16:39, 26 March 2011 (UTC)

Special case

Special case is currently a stub article that could use a lot of work, both within the article and in other articles that should link to it. Get busy. Michael Hardy (talk) 00:45, 27 March 2011 (UTC)

QUERY - Aren't changes on a page supposed to be reported????????????????

Hi! I use Wikipedia very often and thought for sure that a policy of yours was to add in a "page history" page that showed any changes to an article and by whom for that page?

I ask because your page on Summation had early in its write-up an image of an example of Induction ( http://upload.wikimedia.org/math/5/d/1/5d1ba66a7aca2c258985399ff22410ef.png ) ... odd that that very image wasn't there just a few days ago for another image that was the exact same equation but in different form.

I looked for the history of why and who changed that image because its odd I been coincidently writing a paper on the example of Induction used of the original image and linking this very page for that image and sending that paper to leading Set Theory specialists and other university piers and that image was very helpfull in dealing with the issues the paper regarded. Now suddenly someone changed the image to a different example of Induction and I find the timing very peculiar. It doesn't change anything about my paper except for it to be easier to understand for anyone needing to see the example of Induction I was using from here but is now changed. I only linked to the page on Summation.

Anyways, how did that image change on the Summation page without anyone ever knowing it happened or why in the pages history?? — Preceding unsigned comment added by G2thef (talk • contribs)

The history of summation is here. The sum you mention was put into the article on April 17, 2010, in exactly the same form it is there now. It is possible that some time in between then and now, someone changed it into the form you prefer and that is was then soon after changed back, but that sort of thing is much harder to find since it would take scanning all the changes to the article rather than simply doing a binary search. —David Eppstein (talk) 20:50, 27 March 2011 (UTC)

The assistance of WikiProject Mathematics requested

In looking over some project work I did for an undergrduate computing degree I noted that the academic supervising me had come up with what he called a 'slew' transform.

I've put a rough note in my userspace at Wikiversity (because of concerns about verifability here) The link is : http://en.wikiversity.org/wiki/User:ShakespeareFan00/Slew_transform

I'd appreciate someone from the WikiProject that understand 3D transformation stuff, to help provide a better citation , or indeed a creative commons licensed proof that will show what's stated is correct.

A 'slew' transform is a transform where 'distances' parrallel to an axes before a 'slew' are preserved, as opposed to a 'shear' where they are not.

I'm also trying to understand how to abstractly define a 'grid'. ( The best definition I can think of for 2D is that a 'grid' is a regular arrangement of points and lines that fills a plane.

For a 'cubic' style of grid, this regular arrangement can be more formally considered as a (Lattice Graph?) formed by the Cartesian product of 2 path graphs, representing lines perpendicular to each other. However, I'm thinking I need to put in some kind of constraint on where the grid points can be placed, and I'm not entirly sure how I specfiy that constraint in an abstract math way...

A 'polar' style of grid is however more complex, being the Cartesian product of a number of path graphs(?) with some kind of cycle graph , ( aka a Prism Graph?). Again some kind of constraint would need to be defined on where grid points can be placed..

And finally Has this sort of thing been done before in a textbook a math noob can understand? Sfan00 IMG (talk) 22:36, 27 March 2011 (UTC)

Regarding your first request, I am not clear exactly what the text on that page is trying to say, but I do not see how the examples can be correct, as they claim to modify the Z or Y axes but do nothing in those directions.

Regarding your second request, I think you want lattice (group).

Also, I suggest you ask these types of questions at Wikipedia:Reference desk/Mathematics in the future. Ozob (talk) 23:23, 27 March 2011 (UTC)

Thanks, re the 'slew' transform, can you leave some thoughts on my Wikiversity talk page ?

The context of the slew transform by the way in the original project was based on being able to convert a 'cubic' lattice to be transformed into a 'heaxagonal' or 'parallelogrammic lattice' one (in 2 dimensions).

Can you suggest a better way to describe what a slew transform appears to be doing, because I'd like to be able to explain it clearly to other people? Sfan00 IMG (talk) 09:52, 28 March 2011 (UTC)

You might find the explanation at Affine transformation#Affine transformation of the plane more helpful. The problem you mention is a special case of what is talked about there. Charles Matthews (talk) 10:17, 28 March 2011 (UTC)

Minimal negation operator

While this unreferenced article looks cool, I can't find anything in google books to support it. WP:OR? Tijfo098 (talk) 05:21, 25 March 2011 (UTC)

The talk page there seem to indicated I'm right (the creator is now indef blocked for something similar.) Tijfo098 (talk) 05:23, 25 March 2011 (UTC)

Looks pretty original to me. — Arthur Rubin (talk) 06:32, 25 March 2011 (UTC)

Wow. A Jon Awbrey article lavishly illustrated by Lipedia. Unfortunately it appears that Peirce never wrote about anything else with a similar name. In that case we might have hit a logic crankery jackpot. Let's take this to AfD. If this was a real notable topic, some mathematician would have noticed through all the years and especially since 11 August. Hans Adler 06:59, 25 March 2011 (UTC)

I just had a look through Awbrey's contributions and the following just strike me as being iffy. Some are redirects, others are just bits of Pierce's writings that probably could be a paragraph somewhere else I think. Things like boolean domain I just cant see the point of a separate article from boolean but logical matrix I can see is probably okay. Others like sign relation I just plain don't understand. Semeiotic seems to be some variant spelling of Semiotic by Charles Saunders Pierce.

• Ampheck
• Boolean domain
• Boolean-valued function
• Categorical set theory
• Comprehension (logic)
• Continuous predicate
• Descriptive science
• Entitative graph
• Finitary boolean function
• Formal sciences
• Hypostatic abstraction
• Hypostatic object
• Logic of Relatives (1870)
• Logic of Relatives (1883)
• Logic of information
• Logic of relatives
• Logical graph
• Logical matrix
• Multigrade operator
• Normative science
• Parametric operator
• Pragmatic maxim
• Prescisive abstraction
• Projection (mathematics)
• Projection (set theory)
• Relation construction
• Relation reduction
• Relative term
• Semeiotic
• Semiotic information theory
• Sign relation
• Sole sufficient operator
• Zeroth-order logic

I guess most of these are perfectly okay but is there some that even someone familiar with Charles Saunders Pierce isn't familiar with or thinks is unnecessary? Dmcq (talk) 18:50, 25 March 2011 (UTC)

I recognize most of these terms as being used by Peirce in his logical writings. Peirce's preferred spelling "semiotic" as "semeiotic", as you suspected.

I have only an amateur understanding of his logic. Peirce had an anti-Fisherian approach to terminology, where he thought it bad sport to use an existing word for a new idea (and would have denounced the Fisherian vice of switching between the two, e.g. "information", etc.). This explains why Peirce introduced so much novel terminology, and why he was less successful as a salesman than Fisher.  Kiefer.Wolfowitz  (Discussion) 20:47, 26 March 2011 (UTC)

Logical graph is a nebulous article that could use work. I think the term existential graph has been used more recently, and perhaps even by Pierce. Tijfo098 (talk) 04:09, 30 March 2011 (UTC)

Jacob Barnett

There is a deletion discussion under the auspices of our project that could benefit from its input. Sławomir Biały (talk) 00:21, 31 March 2011 (UTC)