User talk:R.e.b./Archive 4

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Dickson polynomial and Cartan subalgebra questions

Howdy, I think you've already answered my question (Talk:Dickson polynomial#Schur conjecture reference) on Dickson polynomials, but I wanted to make sure. I am not terribly familiar with these sorts of objects, and so it was not entirely clear to me exactly when they were equivalent to Chebyshev polynomials. I think you explicitly say they are equivalent over the complexes, but I think some people might believe the article is implying they are equivalent over the rationals. I think they are not equivalent over the rationals, but the Schur conjecture part seems to suggest they are. Basically, I find the article confusing, but I cannot say whether it is the text of the article or my dim mind which is the cause.

I had another question (Talk:Cartan subalgebra#Maximal abelian subalgebras) about maximal abelian subalgebras that are not cartan subalgebras. Your recent sl(2n) example indirectly proves they exist, but I think it might be nice to give one explicitly. I tried to fill in a little of the detail of the argument, but I think all I showed was that an even larger abelian subalgebra existed. I think this is a standard remark explained perhaps in Jacobson's text, but I don't have it handy. Basically, I think the example can be improved with only a minor change, but I fear I don't know how to do it. JackSchmidt (talk) 18:34, 11 February 2008 (UTC)

Dickson polynomials are more or less the same as Chebyshev ones whenever the field has enough square roots (and contains 1/2), but as you say they are not equivalent over the rationals. I have no plans to add anything more to this (rather obscure) topic; feel free to make the article clearer.
The larger abelian algebra you found is in gl2n (and is in fact maximal in gl2n) but is not in sl2n, at least not when the field has characteristic 0, as sl does not contain the identity matrix. R.e.b. (talk) 19:06, 11 February 2008 (UTC)
Thanks! Your correction to Cartan subalgebra is exactly what I was looking for. Sorry, I am used to working in (finite) Lie groups, and forgot I was looking for trace zero not determinant one. I don't know how to fix Dickson polynomial. I just marked the statement with {{fact}} and a comment. I suspect the explanation is simple, and there are lots of wikipedians who know more about polynomial families than I do. JackSchmidt (talk) 19:20, 11 February 2008 (UTC)

Thanks for Bad group fix

Merging the definition into the article where it is relevant whether they exist is a very clean solution. Thanks for taking care of it; all I know about Morely rank is it clutters my google searches for finite simple groups. I'll let the bad group author know the prod was changed to a redirect. JackSchmidt (talk) 05:29, 15 February 2008 (UTC)

Colleague request!

Dear colleague , please tell me how you got the formula

(This is an emergent request )

please answer here!

Thank you. —Preceding unsigned comment added by (talk) 20:18, 16 February 2008 (UTC)

I just happened to notice that the formula for Bn in the article was very similar to the usual explicit formula for Chebyshev polynomials. If you want to know how to prove it, it follows easily from the explicit formulas in Abramowitz and Stegun. R.e.b. (talk) 20:38, 16 February 2008 (UTC)

Colleague gratefulness!

Thank you R.e.b.

If only you can help us finding a 2-order differential equation for these polynomials as you did to the explicit expression above!! We can provide basical equations.. Thanks

P.S. Dear colleague can you help us writng this letter : B with the sign ~ on it?? (which is pronounced B-Tilda, in french?) Thank you for help and understanding.

You could find a 2nd order differential equation for Bn by expressing it as
Differentiating twice expresses Bn and its first two derivatives as linear combinations of derivatives of the Chebyshev polynomials. The differential equation of the Chebyshev polynomial gives two relations between Chebyshev polynomials and their first 3 derivatives. This gives 5 linear equations in Bn and its first two derivatives and Tn and its first 3 derivatives. Eliminating Tn and its first 3 derivatives from these equations should give a second order differential equation for Bn.
The differential equation you get like this is probably rather complicated. You can instead write Bn as the sum 4Un(x/2)−6Tn(x/2) for n>0, both of which satisfy well known differential equations.
<math>\tilde B_n</math> produces . R.e.b. (talk) 19:39, 17 February 2008 (UTC)

Colleague gratefulness and thanks!

This is great!

Thank you Sir! —Preceding unsigned comment added by (talk) 22:47, 17 February 2008 (UTC)

Stability theory

Hello R.e.b., I see you have been active around stability theory. I haven't got the time to finish my draft article User:Hans_Adler/Stability_spectrum right now, but since you have just created a redlink for stability spectrum I thought I should mention its existence to avoid unnecessary duplication. You are very welcome to edit the draft, and to move it to article space whenever you feel it makes sense. --Hans Adler (talk) 18:20, 19 February 2008 (UTC)

OK; your draft looks fine apart from not yet having references, so I'll probably add these and move it into article space in a few days if you don't do so first. R.e.b. (talk) 18:52, 19 February 2008 (UTC)

Emergent Scientific request

Dear Colleague: you said : ...The differential equation of the Chebyshev polynomial gives two relations between Chebyshev polynomials and their first 3 derivatives..

We found only one differential equation (for each kind):


Please can you write here the relations between Chebyshev polynomials and their first 3 derivatives ???

Thank you for patience !! —Preceding unsigned comment added by (talk) 19:06, 19 February 2008 (UTC)

If you differentiate these differential equations you get extra linear relations between y', y'', and y''' R.e.b. (talk) 19:12, 19 February 2008 (UTC)

Emergent Scientific request, Thanks !!

Thank you for help! Can you provide links to these items?? —Preceding unsigned comment added by (talk) 11:52, 20 February 2008 (UTC)

Links to which items?R.e.b. (talk) 15:21, 20 February 2008 (UTC)

Expressions of Chebychev Polynomials.... —Preceding unsigned comment added by (talk) 15:40, 20 February 2008 (UTC)

This link and the following pages gives most of the properties of Chebyshev polynomials. There is also the article Chebyshev polynomials, which you probably know about. R.e.b. (talk) 15:49, 20 February 2008 (UTC)

Thanks !! we won't bother you more !!

Sir, we bothered you enough. We must not abuse .. Now, thanks to you we have a very intresting paper-project. We would add acknowledgment for you in this paper (or send it to you for eventual pre-revision and hints, and you will see the magnitude of your help!!), would you mind tell us if you agree?? We are waiting for a favorable answer.

No problem. There is no need to acknowledge me in your paper. R.e.b. (talk) 01:58, 22 February 2008 (UTC)

back-and-forth method

In this edit you said that in "more complicated situations" this can fail to be bijective. In the case actually considered, would it always be bijective? E.g. if the two sets are the rationals in their usual ordering and the real algebraic numbers in their usual order, would it always be bijective? I'd have thought not. In fact, I'd guess it would depend on which enumerations are chosen. I've never actually thought this through. Michael Hardy (talk) 03:39, 23 February 2008 (UTC)

I think it is indeed always bijective in the case you gave even if you only use step 1. This does not depend on the orders you choose, or whether one set is real algebraic numbers. (Though my edit was carefully phrased so it is still correct even if I made a mistake about this...) You need both directions in more complicated cases, such as showing two equivalent countable atomic models of a theory are isomorphic. If you want to modify your example so both directions are needed, then take a random element in the image satisfying the needed conditions instead of the first element. R.e.b. (talk) 04:22, 23 February 2008 (UTC)

You seem at least a little bit uncertain. Maybe the answers to these questions should eventually be made explicit in the article with any relevant proofs or counterexamples. After your edit linked to above, I changed it so that instead of saying in more complicated cases it might fail, it said in some more complicated cases it would fail. "Might" could be taken to imply uncertainty about whether there are any such cases. Michael Hardy (talk) 18:25, 23 February 2008 (UTC)

I changed your proof slightly so that "back and forth" is really needed, and added a note explaining this. R.e.b. (talk) 18:50, 23 February 2008 (UTC)

Boubaker polynomials?

I noticed you comments at talk:Boubaker polynomials. Do you have any particular opinion that would be relevant at Wikipedia:Articles for deletion/Boubaker polynomials (2nd nomination)?

I don't (yet?) have an opinion on whether the article should be kept, but I find some of the arguments purporting to support deletion somewhat disturbing, and I've commented accordingly on the deletion page. Michael Hardy (talk) 22:32, 27 February 2008 (UTC)

It looks like a rather strange discussion. I dont have anything useful to say about these polynomials (beyond my comment on the talk page that they are a trivial variation of Chebyshev polynomials). I had some questions about them on my talk page (see above) from someone who seems to be working on them. R.e.b. (talk) 23:52, 27 February 2008 (UTC)

Commutative von Neumann regular rings

Howdy, I changed the "Commutative vN regular if and only if subring of fields" to "only if", but I think more is true. It is not completely iff, since an integral domain that is not a field is never vN regular (Frac(D)/D is not flat). However, the point really is that these rings are special subrings of infinite direct products of fields that act very much like direct products of fields. I couldn't find a reference, but I think it was something like "subrings such that the projection map for each factor is surjective". So "1 + Sum(K_i)" as a subring of "Prod(K_i)" should be vN regular, and should be something similar to the "ring of compact operators with 1 adjoined".

I tend to stick with finite or at least very special rings these days, so I could easily be wrong. I figured if you had the reference at hand, it would be easy to fix. Otherwise I'll check Goodearl's text sometime this week. JackSchmidt (talk) 18:09, 27 February 2008 (UTC)

I'm at least a little wrong. Every von Neumann regular ring is semiprimitive, and the commuative semiprimitive rings are the ones I described (subdirect products of fields). So there are some subdirect products of fields that are not von Neumann regular. Hopefully the "reduced and Krull dimension 0" characterisation is useful enough. Please let me know if you find a nice if and only if along the lines of subrings of fields. JackSchmidt (talk) 18:34, 27 February 2008 (UTC)

You are right; I was not paying attention when I wrote that, and meant to say "subring of a product of fields that is closed under taking quasi-inverses". R.e.b. (talk) 19:43, 27 February 2008 (UTC)

Thanks for fixing this, and for the steady stream of improvements to the math articles. I enjoy checking my watchlist, and reading your new additions every few days. It is like an eclectic course on all things interesting. You've even convinced me model theory is worth my time to learn, though it might be a few years before I need more than wikipedia already has on the subject. Thanks again, JackSchmidt (talk) 05:51, 3 March 2008 (UTC)

Model companion

A tag has been placed on Model companion, requesting that it be speedily deleted from Wikipedia. This has been done under the criteria for speedy deletion, because it is a redirect to a nonexistent page.

If you can fix this redirect to point to an existing Wikipedia page, please do so and remove the speedy deletion tag. However, please do not remove the speedy deletion tag unless you also fix the redirect. Feel free to leave a note on my talk page if you have any questions about this. -WarthogDemon 19:07, 29 February 2008 (UTC)


I was fulfilling an editprotected request, where the author had made a one-character error that nonetheless made a huge mess. I hope I've now fixed the problem - let me know if there are any outstanding errors and I'll revert and let them work out what's wrong. Happymelon 15:56, 3 March 2008 (UTC)

For the caching issue, see WP:BYC#Server cache: it's slightly quicker to purge than make a trivial edit. Geometry guy 17:10, 3 March 2008 (UTC)

Sync of the ordinal analysis and large countable ordinal articles

Hi! I agree with the move of creating the article on ordinal analysis, however I draw your attention to the existence of the article on large countable ordinals: it would be nice to keep them from overlapping too much, by moving material from one to the other, and by adding abundant links. I did a bit of that, I'll let you judge of what else needs to be done. (Unfortunately we have quite a mess of ordinal-related articles sharing much of the same content without clear relations between them.) --Gro-Tsen (talk) 19:06, 4 March 2008 (UTC)

Thanks. I already know about large countable ordinals (having written some of it in the days before it was split off). I was wondering whether to give Feferman-Schutte and Bachmann-Howard ordinals their own articles, but havn't yet decided whether this would make the ordinal mess better or worse. R.e.b. (talk) 19:35, 4 March 2008 (UTC)


Hello. Do you know anything about Troy Raeder? It has been suggested that the article is a hoax. Michael Hardy (talk) 15:59, 5 March 2008 (UTC)

Yes, its a hoax. R.e.b. (talk) 16:01, 5 March 2008 (UTC)
...and I now see that the person who created it has no other edits. Michael Hardy (talk) 16:14, 5 March 2008 (UTC)

Iwasawa decomposition and unipotent

Howdy, I wanted to salvage NBarth's edit, but I don't know enough math to handle part of it. I think it might be nice to phrase the example also in a "basis-free way", so that one could link to unipotent. Basically, the factorization is KAN, where K is a ???, A is a "maximal torus", and N is a "maximal unipotent subgroup" or "the unipotent radical of the normalizer of A" or something. K seems a little like a Weyl group, but I don't think it is (seems to contain it as a small subgroup). Is there something like this that is true? Maybe more specific questions are easier:

  • Is A a maximal torus?
  • Does A always normalize N?
  • Is N always the unipotent radical of the normalizer of A?
  • Is K a "Cartan subgroup"?

Thanks for any help, and no worries if they don't sound sane to answer. I'm still trying to learn this material, so there is no reason at all to think my questions are on target. JackSchmidt (talk) 00:54, 9 March 2008 (UTC)

  • A is not a maximal torus, but is a connected component of a maximal split torus (where "torus" is used in the algebraic group sense, not the Lie group sense).
  • Yes, A normalizes N
  • N is almost never the unipotent radical of the normalizer of A.
  • K is a maximal compact subgroup, and has little to do with Cartan subgroups.

These apply if G is well behaved (connected, semisimple, etc); I'd have to think more carefully about the general case. R.e.b. (talk) 01:10, 9 March 2008 (UTC)

Re Request for expert help

Request for expert help

The new article Landau-Lifshitz equation needs some expert help in expanding it; your comments suggest you might know about this topic.

As you have probably figured out by now, it is a complete waste of your time to argue with rude and ignorant editors about topics they do not understand. Wikipedia has an unlimited supply of such editors, and it is best just to ignore them. R.e.b. (talk) 19:28, 25 March 2008 (UTC)

  • Thanks for the offer, and the consoling remarks, but I am afraid I will not have the time to help on this. In fact - although it is obviously with good intentions, the equation that you have identified as the Landau-Lifschitz equation is not the right one. There are more than one equations going under this name. The ones being referred to in the discussion in hand are PDE's with one time and either one, or two space variables. This one is an ODE, with only time, an external magnetic field, and no space variables. (i.e. the PDE's represent a field theory of magnetism; these ODE's just represent the motion of a single spinning, charged object in an external magnetic field. A different problem.)

If you would like a good source for the correct L.L. equations, try looking up the book: L.D. Faddeev, L. A. Takhtajan (1987). Hamiltonian Methods in the Theory of Solitons. Addison-Wesley. ISBN 0387155791, ISBN 978-0387155791. R_Physicist (talk) 19:58, 25 March 2008 (UTC)

Thanks; I hadn't realized that there was more than 1 equation called this. R.e.b. (talk) 03:31, 26 March 2008 (UTC)
  • Thanks for creating the page for LLE. LLE or in other words LL model is a fundamental basic of the classical theory of magnetism. I added some information to your page. Ngn (talk) 17:06, 26 March 2008 (UTC)

Thanks for your additions; it seems there are even more of these equations than I realized. Do you know any good references for the 1+2 dimensional case?

If you get a wikipedia account it would be much easier for other editors to send you messages. R.e.b. (talk) 18:11, 26 March 2008 (UTC)

  • Now it is OK. Please see my page: Barstaw. Barstaw (talk) 18:48, 26 March 2008 (UTC)
  • Here time is 01:00 a.m. So may be tommorrow I return to you. Barstaw (talk) 19:01, 26 March 2008 (UTC)

Speedy deletion of EqWorld

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A tag has been placed on EqWorld requesting that it be speedily deleted from Wikipedia. This has been done under section A7 of the criteria for speedy deletion, because the article appears to be about web content, but it does not indicate how or why the subject is notable: that is, why an article about that subject should be included in an encyclopedia. Under the criteria for speedy deletion, articles that do not indicate the subject's importance or significance may be deleted at any time. Please see the guidelines for what is generally accepted as notable, as well as our subject-specific notability guideline for web content.

If you think that this notice was placed here in error, you may contest the deletion by adding {{hangon}} to the top of the page (just below the existing speedy deletion or "db" tag), coupled with adding a note on the talk page explaining your position, but be aware that once tagged for speedy deletion, if the article meets the criterion it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the article that would would render it more in conformance with Wikipedia's policies and guidelines. Lastly, please note that if the article does get deleted, you can contact one of these admins to request that a copy be emailed to you. Wisdom89 (T / C) 01:25, 28 March 2008 (UTC)

Davey–Stewartson equation

The mention of "finite depth" in Davey–Stewartson equation makes me wonder if this article and shallow water equations should link to each other? (I've really only glanced at the former article for a few seconds, so maybe this doesn't make sense.) Michael Hardy (talk) 22:08, 31 March 2008 (UTC)

I dont know. They dont seem all that close mathematically, though they are both describing waves in fluids. Maybe just add them both to some category about waves in fluids (there seem to be loads of different differential equations related to this). R.e.b. (talk) 22:26, 31 March 2008 (UTC)

April Fool's Day DYK

Updated DYK query On 1 April, 2008, Did you know? was updated with a fact from the article Wiener sausage, which you created or substantially expanded. If you know of another interesting fact from a recently created article, then please suggest it on the Did you know? talk page.

Thank you for your part in the successful event! I really enjoyed seeing a math article on DYK, as math was my major at college! --Royalbroil 13:20, 1 April 2008 (UTC)

Conway groups

Is it settled that there are exactly 22 conjugacy classes of maximal subgroups of Co1? Griess (1998) was not certain at the time. Scott Tillinghast, Houston TX (talk) 07:31, 2 April 2008 (UTC)

No, but it is settled that a reliable source (Robert Wilson) currently claims that there are exactly 22 conjugacy classes, which is good enough for wikipedia. R.e.b. (talk) 14:58, 2 April 2008 (UTC)
Is there a simple way to handle a reliable source being wrong? Image:Finitesubgroups.svg is a copy of the diagram on page 247 of Ronan's book on Symmetry and the Monster, ISBN 9780192807229. However, it has at least two errors. How should these be pointed out?
In case someone wants to check (my previous talk posts were blanked): The first error is clear: the diagram does not indicate that the Mathieu group on 11 points is a (maximal) subgroup of the O'Nan simple group (this is an error in the book). The second error is that either the line indicating M22 as a subquotient of HN is missing (this is an error in the book), or the line indicating M23 as a subquotient of Fi23 should be removed (this fixes an error in the caption on wikipedia, which claims all lines represent subgroup containment). JackSchmidt (talk) 15:16, 2 April 2008 (UTC)
You could try sending a note to whoever made the image, or put a warning where it is used, or if you are feeling really ambitious you could redraw it correctly. (Or you could adopt my solution of not worrying too much about minor errors on the grounds that wikipedia has so many major errors.) R.e.b. (talk) 16:07, 2 April 2008 (UTC)

I have used Robert Wilson's websites often and I find at times there is information that is incomplete. For example there are presentations of finite simple groups that alone would define infinite groups.

I want to find out more about the history of research on the structure of the Conway groups. Scott Tillinghast, Houston TX (talk) 16:41, 2 April 2008 (UTC)

For the history, try the book Thompson, Thomas M. "From error-correcting codes through sphere packings to simple groups." Carus Mathematical Monographs, 21. Mathematical Association of America, Washington, DC, 1983. xiv+228 pp. ISBN 0-88385-023-0 R.e.b. (talk) 16:52, 2 April 2008 (UTC)

Thank you. I have a copy of Thompson's Carus Monograph.

Now, about Ronan's diagram. A complete diagram could be pretty cluttered. For example, the Monster is shown as directly containing 3 sporadic groups: Fischer 24, the Baby Monster, Conway 1. I just looked at the list of maximal subgroups on Robert A. Wilson's website, and I count 7 more. Of the 3, only Conway 1 is actually a subgroup and the other 2 are subquotients.

I have checked the lines between the 3 Fischer groups and 3 Mathieu groups against version 2 of Robert A. Wilson's website and they are correct at least as subquotients. For some reason version 3 does not list maximal subgroups of Fischer 24'.

The distinction between subgroups and subquotients is essential to serious study of simple groups, but I doubt it can be clearly incorporated into the diagram. For example, Hall-Janko is a subgroup both of Suzuki and Conway 1, but Suzuki is just a subquotient in Conway 1.

So I would not try to perfect the diagram, but make a cautionary note about its limitations. Scott Tillinghast, Houston TX (talk) 19:43, 2 April 2008 (UTC)

List of non-linear partial differential equations

(The comments below are replies to a comment here that was later removed by its writer)

Laws and wikipedia articles are like sausages. It's better not to see them being made. Bismarck (talk) 15:49, 2 April 2008 (UTC)
Wikipedia:Lists defines three purposes (Information, Navigation, Development) for lists. A list of nonlinear PDES could therefore be criticised if it failed all of these. But this is not so likely. In particular the Navigation purpose is fundamental, for people with a general interest in a topic. Charles Matthews (talk) 19:46, 2 April 2008 (UTC)

"First of all, the title is such a catch-all expression" That does not seem like a valid objection. List of Germans could be criticized in the same way. But of course it is not intended to list all Germans, but only those considered notable enough to be the topic of a Wikipedia article. The same thing applies here. Michael Hardy (talk) 21:11, 2 April 2008 (UTC)

Above, the anonymous comentator wrote:

"Integrability" has a very specific meaning. (Please look up the article on Integrable systems for a discussion of what this is. That article remains, for the moment, one of the more reliable ones in Wilkipedia

I just looked at that article. It never attempts to explain what that precise meaning is. Michael Hardy (talk) 21:18, 2 April 2008 (UTC) ....OK, I see that at one point it gives a terse definition of one of the kinds of integrability. Not really the more leisurely explanation such as one might hope to see. Michael Hardy (talk) 21:27, 2 April 2008 (UTC)

In response to Michael Hardy: Please have a more careful look at it (some improvements have since been made). It gives a precise definition of each of the notions of "integrability" listed: 1) Frobenius integrability (differential systems) 2) Liouville integrability (Hamiltonian systems) 3) Superintegrability and partial integrability (Hamiltonian systems). It furthermore discusses how this expression is used in more general dynamical systems, as well as in "quantum integrable systems" where, as is known, no good definition really exists. It also explains how the notion of "canonical transformation to linearizing variables" extends to the case of PDE's, through inverse spectral methods. The details are referred to the pages in which these various concepts are individually treated, with links. (talk) 12:40, 4 April 2008 (UTC)(alias "R Physicist")

To R.e.b.: I see that you took my comments to heart, though not quite in the way I had suggested. Fair enough; there is also room for "formularies" - this is the way that Ramanujan learned mathematics, after all. I wish you good luck in keeping it "on track" through the sausage factory. (talk) 00:14, 3 April 2008 (UTC) (alias "R Physicist")

R.e.b., the article Clairaut equation says that it is an ordinary differential equation. Looks like we need to disambiguate. Giftlite (talk) 22:12, 8 April 2008 (UTC)

No need to disambig: the ODE in the article is the 1-dim case of the PDE. R.e.b. (talk) 01:31, 9 April 2008 (UTC)

At the moment "Cauchy momentum" and "Navier-Stokes" are essentially the same. It appears to me that in Navier-Stokes equation the equations are interpreted too general as compared to the common notion, i.e. that Navier-Stokes is most often considered to be confined to a Newtonian viscous model for the shear stress tensor. Crowsnest (talk) 02:10, 9 April 2008 (UTC)

You are right; I was just feeling too lazy to write out the usual NS equations and just cut and pasted these

as a stopgap. Feel free to tidy them up. R.e.b. (talk) 03:33, 9 April 2008 (UTC)

Dispersive partial differential equation

Thanks for removing my silly remark about different wavelengths having different frequencies on dispersive partial differential equation. Crowsnest (talk) 19:21, 5 April 2008 (UTC)

No problem. I assumed it was a Thinko. R.e.b. (talk) 01:14, 6 April 2008 (UTC)

P.S. about LNLPDE

Someone (actually, the above user) wrote to say he (or she) thought it was a bad idea to remove the comments I had made at the discussion page, even after they had been attended to. I recalled your Bismarck sausages remark, and replied that I prefer to wash the utensils while cooking the meal, rather than later. If you find my suggestions at all helpful, I will perhaps continue (if there seems anything worthwhile saying) but, if you don't mind, I'll do it henceforth in this location, rather than at the article's "talk" page. (I prefer, as you probably understand, having 1 on 1 exchanges rather than "public ones" on matters like this, but I see from some of the above that anyone viewing such individual exchanges feels entitled to enter their 2c worth in any case.) I hope that you do not object to my deleting my own remarks though, once they seem to have become outdated? (talk) —Preceding comment was added at 19:12, 6 April 2008 (UTC)

I found your comments and suggestions helpful and used most of them (as you presumably noticed). I don't mind whether you leave them here or on the article page. There is no such thing as 1-on-1 privacy on wikipedia: anyone can (and does) read and join in conversations on editor talk pages. (If you ever need to send a private message, you can use the "E-mail this user" link on the left.) For non-controversial subjects I don't see that it matters all that much whether or not old comments are deleted; the main disadvantages of deleting comments are that it can confuse other users, and may trigger wikipedia's anti-vandal defenses. The custom on wikipedia is that talk page comments are not usually deleted except for serious reasons (such as comments that reveal private personal information); instead out-of-date comments are sometimes struck through like this, which makes it easier to follow old conversations. R.e.b. (talk) 21:06, 6 April 2008 (UTC)
The thing in question was whether one may delete one's own outdated comments. I feel there is very little in such intermediate exchanges, on things that have already been dealt with satisfactorily, that is worth preserving for future reference, so I prefer to just delete anything that I have written that has already been dealt with adequately. The user who suggested switching such comments then to your "talk" page thought that, as long as it is limited to deleting one's own old remarks, it is reasonable, but less so on the article's "talk" page. I have no strong thoughts on this, and had placed the remarks on the articles "talk" page because they were just suggestions or comments about the article. I prefer to delete old comments that are no longer an issue in order not to clutter current things with old things that have already been resolved. (talk) 22:17, 6 April 2008 (UTC)
Another option is to use a bot to archive old comments automatically. To see how to do this, look at the top of the source of my talk page, or see User:MiszaBot/Archive_HowTo. R.e.b. (talk) 23:03, 6 April 2008 (UTC)

Emmy Noether

Everything in the mainspace article exists on my drawing board as well. I just want to get the basics of the math part done, then move it over to the mainspace to hammer out the details. I just need 3 paragraphs or so. – Scartol • Tok 11:09, 15 April 2008 (UTC)

Okay, I made the tweaks necessary for now and moved it into the mainspace. Sorry for the confusion! – Scartol • Tok 15:44, 15 April 2008 (UTC)
Barnstar-atom3.png The E=mc² Barnstar
For inserting oodles of relevant and (I assume) insightful mathematical information into Emmy Noether, I award you this science-dealie barnstar. This numerical illiterate greatly appreciates your generous assistance. – Scartol • Tok 01:47, 17 April 2008 (UTC)

Abbreviations of journal names

I see you're editing the Harvard citations template:

At Wikipedia talk:Citing sources I've attempted a sort of case against the conventional practice of abbreviating journal names. Have you seen that? Do you have any views on this? Michael Hardy (talk) 02:02, 20 April 2008 (UTC)

I usually abbreviate journal names because I am cut-and-pasting them from some other source, and am too lazy to expand them (it's tiresome enough formatting them correctly without this extra burden). It might be slightly better to have journal names in full if there is no standard abbreviation but I think it will be hard to persuade anyone to do this rather tedious job. Probably someone will write a bot to do this sooner or later, so I would just wait. R.e.b. (talk) 04:06, 20 April 2008 (UTC)
I'm happy to fix any math references that need fixing. I think Ann Math and TransAm are pretty standard, and I take it these are in the template talk namespace, so don't need real fixing? I definitely agree that it is better to give full journal names, but this is just one of hundreds of cleanup tasks.
One reason I am happy to fix references is because it is so *easy*. I use zeteo and MathSciNet. First find the article at MathSci, export as BibTeX, then paste the bibtex into zeteo, fix anything missing (like DOI or online URL or wikilink for author), and then zeteo formats the {{citation}} for you. If you need the same article again later, it is easy to look it up.
On the other hand, I am all for division of labor. I would prefer R.e.b. spend his time writing well referenced articles, and leave expanding abbreviations to bots or wiki gnomes like myself. I enjoy checking and formatting references as it a good excuse to read them. JackSchmidt (talk) 04:32, 20 April 2008 (UTC)

Maybe Jakob Scholbach would be willing to set up zeteo so it automatically expands journal abbreviations. R.e.b. (talk) 14:46, 20 April 2008 (UTC)

Ann. of Math.
Annals of Mathematics  
Language English
ISSN 0003-486X
Hi. Here is the reply to your post at my talk page: What exactly do you want me to do? At this time, zeteo does have a field for an abbreviated journal name. If somebody happens to add an item with journal name "Ann. of Math. (2)", for example, it will instead use the full name "Annals of Mathematics. Second Series". So this should already work. On the other hand, what I wanted to do, is adding all journals (also mentioned in the thread) to the database including their ISSNs, so that people don't have to add the stuff. But there are also many misspelled names etc. Does this help? I'm currently also thinking of other means, such as scanning all WP articles for these journal templates such as so that we can get all information somewhere available. Jakob.scholbach (talk) 13:40, 21 April 2008 (UTC)
As an addendum: the abbreviated journal names usually come from MathSciNet bibtex items. Most entries in the db are, however, the result of parsing the citation templates present in WP articles (math, and partly physics, I'm just doing physics). So, most journals don't feature an abbreaviated name. As I said, I will try to fill up the db with all math journals, taken from this list. But this list is probably far from exhaustive. Jakob.scholbach (talk) 14:07, 21 April 2008 (UTC)


Greetings. E's skills of diplomacy are not what they used to be, as evidenced by my user page. (talk) 19:12, 29 May 2008 (UTC)

Answer not a fool according to his (or her) folly, lest thou also be like unto him (or her). R.e.b. (talk) 21:16, 29 May 2008 (UTC)
Indeed. In hindsight, some stones are better left unturned. (talk) 15:44, 1 June 2008 (UTC)

Codegrees of complex reflections groups?

Regarding this very useful page Complex reflection group, any chance that someone will add in to the table a new column containing the also very useful "codegrees" of the irreducible complex reflection groups, available at the end of this article by Broue, Malle, Rouquier. -- Vic Reiner, Univ. of Minnesota (talk) 20:03, 29 May 2008 (UTC)

I've added this reference to the page. The codegrees would indeed be good to add to the table, but I'm too lazy to do this now. This being wikipedia, there is nothing to stop you adding them yourself. R.e.b. (talk) 21:16, 29 May 2008 (UTC)

Nothing stopping me except underconfidence about my Wiki skills, so I'm very grateful that you did add them-- thank you! Vic R. (talk) 7:36, 3 June 2008


I vaguely seem to recall that you may have worked on one or more articles related to the topic of this one: Wikipedia:Articles for deletion/Anti-knot. I could be wrong. I suspect that this non-existence result already appears in more than one article. Can you shed any light? Michael Hardy (talk) 06:16, 31 May 2008 (UTC)

No, I havn't worked on this article, which as C S says seems to be little more than some hopelessly garbled attempts to prove a standard result. Come to think of it, I did indeed write an article related to this: you may be thinking of Mazur swindle. R.e.b. (talk) 00:06, 2 June 2008 (UTC)

That's the one I had in mind. If you hadn't identified it, I don't know if I'd ever have found it. I'm thinking about whether the title should redirect to some other article, and I couldn't clearly remember what I had seen. Thanks. Michael Hardy (talk) 00:53, 2 June 2008 (UTC)

Problem of Apollonius

Hi R.e.b.!

We're preparing the problem of Apollonius for FA, and we need a reference for the connection to the circle method, which you added on May 7th to the Applications section? If you could come up with one, that's be great! More generally, if you had any suggestions for the article, I'd appreciate it very much. Thanks muchly, Willow (talk) 09:34, 31 May 2008 (UTC)

The example I added is somewhat bogus, as it only uses the easy special case when the three initial circles are tangent, so maybe the honest thing to do is just delete it. If you still want to keep it, anything about the circle method would do as a reference; for example, sections 5.5 and 5.6 of
Apostol, Tom M. (1990), Modular functions and Dirichlet series in number theory (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-97127-8 
The article Ford circle has a nice picture of what is going on. R.e.b. (talk) 00:22, 2 June 2008 (UTC)

Do you have a spare moment?

Hello. Although it is probably rather irksome, if you are at a loose end could you please look over my recent spherical function article to check for obvious errors or omissions. I have restricted attention to positive-definite ones because these are the ones occurring in the unitary representation theory, but there could easily be extra notes added to cover the general case. I could quite easily have made an error somewhere. Regards to all. (talk) 17:39, 17 June 2008 (UTC)

I cant offhand see anything to add to the math; it looks good. A few minor formatting suggestions:
  • Some of the displayed formulas are a bit small: you can fix this using \displaystyle
  • It's less work to format the references if you use zeteo: what you do is ask mathscinet to output the refernces in bibtex format, copy and paste this into zeteo, which automatically formats everything as a citation template.
  • If you use the harvnb template, as in <ref>{{harvnb|Dieudonne|1900}}</ref>, it creates a link to the reference.
  • I reserve judgement on the weird orange formulas. R.e.b. (talk) 18:22, 17 June 2008 (UTC)
At the moment the article only covers the case of spherical functions with respect to a maximal compact subgroup. One could also say something about the case when G itself is compact (or even finite). R.e.b. (talk) 18:36, 17 June 2008 (UTC)
Thanks. Helgason treats the Euclidean and compact case, which are easier. There is also the p-adic case. I would have liked to put the key formulas in Serge Lang boxes but didn't know how. Do you know? It is doubtless against the mathematics MOS. (talk) 19:55, 17 June 2008 (UTC)

R.e.b. (talk) 20:20, 17 June 2008 (UTC)

That's exactly what I need. Thanks, Mathsci (talk) 22:32, 17 June 2008 (UTC)

Locally finite, direct product, direct sum

Thanks for the correction. Robinson's book uses direct product to mean the restricted direct product, a.k.a. the direct sum. At the time I was a little distracted, couldn't remember which he used, couldn't decide if it mattered, and couldn't find a wikipedia article explaining the difference anyways, so I just went with exactly what the source said. Of course the (unrestricted) direct product of finite groups of unbounded exponent has elements of infinite order, so is not locally finite.

Do you think the (unrestricted) direct power of a finite group is locally finite? The example I considered at the time was a direct product of countably many copies of the nonabelian group of order 6, and I couldn't decide if it was locally finite. It seemed like something akin to a pigeonhole principle should reduce it to only finitely many equivalence classes of components (where two components are considered equivalent if all the finitely many generators of the subgroup each have equal entries in those two components, equal per generator, not across generators), so that every finitely generated subgroup was isomorphic to a subgroup of a direct product of finitely many copies.

If that argument works, then I think putting a bound on the order the factors should result in a locally finite group too (since it is a finite direct product of such direct powers). Even if the argument works, I am unsure if putting a bound on the exponents of the direct factors results in local finiteness. If it did, then that would make a nice contrast to the restricted direct product: an unrestricted direct product of finite groups is locally finite iff(?) there is a uniform bound on the exponents of the groups. JackSchmidt (talk) 05:13, 24 June 2008 (UTC)

I think a bound on the order of the factors gives local finiteness by something like the argument you sketch above. The restricted Burnside problem seems to imply that a bound on the exponents of the direct factors is also good enough, though I havn't thought about this carefully so might be wrong. R.e.b. (talk) 05:27, 24 June 2008 (UTC)

Redirects/dab pages

Hi R.e.b: Thanks very much for that pointer; I wasn't aware of the policy and I'll refrain from 'fixing' such links in the future. Zero sharp (talk) 20:31, 10 July 2008 (UTC)

"In set theory,..."

I have doubts about whether this phrase can serve the way "In algebra,..." or "In geometry,..." can, to tell the lay reader that mathematics is what an article is about. There was a time when every 7th-grader was told what "union", "intersection", and "complement" mean and what "∈" means and what "{x : φ(x)} means and then they went throught the rest of their lives thinking they knew all of set theory, having learned all of it one day in 7th grade. But now I think most people have never heard of this stuff. Michael Hardy (talk) 18:22, 17 July 2008 (UTC)

Unfortunately, you are probably right. R.e.b. (talk) 18:52, 17 July 2008 (UTC)

Actually, I'm not sure that that's all that unfortunate. If an outsider to the field is going to learn a little bit of mathematics before graduating from college, I don't think I'd pick set theory as a topic to include, unless it's construed as meaning finitary combinatorics. But for now, I'm comfortable saying "In algebra,..." at he beginning of a Wikipedia article and assuming the lay person will have heard of that. Michael Hardy (talk) 20:42, 17 July 2008 (UTC)

My usual formulation is in the mathematical field of foo theory..., explicitly not wikilinking "mathematical". For algebra per se one might be tempted to leave out "mathematical field of" as obvious, but actually it's probably better to say "in the mathematical field of abstract algebra", which gives a convenient wikilink for the context and warns the reader that it's not the subject he slept through in ninth grade. --Trovatore (talk) 20:48, 17 July 2008 (UTC)

Missing arrow

It took me a while to find time to do this, but I did remember to add the missing arrow to the operator topologies diagram. Greg Kuperberg (talk) 22:23, 27 July 2008 (UTC)


RfC by Perusnarpk against Fowler&fowler. Mathsci (talk) 00:22, 29 July 2008 (UTC)

It's probably best to ignore it, but I'll keep an eye on it. By the way, [[User|X]] should be [[User:X]] or [[User:X|X]].R.e.b. (talk) 01:55, 29 July 2008 (UTC)


please do not archive while the discussion is going on. Abhimars (talk) 14:26, 30 July 2008 (UTC)

Here you are

see also [1] Jakob.scholbach (talk) 15:24, 31 July 2008 (UTC)

Thanks, but I added these to zeteo a few days ago! R.e.b. (talk) 15:49, 31 July 2008 (UTC)
I also put a lot of his papers in Atiyah-Singer index theorem before I knew about zeteo; is there a way to add all the citation templates on a page to zeteo?R.e.b. (talk) 15:53, 31 July 2008 (UTC)
Oh, people are actually using it. Nice. Anyway, you can paste the WP source code (including multiple templates, and possibly also other stuff in between, which will be disregarded) into zeteo and let it parse all. It does it one-by-one. Jakob.scholbach (talk) 16:01, 31 July 2008 (UTC)


I think the biography is not quite right about St Catherine's College, Oxford, where he was a fellow for a large number of years (certainly in 1989, he and GBS were there). Possibly a picture of the Mathematics Institute in Oxford rather than the I.A.S.? He supervised almost all his students there. The pictures are very nice by the way. Mathsci (talk) 07:44, 9 August 2008 (UTC)

I think 1961-1963 were the dates given in his CV; you could quietly fix this if it's wrong. I found a picture of the math inst at oxford. I'm trying to find one of Singer and a better one of Bott. R.e.b. (talk) 14:30, 9 August 2008 (UTC)

Segal image

The less said the better ... Best wishes, Mathsci (talk) 01:52, 13 August 2008 (UTC)


AWB recognise the [[en: link and moves it to the end with the others. Rich Farmbrough, 11:55 18 July 2008 (GMT).

Speedy deletion of ALLEA

Ambox warning pn.svg
A tag has been placed on ALLEA requesting that it be speedily deleted from Wikipedia. This has been done under section A7 of the criteria for speedy deletion, because the article appears to be about a club, but it does not indicate how or why the subject is notable: that is, why an article about that subject should be included in an encyclopedia. Under the criteria for speedy deletion, articles that do not indicate the subject's importance or significance may be deleted at any time. Please see the guidelines for what is generally accepted as notable, as well as our subject-specific notability guidelines for people and for organizations.

If you think that this notice was placed here in error, you may contest the deletion by adding {{hangon}} to the top of the page that has been nominated for deletion (just below the existing speedy deletion or "db" tag), coupled with adding a note on the talk page explaining your position, but be aware that once tagged for speedy deletion, if the article meets the criterion it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the article that would would render it more in conformance with Wikipedia's policies and guidelines. Lastly, please note that if the article does get deleted, you can contact one of these admins to request that a copy be emailed to you. LAAFan 01:54, 18 August 2008 (UTC)

I removed the "speedy" tag. Michael Hardy (talk) 05:55, 18 August 2008 (UTC)

Thanks. (I'm not convinced that ALLEA is notable; I was just filling in a minor redlink!) R.e.b. (talk) 14:01, 18 August 2008 (UTC)

Definitely it's notable if Warsaw, North Dakota is notable. Michael Hardy (talk) 22:57, 18 August 2008 (UTC)

You are obviously unaware of the new CSD criterion: CSD0: "I have not heard of this or do not understand it". Articles tagged with this may be deleted by admins without bothering to look at them. R.e.b. (talk) 01:16, 19 August 2008 (UTC)

That one was used quite a lot in February and March of this year. I hope it doesn't return with as much frequency as we saw then. Michael Hardy (talk) 02:31, 19 August 2008 (UTC)

n! conjecture


I recently created a new page with a greater emphasis on Adriano Garsia's contribution. If you feel it is appropriate perhaps some formulas could be added as well. Katzmik (talk) 11:16, 26 August 2008 (UTC)

It looks fine so far. You could copy over more stuff from Macdonald polynomial about the conjecture. (I won't do this while you are working on the article so that I don't get in your way.) R.e.b. (talk) 14:05, 26 August 2008 (UTC)
I am finished so you can take over. Katzmik (talk) 11:37, 27 August 2008 (UTC)

Question on the master equation

Reading through Kirillov's book Lectures on the orbit method, he mentions the "master equation" in connection with induced representations. Specifically, if X=H\G is a homogeneous space for the right action of a Lie group G, then (according to Kirillov) the master equation for a section of the tautological bundle s : X → G is an equation of the form

which determines the H-valued function h on X×G. The function h is essentially a cocycle for the tautological principal H bundle over X. Do you have any idea whether this is related to what most people would call the master equation? If so, how? (Warning: I'm a complete novice about such things, so be gentle.) siℓℓy rabbit (talk) 12:24, 3 September 2008 (UTC)

I do not see any relation between these (or with another use of master equation). My guess is that the term "master equation" is used for many unrelated concepts in different subjects (like "fundamental theorem"). R.e.b. (talk) 13:46, 3 September 2008 (UTC)
It is most likely a case of awkward translation from the original Russian that is not entirely consistent with English usage. Katzmik (talk) 13:52, 3 September 2008 (UTC)
Thanks to both of you. siℓℓy rabbit (talk) 20:28, 3 September 2008 (UTC)


Can sometimes be very useful! Thanks, Mathsci (talk) 21:58, 5 September 2008 (UTC)

Lebedev–Milin inequality

I've added Lebedev–Milin inequality to the list of inequalities. This raises two concerns:

Michael Hardy (talk) 19:09, 14 September 2008 (UTC)

I just wrote Askey-Gasper inequality, and Category:inequalities might have a few more. R.e.b. (talk) 19:25, 14 September 2008 (UTC)

In the last few days you've created a number of short articles on particular families of orthogonal polynomials. Maybe saying with respect to which measures they're orthogonal would be useful. Michael Hardy (talk) 01:16, 6 October 2008 (UTC)

This would indeed be a good idea, but requires effort. R.e.b. (talk) 02:20, 6 October 2008 (UTC)
A Barnstar!
The E=MC² Barnstar

For uncountably many contributions to Wikipedia articles on group theory, mathematical logic, special functions, and other mathematical topics. Michael Hardy (talk) 03:06, 6 October 2008 (UTC)

Hilbert vs Banach

I think they usually use a Sobolev norm rather than a C^r norm to get a Hilbert manifold. Mathsci (talk) 21:09, 10 October 2008 (UTC)

But then it is not at all clear (at least to me) that the Hilbert space you get is the tangent space of the diffeomorphism group. R.e.b. (talk) 21:43, 10 October 2008 (UTC)
I think that's right. It already goes wrong for Diff(S1) and the 3/2-Sobolev space as far as I remember. Mathsci (talk) 10:56, 11 October 2008 (UTC)

Simple Lie algebras

Are Serre's construction or the vertex algebra construction anywhere on wikipedia? I found a reference to "Serre relations" in quantum group, but nowhere else, not even where they appear in Kac-Moody algebra. I'm not quite sure what to do about this. Perhaps an expansion of simple Lie algebra to contain the defining relations in Kac-Moody algebra. What do you think? (P.S. U. might like to know that I got an organ pedalboard to hook up to my chamber organ; this is to practice bits of Clavier-Übung III and "The Great Eighteen" for my next visit to ESI.) Mathsci (talk) 10:32, 15 October 2008 (UTC)

I havn't seen the Serre relations anywhere other than Kac-Moody algebra. I was thinking of doing something about this some time ago, but somehow never got round to it. R.e.b. (talk) 13:56, 15 October 2008 (UTC)
I also looked at the page affine Lie algebra which confuses central charge and level, as well as other sloppy errors (the characters are not modular forms unless specialised etc). I intend to rewrite this article to include the twisted case. This will involve putting some info on automorphisms of simple Lie algebras on WP. On the other hand simple Lie group is a rather strangely written article. The inability to talk about compact groups and different real forms is a problem. The standard reference is Helgason's Differential geometry, Lie groups and symmetric spaces, but there are no references. There isn't even a proper definition of real form. I suppose that it should be possible to change the redirect from simple Lie algebra into a proper article, with a discussion of Serre relations, automorphisms, vertex algebra construction, and then include the material from Helgason in simple Lie group. Mathsci (talk) 07:14, 16 October 2008 (UTC)
I must admit I thought the central charge and level were essentially the same. I gave up editing Lie groups articles some time ago as I found they have rather too many incompetent editors and I was spending too much time correcting blunders. (E8 in particular is for some strange reason a magnet for crackpots.) For real forms see the list of simple Lie groups. R.e.b. (talk) 13:44, 16 October 2008 (UTC)

Massey product

Hi, please see my comment at the talk page there again. Katzmik (talk) 09:06, 28 October 2008 (UTC)

Complex logarithm

Dear R.e.b.: I was wondering whether you might be willing to look at my proposed draft of the complex logarithm page. To me it seems like a big improvement, though on the Talk:complex logarithm page I have been getting a lot of opposition from one particular editor (and not much positive or negative from others). It would help to have an expert opinion. --FactSpewer (talk) 06:54, 30 October 2008 (UTC)

My main suggestion is that you implement any changes gradually rather than trying to replace the entire page at once, otherwise you will run into opposition from those who have written the page. R.e.b. (talk) 15:05, 30 October 2008 (UTC)
OK, thank you for the advice. --FactSpewer (talk) 01:30, 31 October 2008 (UTC)

Skolem's paradox

If you have a moment, could you look at the recent history of Skolem's paradox? You had helped fix this article a few months ago. — Carl (CBM · talk) 14:21, 9 November 2008 (UTC)

Argggh, no, what a cesspool (on the talk page). (talk) 09:35, 13 November 2008 (UTC)

logic of causal quantum evolution

Do you have a view of whether this is interesting? It points to this, about an apparently unexpected connection between an already-known deep inference logic and quantum evolution. I don't have my head around any of these subjects although I've spent a little time poking around the deep inference site. (talk) 09:34, 13 November 2008 (UTC)

It's not an area I know much about (or have even heard of). It looks interesting enough to add to the wikipedia article, if that's what you want to know. r.e.b. (talk) 15:14, 13 November 2008 (UTC)
Thanks. I actually was wondering if it was interesting from a foundations-of-physics point of view. I added a sentence about it to the article about quantum logic[2] which I hope is not too bogus. (talk) 06:49, 16 November 2008 (UTC)

Blaschke products

I notice you trimmed some fat out of Blaschke product, it seemed a tad much, I wondered why on the talk page there. Nothing urgent, just curious. linas (talk) 03:34, 17 November 2008 (UTC)

Measures on distributive lattices

At Holley inequality I thought of linking to the article that defines the concept of measure on a distributive lattice, if such a thing exists. But it didn't seem obvious that it does. Do you happen to know of some article in which that appears? Michael Hardy (talk) 21:05, 20 November 2008 (UTC)

It's the same as a measure on a finite set, in other words just a function to non-negative reals. Seems too trivial to have its own article. r.e.b. (talk) 21:23, 20 November 2008 (UTC)

Nonetheless, there should be an article in which it is defined. "Just a function to non-negative reals" isn't right because it has to be additive. The definition of additivity of measures relies on pairwise disjointness. My guess is in distributive lattices that would just mean the meet of any two of the elements said to be "pairwise disjoint" is the 0 element of the lattice. Michael Hardy (talk) 22:55, 20 November 2008 (UTC)

....OK, now I've linked to measure (mathematics). But that article gives a definition requiring the domain of a measure to be a sigma-algebra of subsets of some set, rather than a more general sort of distributive lattice. Michael Hardy (talk) 22:58, 20 November 2008 (UTC)

....The "Generalizations" section of that article goes into complex measures, signed measures, and some things are are finitely but not countably additive, but the domain is still some family of subsets of some set. Maybe the thing to do is to split the "Generalizations" section into two subsections: one on that sort of generalization, and another on more general sorts of domains. Michael Hardy (talk) 23:03, 20 November 2008 (UTC)

No, in this case a measure on a lattice really does mean a function to non-negative reals. You can if you want extend it by additivity to all subsets of the lattice; see Ahlswede–Daykin inequality for an example of this. r.e.b. (talk) 00:10, 21 November 2008 (UTC)

That seems like an unwise definition to me. Every Boolean algebra is a distributive lattice, but not every non-negative-valued real function whose domain is a Boolean algebra is a case of what is conventionally called a measure on the Boolean algebra. And there are excellent reasons for that convention. Michael Hardy (talk) 04:17, 21 November 2008 (UTC)

Would it be better to call it a probability distribution rather than a measure? I may be misuing probability terminology. r.e.b. (talk) 04:33, 21 November 2008 (UTC)

That depends on what you intend it to be. Are you assigning probabilities to members of the lattice? If you assign a non-negative number to each member of the lattice, and then divide that number by the sum of all such assigned numbers, then you'd have a probability distribution. "On the lattice" may be an unfortunate phrase because people sometimes speak of probability measures on Boolean algebras meaning something quite different from that, and a Boolean algebra is just a complemented distributive lattice, and I wouldn't be surprised if some people have generalized that concept to other distributive lattices. Is that in fact what you had in mind? Michael Hardy (talk) 18:12, 23 November 2008 (UTC)

I rewrote the articles to aviod this confusion. r.e.b. (talk) 18:53, 23 November 2008 (UTC)

Your edits at Criticism of non-standard analysis

Hi, I appreciate your interest in the page, even though you did not participate in the recent AfD. I think your moving the page to elementary calculus is not consistent with the decision there. If you would like to change the title of the page, please discuss it on the talkpage. The current title was suggested by CBM and received a favorable response from a majority of participants in the AfD. If the discussion were not prematurely closed, it would most likely have resulted in a "keep under new name "criticm etc". Katzmik (talk) 09:22, 21 December 2008 (UTC) P.S. I should emphasize that I am open to discussion of your reasons for opposing this page. I recall you expressed yourself strongly at the AfD Manifold destiny in favor of deleting the article. I have the impression that you oppose controversy in general, and I share your view. In the case of non-standard analysis, I feel that the arguments over it illustrate a significant philosophical disagreement among mathematicians, and as such are intrinsically interesting. I would be interested in hearing your view. Katzmik (talk) 09:35, 21 December 2008 (UTC)

I merged a page about a book review into a page about the book, and am surprised that anyone would object to this. r.e.b. (talk) 15:21, 21 December 2008 (UTC)
There is a lengthy AfD on Criticism of non-standard analysis. The current title reflects what seems to be a dominant feeling at the AfD that the earlier title, "Bishop-Keisler controversy", is inappropriate for a number of reasons, including the fact that the scope is too narrow. The current title reflects a broader scope, including a number of criticisms. Editors have expressed themselves at the AfD to the effect that "there certainly have been many criticisms of NSA and they deserve a separate page". I notice that you are something of an expert on Halmos' role in particular and invariant subspace problem in general; perhaps you could flesh out the Halmos section by adding whatever material you may be aware of. Katzmik (talk) 16:40, 21 December 2008 (UTC)
P.S. Your edits at Transfer principle suggest you may have expertise in this area, as well. If you get a chance, please take a look at my recent addition at internal set to see if it is correct at least in first approximation. Katzmik (talk) 17:53, 21 December 2008 (UTC)
Your edit at transfer principle is very helpful, thanks. Incidentally, could it be worth creating a page for Lefschetz principle? As a result that apparently bridges two fields (algebraic geometry and model theory), it may be sufficiently notable. Katzmik (talk) 13:35, 22 December 2008 (UTC)


for Dixmier trace, it looks terrific. Katzmik (talk) 09:05, 4 January 2009 (UTC) Please check my latest edit, hope I have understood correctly. Incidentally, it may be helpful to include a note on the foundational status of the material, similar to Banach limit. Katzmik (talk) 11:17, 7 January 2009 (UTC)


You made one of the standard mistakes in this edit : apparently you thought you were simply deleting a section, but actually you also created extra blank space between the two sections before and after it. A single blank line between sections has the same effect as no blank lines at all between them, but additional lines beyond that create extra vertical blank space that the reader sees. You left the usual three blank lines between sections—that's what always happens when someone tries to delete a section by editing ONLY that section. (I've since deleted the extra blank lines.) Michael Hardy (talk) 18:04, 9 February 2009 (UTC)

I believe in giving wikignomes plenty to do to keep them out of mischief. r.e.b. (talk) 18:11, 9 February 2009 (UTC)
Yup, I like to feel like I'm helping when I read the articles. I fixed a similar problem, my greatest contribution to the Riemann hypothesis to date. I try to correct any minor typos I see in the recent changes while I read, and I think the two step approach (content providing, and then editorial revision) works well. Thanks to Michael for pointing out a new wikignome task. JackSchmidt (talk) 19:40, 9 February 2009 (UTC)

Euclid's Elements

Thanks for your excellent contributions to Euclid's Elements. It is rare to see such a string of substantial improvements by one editor, especially in a mature, stable article on a subject of interet to a large number of Wikipecians. Finell (talk) 03:47, 11 February 2009 (UTC)

Atiyah: Please take a look

at: Talk:Michael_Atiyah#Working_on_the_article_again. Your feedback will be great. Fowler&fowler«Talk» 01:35, 15 February 2009 (UTC)

Reversion of reference formatting

Re this diff: it's not disk space, but screen real estate, that I was attempting to save, and I think the savings are due more to the two-column format than to the small fonts. If you want normal-sized fonts, but would like to make it easier to scroll through the reference listing by using two columns, it's also possible to use {{colbegin}} and {{colend}} instead of {{refbegin}} and {{refend}}. —David Eppstein (talk) 04:41, 17 February 2009 (UTC)

Why are you trying to save screen real estate? This is the reference section, which most people do not read anyway. r.e.b. (talk) 04:48, 17 February 2009 (UTC)
Because it's so long as to be annoying to scroll through it to find any particular reference. —David Eppstein (talk) 06:09, 17 February 2009 (UTC)
That's why the citation template gives a direct link to the references: click on the year. r.e.b. (talk) 06:14, 17 February 2009 (UTC)

Fundamental theorem of arithmetic proof

Hi there. I see that you replaced the old step-by-step proof of uniqueness with a new one. This would be OK, except that I can't follow the new "proof" at all. Probably my senile old gray cells are failing me, but if you could fill in the gaps and make the new proof a step-by-step affair then I would be happy. Cheers. Grover cleveland (talk) 07:18, 18 February 2009 (UTC)

I'm probably the wrong person for this, as I was under the illusion that I was simplifying the proof. If the old version is really easier to follow you could just revert back to it. r.e.b. (talk) 15:04, 18 February 2009 (UTC)

Hi R.e.b.

Hi Reb, First, sorry about messing up the work you were doing. I've added UK, and Canada dictionaries to my spell check in an effort to not make these mistakes - but I still mess up sometimes. Is that a cultural spelling - or just because it's spelled that way in the cite? Should I add to my US dictionary? Again, sorry. — Ched ~ (yes?) 06:20, 5 March 2009 (UTC)

No problem. The authors of the book use a different spelling from you and the OED. I'm not sure if this is a mistake on their part or just an alternative US spelling. r.e.b. (talk) 06:29, 5 March 2009 (UTC)

Ternary Golay code

I noticed that you nominated the article for the April Fool's Day DYK hooks. The article has 2 problems: 1) Articles need to be either new (counted from April 1 of the previous year) or have been expanded 5x during that time period. This article is neither. 2) The article needs to be referenced. In particular, the hook definitely needs to be cited with a reliable source. Royalbroil 02:26, 16 March 2009 (UTC)

It would be easy to find a couple of sources, but it is unlikely that the article will be expanded 5 fold in the next few days, so it is probably best to forget about it. r.e.b. (talk) 03:01, 16 March 2009 (UTC)

Cayley's omega process

Howdy, I tried to move this to Cayley's Ω process, but I think one of the vandalism protection settings prevented the move. I asked on WP:Requested moves to have it moved since I figured you had better things to do, but apparently it has been slow-tracked.

Assuming you agree with the move, could you move it? Here is the title for easy cut and paste: Cayley's Ω process. JackSchmidt (talk) 01:19, 23 March 2009 (UTC)

I moved it by copying and pasting by hand. r.e.b. (talk) 01:58, 23 March 2009 (UTC)

Awesome thanks. Since you are the only contributor that even preserves the history! Sorry for making the redirects in the way (one of them was on a broken redirect bot's to-delete list so I was trying to fix that up). Sorry also for troubling you with trivialities, but I think it would have taken at least a week for me to push it through WP:RM. JackSchmidt (talk) 02:12, 23 March 2009 (UTC)
Information.svg Hi, and thank you for your contributions to Wikipedia. It appears that you recently tried to give a page a different title by copying its content and pasting it into another page with a different name. This is known as a "cut and paste move", and it is undesirable because it splits the page history which is needed for attribution and various other purposes. Instead, the software used by Wikipedia has a feature that allows pages to be moved to a new title together with their edit history.

In most cases, once your account is four days old and has ten edits, you should be able to move an article yourself using the "Move" tab at the top of the page. This both preserves the page history intact and automatically creates a redirect from the old title to the new. If you cannot perform a particular page move yourself this way (e.g. because a page already exists at the target title), please follow the instructions at requested moves to have it moved by someone else. Also, if there are any other articles that you moved by copying and pasting, even if it was a long time ago, please list them at Wikipedia:Cut and paste move repair holding pen. Thank you. TJ Spyke 02:52, 23 March 2009 (UTC)


User:Mathsci suggested that you were interested in discussing certain issues that he and I were unable to agree on. If so, perhaps you could look at Talk:Minimal subtraction scheme and explain why, or whether, the proposed material is incorrect? Thanks in advance. A.K.Nole (talk) 20:24, 30 June 2009 (UTC)

Hmmm. After reading the discussions, I recommend that you and MathSci stay clear of each other, stop commenting about each other, and do not try to edit the same pages. As Wikipedia:COOL suggests, the easiest way to end most disputes is to walk away from them. r.e.b. (talk) 20:54, 30 June 2009 (UTC)
Thank you for that. A.K.Nole (talk) 20:57, 30 June 2009 (UTC)
I agree with your advice in principle, but if you find a way to convince your honorable colleague with a long history of harrassment and obfuscation to stop picking fights that deter countless good editors from constructive contributions to wikipedia and only generate acrimony, that would be greatly appreciated by many of us. Arcfrk (talk) 07:29, 3 July 2009 (UTC)

Riemann hypothesis and main conjecture of Iwasawa theory

Hi, here you added that the main conjecture is an analogue of RH, citing an article of Wiles, however I'm not sure that's what he's saying. I believe all he's saying is that proving the RH for varieties over finite fields comes down to identifying the zeta function with a product of characteristic polynomials of Frobenius acting on some Galois representations (Etale cohomology), and that similarly the main conjecture is about identifying the characteristic power series of Frobenius with a p-adic zeta function. The location of (non-trivial) zeroes of p-adic L-functions should be related to certain Selmer groups having large Zp-corank, but I fail to see the analogy with RH. Am I simply being thick? Cheers. RobHar (talk) 21:47, 4 August 2009 (UTC)

Calling the main conjecture an analogue of the Riemann hypothesis does indeed seem to be somewhat misleading. It might be better to call it an analogue of the Hilbert-Polya conjecture that implies the Riemann hypothesis. r.e.b. (talk) 14:58, 9 August 2009 (UTC)

Hunt extension "rather obvious"?

I was very surprised to have another look at Carleson's paper and observe that you're quite right that he dismisses the general p case as "rather obvious". Apologies for my assuming otherwise in my edit! (Not having managed to get hold of a copy of Hunt's paper, it's hard to establish the veracity of his claim - mathematicians do have something of a history of exaggerating the simplicity of extensions in this kind of case, of course!) Thanks for the fantastic efforts to expand the article, anyway. It's really taking shape now. :-) Tcnuk (talk) 07:48, 21 September 2009 (UTC)

I was rather surprised too, especially since he states and proves a weaker result. Kahane did not think that the general p case was obvious, as he stated it as an open problem in his report on Carleson's paper. r.e.b. (talk) 15:59, 21 September 2009 (UTC)


Barnstar-atom3.png The E=mc² Barnstar
Just wanted to send this your way to thank you for your significant hard work (particularly your persistence) both in expanding on Carleson's theorem (well, the Wikipedia article at least!) and creating the Littlewood-Paley theory article that I've long been waiting for Wikipedia to have! Cheers! Tcnuk (talk) 20:46, 29 September 2009 (UTC)


Just wanted to say, thanks for having the guts to delete the useless trivia at Aleph number!—Tetracube (talk) 20:56, 7 October 2009 (UTC)


Hi R.e.b.,

I do not agree with your merge of list of large cardinal properties into large cardinal, and have reverted. If you disagree, please open a discussion.

On the other hand the move to large cardinal from large cardinal property is plausible.

Thanks, --Trovatore (talk) 07:21, 27 November 2009 (UTC)

fast-growing hierarchy

Hi R.e.b., perhaps you could help us out with something at talk:fast-growing hierarchy. The article is based partially off of Gallier (1991), but several of the "Theorems" stated in that paper don't seem to agree with other sources. The theorems are not proven in Gallier, he simply references other works, which often don't seem to prove the claims either. You originally made this change. The original claim was due to Gallier, but your change appears to be supported by Cichon and Wainer. It appears that you have some experise in the area, would you care to comment in the discussion? Do you think that Gallier is a reliable source? Thanks, — sligocki (talk) 20:59, 9 December 2009 (UTC)

I'm not really sure: the papers use different notation and terminology, which makes it confusing to compare them. What you say makes it sound as if Gallier may have misquoted some papers, so I would not his paper for anything more than general background. I'm also rather wary of attempts to extend the hierarchies to the Church-Kleene ordinal: one runs into severe problems about encoding ordinals. r.e.b. (talk) 00:40, 10 December 2009 (UTC)
I'm not suggesting writing about such an extension in Wikipedia, just a personal interest. I was interested by the facts that fω is not primitive recursive and fε0 cannot be proven total in PA. I am interested in similar facts for larger ordinals, could fΓ0 be defined naturally so that it is the first not provably total in arithmetical transfinite recursion? fβ for β the Bachmann–Howard ordinal to be not provably total in constructive set theory? fωCK not provably total by computable methods? would that mean that it is not computable? We know that it is total by construction. If you had any thoughts I'd be interested. Cheers, — sligocki (talk) 01:49, 10 December 2009 (UTC)
There has been some work along these lines, showing that provably recursive functions of various theories are exactly those in some hierarchy up to the proof-theoretic ordinal of the theory. For example, the paper Fairtlough, Matt; Wainer, Stanley S. Hierarchies of provably recursive functions. Handbook of proof theory, 149--207,Stud. Logic Found. Math., 137, North-Holland, Amsterdam, 1998 briefly discusses the case of Peano arithmetic with transfinite induction added, but I would guess people have by now got as far as the constructive ordinals you mention. My impression is that you should in principle be able to get up to any given constructive ordinal, but there is no honest way to get all the way to the Church-Kleene ordinal. r.e.b. (talk) 03:02, 10 December 2009 (UTC)
Thanks for the ref. I'm like by your use of "honest", as if I'm claiming some sort of devious idea :) I am sure that I can define fundamental sequences up to (and including) the CK-ord and thus that I could define the fast-growing hierarchy that high. However, I don't know if that construction will allow me to say anything about it. I'd like to be able to show that it grows like the busy beaver function (or some other uncomputable function). Cheers, — sligocki (talk) 03:21, 10 December 2009 (UTC)


A criticism has been raised of an edit of yours on the talk page of the article J-invariant. You may like to read the criticism, and perhaps respond to it, even though it is now some years since you made the edit in question. JamesBWatson (talk) 11:44, 10 December 2009 (UTC)

It occurs to me that the above note may have been less helpful than it was intended to be. You put a link in the article the meaning of which was not clear. Someone queried it, and I removed the link. Later it occurred to me that it might be more constructive to ask you to clarify the link, so I posted the above note, but by now the link was not there, so even if you did try looking at the article you may not have understood the point. The link was to this pdf file, and it can be seen in this version of the article. JamesBWatson (talk) 10:38, 11 December 2009 (UTC)

Scale property

Hi R.e.b.,

I saw that you put the copyvio tag on scale property; when I went to see where the text had supposedly been copied from, all I saw was "presumptively tagged". Does that mean you tagged it because of who had contributed to it?

It's not a big deal, as there wasn't that much there, and what content there was, inappropriately treated two very disparate concepts that accidentally shared a name. Also there was no motivation or application, just a bare definition. So probably needs a complete rewrite anyway. I was just curious whether you had identified the putative copyrighted source. --Trovatore (talk) 01:53, 22 December 2009 (UTC)

Sorry to insert myself into someone else's talk page like this, but I can answer the last part of your question. The History section, at least, is copied from [3], with only one or two minimal changes. Probably the rest of the article is copied as well. See Wikipedia:Contributor copyright investigations/Henry Delforn. Sławomir Biały (talk) 12:39, 22 December 2009 (UTC)

Presumptive tagging of Quantum KZ equations

I see that the lead section of Quantum KZ equations was completely rewritten by User:Mathsci. I'm fairly certain that most of the history section is copied from Etingof, Frenkel, and Kirillov or is at least a close paraphrase. Would it be better to stub the article by leaving the lead in place and removing all of the subsequent sections as presumptive copyright violations? The talk-page template {{cclean}} seems like it would be relevant for this purpose. Sławomir Biały (talk) 12:29, 22 December 2009 (UTC)

I've already left Mathsci a note about this on the grounds that he has a better idea of which parts he wrote. The copyright notice has a link to a temporary page where one move stuff to rebuild a clean version of the article. His addition is worth salvaging, so if he does nothing I'll probably try to move it there. r.e.b. (talk) 15:57, 22 December 2009 (UTC)

Albert–Brauer–Hasse–Noether theorem

Hi. I see you have re-tagged this as copyvio. I reckon it has been reduced to a viable but non-copyvio stub - see conversation with Moonriddengirl here. The actual dozen or so words which state the theorem are probably identical with sources, but it wouldn't be possible to write about it without stating it. This is just a heads-up in case you hadn't seen the history; if it's reckoned that this contributor is so dangerous that anything he originated in must go, then go ahead. Regards, JohnCD (talk) 10:23, 23 December 2009 (UTC)

If it's anything like his other pages, it's still just 3 copyvios pasted together, though I don't think it's worth the bother of checking. Even ignoring the copyvios, his math articles tend to have so many other problems that fixing them is more trouble than rewriting them from scratch, so it's best just to delete the lot. r.e.b. (talk) 15:31, 23 December 2009 (UTC)

Hoax spotting

Well done for PRODding Fermat differentiation. FYI, I've just prodded the same editor's non-mathematical articles as hoaxes too. - Fayenatic (talk) 22:00, 9 January 2010 (UTC)

I somehow missed those; I guess I should have looked more carefully at his other edits. r.e.b. (talk) 22:26, 9 January 2010 (UTC)

I did some style edits on that one without paying any attention to what it said. So I guess paying attention can be useful sometimes. Michael Hardy (talk) 19:05, 12 January 2010 (UTC)

Thank you

CopyClean Barnstar.png The Copyright Cleanup Barnstar
Your work on this contributor copyright investigation is very much appreciated. Moonriddengirl (talk) 17:15, 12 January 2010 (UTC)
Thanks. :) --Moonriddengirl (talk) 17:15, 12 January 2010 (UTC)

Barnstar for Arf

Original Barnstar.png The Original Barnstar
Thanks for adding the Arf banknote to the Arf invariant article in this edit – beautifying and informative! —Nils von Barth (nbarth) (talk) 04:59, 22 January 2010 (UTC)

Timeline for the Weil conjectures

I noticed you were improving Weil conjectures with a bit more history. I have had in mind for a while to post a dedicated timeline of the whole business: see User:Charles Matthews/Weildraft for a draft that is not particularly complete. Before adding recent history (which is not really that obscure or difficult) I was going to worry over the pre-(Emil) Artin days. In particular the examples of classical groups and their homogeneous spaces would all have been known around 1900, to someone; the question for the historian is exactly who? I suspect Dickson would have known the order of some of the classical groups over all finite fields, which therefore implicitly gives the local zeta-functions of, say, Grassmannians. I was guessing that it could prove a bit nightmarish to determine exactly who knew what when about the size of various coset spaces for classical groups over general finite fields and actually wrote it down. Anyway I ducked that research (along with trying to figure out how many examples Carlitz and others could have known and at what point). I don't know, is trying to keep track of examples just doomed? The case Gauss knew from cyclotomy is interesting, at least. Any thoughts? Charles Matthews (talk) 15:27, 29 January 2010 (UTC)

As far as I know the examples related to classical groups, other than projective space, had little to do with the historical development of the Weil conjectures, and in any case are rather trivial as they tend to be unions of affine spaces. Any competent mathematician who studied them would have known their orders. The history could say more about Artin and Gauss sums. r.e.b. (talk) 15:50, 29 January 2010 (UTC)
Did you notice the IP edits from I believe this is French, and there are a couple of intriguing edit summaries. Charles Matthews (talk) 08:13, 31 January 2010 (UTC)
I hadn't noticed the unusual edit summary. I'm not sure what to make of it. r.e.b. (talk) 16:01, 31 January 2010 (UTC)
Well, scary, really. Same IP has been active on frWP, and I'm prepared to believe it. A demanding reader. Charles Matthews (talk) 16:44, 31 January 2010 (UTC)
Possible, but I'm skeptical. The IP has shown no signs of anything beyond grad student level, and as you know only too well we get a lot of weird hoaxers and trolls. We could keep half an eye on it, and send J-P an email if it starts to do anything odd. r.e.b. (talk) 21:11, 31 January 2010 (UTC)
Would be a grad student who knows the first thing S would do with your paper is to look for typos in your references, then. Small bet? Charles Matthews (talk) 22:12, 31 January 2010 (UTC)