lflage/wiki-talks huggingface dataset:
Talk:Arithmetic group

message: There is a slight error in given definition. In given definition, one considers points with value in O, whereas G is only defined over K. One should remark: first that one need to consider a model of G over its ring of integers, and consider G(O); then that the notion of arithmetic group is independant of the choice of a model for G.
In Discrete subgroups of semisimple Lie groups Margulis defines S-arithmetic subgroups for algebraic subgroups of GL(N) over number fields. He defines arithmetic subgroups only for fields over Q (S contaning only the unique archmedean place). He notes that such a (I quote) is intrinsic with respect to the K-structure on H.
Milne's Algebraic Groups and Arithmetic Groups defines an arithmetic subgroup of G(Q) as a subgroup commensurable with the stabilizer of a lattice in a faithfull rational representation.
Same definition in Borel Reduction Theory for Arithmetic Groups in PSPUM 9 - Algebraic groups and Discontinuous subgroups. 
But in N.D. Alan's The problem of the Maximality of Arithmetic groups (in PSPUM9 too) considers subgroups of G(R) or G(C) commensurable with G(Z) (whatever the integral structure). This is especially relevant for algebraic groups with nontrivial center and when working with arithmetic subgroups of Lie groups (not every connected Lie group, even almost simple, is linear algebraic).  —Preceding unsigned comment added by 129.20.38.126 (talk) 19:26, 3 April 2009 (UTC)

message: I rewrote the article including many more topics, bibliography items and links to other pages. Possible things to be added: lattices in solvable groups, Prasad's volume formula (should have its own page), more about arithmetic locally symmetric spaces (systole, Wang's finiteness theorem), adelic theory and automorphic forms (very short w/ links to the relevant articles, in particular strong approximation),... Probably the history section could be better-written. jraimbau 14:01, 16 June 2016 (UTC)
replies: text: yes the history section should be rewritten. jraimbau (talk) 09:18, 9 February 2021 (UTC)
thread_title:  New version 

message: I notice some discrepancies between the description of how the theory was developed, and the years of publication of the referenced articles. For instance when it says "Shortly afterwards the finiteness of covolume was proven in full generality by Borel and Harish-Chandra.[6]" But the article referenced in [6] is from 1961, whereas the developments it is claimed to have come after are from 1965 and 1982.
: yes the history section should be rewritten. jraimbau (talk) 09:18, 9 February 2021 (UTC)
thread_title: Chronology error?

message: Add a section on Prasad's volume formula and finiteness results ; 
Add something about function fields? 
jraimbau (talk) 09:18, 9 February 2021 (UTC)
thread_title: TODO?
Talk:Arithmetic of abelian varieties

message: This article is so vague and full of jargon that it doesn't even look like an article about math.
If this subject is really so inconstructible that no notable and reliable source has a better explanation of it, then it should be deleted.
198.228.197.178 (talk) 12:48, 19 July 2011 (UTC)
thread_title:  Readability
Talk:Lords of the Starship

message: In the interests of trivia I've put a copy of the map drawn by Jack Gaughan that appears in some editions of the book online here.
:Thanks. I've now added the link to the article. Lee M 20:20, 22 July 2007 (UTC)
thread_title:  Map 

message: I can't find any indication in the novel that Salasar built the Yards, so I've removed that, along with a probably-unintended indication that Toriman was the original Miolnor IV, rather than the mythical resurrection during the battle of Bloody Ford.
It's an interesting idea, that Salasar created the Yards themselves, but that seems improbable, partly for their placement, and largely because if they could do this, they really didn't need the rest of the plot.  It seems more likely they tampered only - with the controls of the Ship, and with the antennae of Westwatch - presumably a short time before Toriman revealed the plan, though I can't be sure. Grothmag (talk) 15:50, 2 October 2017 (UTC)
thread_title:  Yards origin
Talk:Rare FM

message: Rare FM is the largest student radio station in London with the greatest number of DJs and staff and the longest broadcasting hours. It is therefore notable.
87.194.83.207 11:05, 13 May 2007 (UTC)
replies: text: It should also be noted that Rare FM is sponsored by well-known businesses and attracts the attention of many record companies that send Rare FM promotional material to review and play and gig tickets allowing DJs to review gigs for them. Rare FM also has a history of securing interviews with well-known musicians, comedians and actors, such as those mentioned in the article. For these reasons, I believe this broadcasting service is notable. Wolf of Fenric 21:01, 18 May 2007 (UTC)
thread_title: Notability
Talk:Artin L-function

message: What are number theoretic implications of Artin's conjecture?  —Preceding unsigned comment added by 91.21.55.7 (talk) 20:56, 12 February 2008 (UTC)
thread_title:  Number theoretic implications of Artin's conjecture 

message: The article is saying the Euler factors are given by prime ideals of a field, i.e. that there is only one Euler factor. ᛭ LokiClock (talk) 01:34, 7 April 2013 (UTC)
replies: text: A prime ideal of a number field usually means (by abuse) a prime ideal of the ring of integers of the field. -- Taku (talk) 04:31, 8 April 2013 (UTC)
replies: text:  I'm going to change it. Even if that's a common thing to do, there is absolutely no reason to expect anyone to know what they're saying. ᛭ LokiClock (talk) 01:20, 11 April 2013 (UTC)
thread_title:  Prime ideals of a field?
Talk:Artinian ring

message: In the section "Commutative Artinian rings", we can read :
*\operatorname{Spec}A is finite and discrete.
*\operatorname{Spec}A is discrete.
Is it important here to repeat two times that \operatorname{Spec}A is discrete ?
--160.178.210.85 (talk) 18:16, 29 November 2016 (UTC)
replies: text: @User talk:160.178.210.85 Well, I can easily see the equivalence to the first line, but the equivalence to the second line seems like a bit more work. To me, that makes both sets of conditions interesting and valuable. Are you saying that you'd delete the first bullet point you listed above? Rschwieb (talk) 19:12, 29 November 2016 (UTC)

text: @User:Rschwieb I'm sorry. I misread this part of the article. I thought that this section was just stating something like "the following bullet points are true for Artinian rings", in which case saying that "\operatorname{Spec}A is finite and discrete" is enough and no need to repeat that "\operatorname{Spec}A is discrete". --160.178.210.85 (talk) 23:15, 29 November 2016 (UTC)
thread_title:  <math>\operatorname{Spec}A</math> is finite and discrete 

message: This page should discuss the use of artinian rings in deformation theory...  — Preceding unsigned comment added by 128.138.65.151 (talk) 21:47, 28 August 2017 (UTC)
replies: text: Couldn't agree more. We probably should add a section on a formal smoothness, etc. -- Taku (talk) 04:32, 26 November 2018 (UTC)
thread_title:  Deformation Theory 

message: I think it makes sense to mention such a (nontrivial) non-artinian ring example. -- Taku (talk) 04:31, 26 November 2018 (UTC)
replies: text: Go ahead?  Doesn't seem like it would hurt. Here are a couple. Rschwieb (talk) 14:01, 26 November 2018 (UTC)
thread_title:  A non-artinian local ring with nilpotent maximal ideal
Talk:Wedderburn–Artin theorem

message: I added a sketch of the proof of the Wedderburn-Artin theorem, and moved the links to two other proofs that appear elsewhere on Wikipedia to the end of that proof.   By the way, there was a completely bogus proof of Wedderburn-Artin on Simple ring, which many editors had been complaining about since 2005.   I deleted that proof and added more information about simple rings. John Baez (talk) 19:11, 12 June 2023 (UTC)
thread_title:  Added proof
Talk:Ascending chain condition

message: The first sentence of the article appears to suggest that all commutative rings satisfy the ascending chain condition.  Is that true?  Noetherian ring#Introduction suggests the opposite. Hashproduct (talk) 17:42, 4 January 2010 (UTC)
replies: text: That's not true, the sentence was formulated in a confusing way. Hopefully it is more clear now. — Emil J. 17:55, 4 January 2010 (UTC)
thread_title:  Commutative rings 

message: A partially ordered set (poset) P is said to satisfy the ascending chain condition (ACC) if every strictly ascending sequence of elements eventually terminates.  Equivalently, given any sequence
:a_1 \,\leq\, a_2 \,\leq\, a_3 \,\leq\, \cdots,
there exists a positive integer n such that
:a_n = a_{n+1} = a_{n+2} = \cdots.
How is that equivalent? Consider the sequence a_i = a_1 for all i. It clearly satisfies the conditions, therefore any nonempty poset would satisfy ACC by that (incorrect) definition. --Daira Hopwood ⚥ (talk) 15:00, 10 September 2013 (UTC)
replies: text: I was mistaken; it says any sequence, so the condition isn't satisfied by there being one such sequence. --Daira Hopwood ⚥ (talk) 15:15, 10 September 2013 (UTC)
thread_title:  Correctness of definition 

message: In the first bullet of the Comments section, a new set is defined to be the "disjoint union" of the infinite collection of sets {0}, {0,1}, {0,1,2}, ... . Since this is an infinite union, I think we can only assume it is well defined if we invoke the Axiom of Choice. But how will we define it? The only logical way it seems is to start taking a disjoint union (call this union A1) of any two elements of this sequence, and then taking the union of A_1 with one other element not already "unioned", giving a set A_2, and so on, without end. It seems logical (I hope) that no matter how we do this, we will always end up a limiting set (A_n as n -> infinity) equal to the set of nonnegative integers.
Next the comment says this set (non-negative integers) satisfies the ascending chain condition (ACC). This is false, since the nonnegative integers, the even integers, and an infinite number of other unbounded chains inside it, do not terminate.
Also, a lot of this bullet does not make sense to me. It is not clear what is being discussed.
— Preceding unsigned comment added by 146.142.1.10 (talk) 19:01, 23 March 2015
Agree with IP.  If the posets are taken as Pn and if An = Disjoint Union (P0 ... Pn) then the Ai are isomorphic to N, which satisfies DCC but not ACC.  If something else is meant, then it is not clear what it is.  Bullet moved to talk page until it is clarified. All the best: Rich Farmbrough, 19:05, 24 September 2015 (UTC)
thread_title:  First Comment Bullet 
Talk:Coaster

message: An editor has identified a potential problem with the redirect :DVD coaster and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 November 28#DVD coaster until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  Mdewman6 (talk) 18:42, 28 November 2022 (UTC)
thread_title:  "DVD coaster" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]
Talk:Asymmetric relation

message: *symmetric relation
*asymmetric relation
*antisymmetric relation
:True there is currently nothing in asymmetric relation that explains what a nonsymmetric relation is. I think this needs to be remedied. Asymmetric relation has two definitions; which one of these, if any, corresponds with the definition of a nonsymmetric relation? I too dislike redirects to articles that have no mention at all of the first article.
:Gregbard, the notation used in your formula looks rather non-standard (the universal quantifier seems to be implicit), and even so I don't think the formula makes sense because you are quantifying over the same variables twice.
:My searching reveals that the matter was discussed in Wikipedia talk:WikiProject Mathematics/Archive 28#Negation of definitions
:--Egriffin (talk) 17:13, 7 September 2008 (UTC)
thread_title: See also
Talk:Atiyah–Bott fixed-point theorem

message: The article refers to vector bundles Ej as follows in the Formulation section:
"Further data needed relates to the elliptic complex of vector bundles Ej, namely a bundle map from''
:φj:f−1 Ej → Ej''
for each j, such that the resulting maps on sections give rise to an endomorphism of the elliptic complex T."
But nowhere is it stated which vector bundles are being discussed here, or what "elliptic complex" is being discussed.
Later in this Formulation section, it reads:
"Specializing the Atiyah–Bott theorem to the de Rham complex of smooth differential forms yields the original Lefschetz fixed-point formula."
But one cannot specialize something unless it has been stated first in more generality. I hope someone knowledgeable on this subject can fix this serious omission, so that the article might make sense.Daqu (talk) 17:51, 21 October 2016 (UTC)
thread_title:  What vector bundles?
Talk:Atom (measure theory)

message: There seeems to be something wrong in this article, right after "This measure has no atoms".  — Preceding unsigned comment added by 157.92.4.72 (talk) 21:07, 13 October 2011 (UTC)
replies: text: Thank you for your note. I have now restored two sections that had been removed by an anonymous user several weeks ago without anybody noticing. — Tobias Bergemann (talk) 07:53, 14 October 2011 (UTC)
thread_title:  Blanked sections 

message: According to  the article of Sierpinski is only proving a restricted version of what is called Sierpinski's article in this wiki entry. Is this relevant? Leonry (talk) 17:07, 21 May 2019 (UTC)
replies: text: I read that mathexchange question 23 and 1/2 times and it doesn't make sense to me. Just pick a set E_2 with measure zero, what's the problem? I mean, Sierpinski proves a result for E_0 a subset of Cartesian space R^n and Cartesian space is full of points, which are necessarily of measure zero. I mean, you can assign a non-zero measure to at most a finite number of points (or dice it up into a finite number of atomic parts).  So surely, I can just "pick one" that's measure zero!? So is the math-exchange question secretly about the axiom of choice, about the difficulty of finding some point, any point, with a measure of zero? Perhaps something about Zorn's lemma, and Sierpinski's use of it, or failure to use it? Was the questioner too shy to come out and say so? ZFC seems like a plausible foundation? Perhaps I am being a complete moron and am missing something painfully obvious? If there's actually a problem there, it is not posed clearly enough to be understandable. 67.198.37.16 (talk) 06:27, 13 September 2020 (UTC)
thread_title:  Incorrect reference 

message: In [0,1] consider the sigma-algebra of countable and co-countable subsets. Countable has measure 0, co-countable measure 1.
Then co-countables forms the only atomic class, the measure is atomic, but it is not a sum of delta functions  — Preceding unsigned comment added by 83.32.52.102 (talk) 20:29, 6 December 2020 (UTC)
thread_title:  Atomic don't implies sum of delta functions 

message: It doesn't seem right to link the Wiki article its definition to a "Stack Exchange" article question with little comment.
Also there's not an answer, ....
Clearly these atoms in measure have sigma algebras. 97.113.48.144 (talk) 04:44, 29 September 2022 (UTC)
thread_title:  Linking to "Stack Exchange" basic question, "homework"
Talk:Augmentation ideal

message: It is said that the elements of the form $1-g$ are generators only for $g\neq 1$. I take it having the zero element of the group ring as generator as well doesn't make much of a difference, so I remove the statement. If this is wrong, feel free to correct me and please add an example as to why this is wrong.HSNie 20:35, 10 June 2013 (UTC)
Talk:Running on Empty (song)

message: Added concert venue for the town. Beeracuda 11:35, 13 May 2007 (UTC)
Talk:Adlet

message: Five of the woman's ten children were dogs who crossed the seas to engender the European races.
How did the Inuits know about the European races? How old is this myth? 62.47.191.138 11:42, 13 May 2007 (UTC)
replies: text: Well, their first contact with Europeans would've been with the Vikings in Greenland about a thousand years ago.  It's quite possible that that part was simply tacked onto a much older myth, as well.  Nik42 (talk) 03:43, 1 February 2008 (UTC)
thread_title: Myth
Talk:Ric Lansing

message: I removed this section to to the lack of any kind of citations + WP:OR concerns.   Feel free to readd when appropriately cited Corpx 15:44, 25 July 2007 (UTC)
thread_title: History

message: I'm not an expert on Ric Lansing in the slightest and I hardly know his history enough to do a perfect biography for him. I don't know much about his marriage to Alexis Davis and it's not mentioned anywhere in the article. However, it must have been notable enough otherwise the marriage would not have happened. I hope someone can add their marriage somewhere in his article--maybe change some details I might have screwed up somewhere along the line. Thank you! --Miss Burkle 20:31, 19 October 2007 (UTC)
thread_title:  Biography
Talk:Lesley Webber

message: Prior content in this article duplicated one or more previously published sources. The material was copied from: http://soapcentral.com/gh/whoswho/lesley.php (See February 2007 archive, prior to article creation: http://web.archive.org/web/20070214083309/http://www.soapcentral.com/gh/whoswho/lesley.php). Infringing material has been rewritten or removed and must not be restored, unless it is duly released under a compatible license. (For more information, please see "using copyrighted works from others" if you are not the copyright holder of this material, or "donating copyrighted materials" if you are.) For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or published material; such additions will be deleted. Contributors may use copyrighted publications as a source of information, but not as a source of sentences or phrases. Accordingly, the material may be rewritten, but only if it does not infringe on the copyright of the original or plagiarize from that source. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. Wikipedia takes copyright violations very seriously, and persistent violators will be blocked from editing. While we appreciate contributions, we must require all contributors to understand and comply with these policies. Thank you.  NortyNort  (Holla) 08:37, 19 January 2012 (UTC)
thread_title:  Copyright problem removed 

message: *Rain the 1 00:51, 15 March 2012 (UTC)
thread_title:  Sources 

message: — Assignment last updated by ImagineWorldPeace (talk) 18:33, 17 December 2022 (UTC)
thread_title: Wiki Education assignment: Political Sociology
Talk:Axiom of constructibility

message: „and the existence of a simple (\Delta^1_2) non-measurable set of real numbers“
What is a simple non-measurable set? Simple set? Are you sure that it is independent of ZFC? (references?) --Chricho (talk) 15:03, 29 December 2010 (UTC)
replies: text: The parenthetical phrase is the explanation: a "simple", i.e. Δ12, non-measurable set. I agree it's not perfectly clear. I replaced with with "analytic". — Carl (CBM · talk) 15:24, 29 December 2010 (UTC)
replies: text: "Analytic" is \Sigma^1_1.  Did you mean "projective"?  Or maybe "analytical" (a little-used term for "lightface projective")? --Trovatore (talk) 22:35, 29 December 2010 (UTC)
replies: text: I meant analytical; the link went to the right place so I didn't think about it. Thanks, — Carl (CBM · talk) 00:07, 30 December 2010 (UTC)
replies: text: Hmm, "analytical" is not a great word because of the potential for confusion with "analytic", and I don't think it's used much, probably partly because of the possible confusion and partly because the projective hierarchy is usually the more relevant one.  I wonder if it wouldn't be better to say something like "a set of relatively low complexity". --Trovatore (talk) 01:38, 30 December 2010 (UTC)
replies: text: Now there is a link, much nicer… --Chricho (talk) 10:13, 30 December 2010 (UTC)

text: I see "analytical" in computability theory as often as "projective". It just depends whether you start on the lightface side or the boldface side. I'm afraid that if we use any words like "simple" or "complexity" without a link to one of the hierarchies, it will just lead to the same confusion that "simple" did. Since the well-ordering is lightface, we might as well link to the analytical hierarchy. — Carl (CBM · talk) 13:32, 30 December 2010 (UTC)
thread_title:  Simple non-measurable set
Talk:Ankang

message: Fwiw, the former Chinglish version of the page apparently derived from this exchange at Baidu Knowledge and wasn't the work of the editor who added it. — LlywelynII 23:16, 2 August 2016 (UTC)
thread_title: Lead

message: To add to article: what it borders. 173.88.241.33 (talk) 15:33, 8 May 2017 (UTC)
thread_title: To add to article
Talk:Axiom of dependent choice

message: I recently added footnotes 2 and 3 to take care of verifying two statements. However, I was unable to find a reference source for the equivalence between \mathsf{DC} and every pruned tree with ω levels having a branch. Since the proof is straightforward, I have included it. This proof should also help readers understand how \mathsf{DC} can be used. The proof comes up collapsed so readers can easily skip it. (By the way, I left out "nonempty" when describing a tree with ω levels since such a tree is clearly nonempty.) --RJGray (talk) 20:45, 17 September 2017 (UTC)
thread_title:  Couldn't find a ref, so gave a proof 

message: Curiously, this article uses the math environment to denote the axioms mentioned, that is, \mathsf{DC} (\mathsf{DC}) instead of just DC and  \mathsf{AC}  ( \mathsf{AC}  ) instead of just AC. Is there a specific reason for this? Why would you use inline images instead of just letters? – Tea2min (talk) 07:10, 20 July 2020 (UTC)
thread_title:  Unnecessary TeX?
Talk:Axiom of reducibility

message: This article links to Ramified Theory of Types, which is redirected to Mathematica Principia, which doesn't describe any ramified theory of types, but, however, links back to this article. The link probably made sense when it was created, but whatever it might have once linked to is lost to all human knowledge.
71.72.235.91 (talk) 02:34, 10 June 2010 (UTC)
replies: text: Fixed to redirect to Type theory, which does discuss the ramified theory.--Cherlin (talk) 16:14, 7 February 2012 (UTC)
thread_title:  WTF link
Category talk:Obstetrics

message: The articles here cover a wide range of obstetric topics, and should be subcategorised to ease navigation. Jut noting this here, so others can do this if I don't get the time. Carcharoth 11:56, 13 May 2007 (UTC)
thread_title:  Subcategories 

message: Currently, pregnancy is listed as a subcat of obstetrics. I think this is a case of the horse leading the cart; pregnancy comes first, and medical services for it second. I propose switching these around so Cat:Obstetrics is a subcat of Cat:Pregancy. --Ginkgo100talk 14:55, 16 August 2007 (UTC)
thread_title:  Pregnancy & Obstetrics cats