Wikipedia talk:WikiProject Mathematics/Archive/2017/Nov

Is it the gamma function or the Gamma function?
Opinions of this edit?

An argument for capitalizing the initial "G" is that it's a capital Gamma. Michael Hardy (talk) 22:14, 31 October 2017 (UTC)


 * Just to clarify a little, I noticed the vast majority of uses already in place that I happened to see were lower case, so I mainly did this for consistency. I'm about to run out, so I can't look in too much more detail right now, but I'll quickly note that Mathworld and the Springer EOM both use lower case (although EOM hyphenates it) (and we certainly don't have to do the same as them, but it seems to be more common this way).  --Deacon Vorbis (talk) 22:28, 31 October 2017 (UTC)
 * I just did a quick spot-check of the mathematics textbooks I've got lying around, and most of them have gamma uncapitalised. So I would go with that. Reyk  YO!  22:33, 31 October 2017 (UTC)
 * I can't recall seeing a text that capitalizes the g, and spot-checking the books on my shelf, all the examples I find have the g lowercase. XOR&#39;easter (talk) 03:56, 1 November 2017 (UTC)

"cas" typesetting
In this section of Hartley transform I found this line:

2 \mbox{cas} (a+b) = \mbox{cas}(a) \mbox{cas}(b) + \mbox{cas}(-a) \mbox{cas}(b) + \mbox{cas}(a) \mbox{cas}(-b) - \mbox{cas}(-a) \mbox{cas}(-b). \, $$ I changed it to this:

2 \operatorname{cas} (a+b) = \operatorname{cas}(a) \operatorname{cas}(b) + \operatorname{cas}(-a) \operatorname{cas}(b) + \operatorname{cas}(a) \operatorname{cas}(-b) - \operatorname{cas}(-a) \operatorname{cas}(-b). \, $$ Obviously the reason for the deficiency of space between "2" and "cas" was the use of \mbox{} instead of \operatorname{}. But both before and after that edit, we see less than the usual amount of space before and after than plus and minus signs, as exemplified here:

\begin{align} \cos(a+b) & = \cos a\cos b - \sin a\sin b \\ \sin(a+b) & = \sin a \cos b + \cos a \sin b \end{align} $$ And the spacing deficiency in a + b is even worse after the edit than before. Note that the spacing in a + b is normal in the identities for sine and cosine.

Why is there that deficiency of space surrounding plus and minus signs? Michael Hardy (talk) 22:45, 27 October 2017 (UTC)
 * It looks ok to me. What are your math rendering preferences set to? —David Eppstein (talk) 22:49, 27 October 2017 (UTC)
 * Now I find that it looks correct when I'm logged out. As for preferences, I'm going to have to wait until tomorrow to look at that. Michael Hardy (talk) 23:17, 27 October 2017 (UTC)


 * Here are screenshots of the above equations rendered by my Internet Explorer 11 with MathML and PNG


 * MathML makes appropriate spaces around plus and minus better, PNG does not. And MathML creates much nicer glyphs for letters. Anyway I keep PNG rendering in my preferences, because MathML can sometimes fail to render horizontal lines, e.g. in fractions. :( --CiaPan (talk) 19:54, 3 November 2017 (UTC)

Minimal algebra
The new article titled Minimal algebra is an orphan (i.e. no other articles link to it), cites no references, and is severely stubby. It may also have other issues. Michael Hardy (talk) 23:06, 3 November 2017 (UTC)
 * FYI, the same editor also created Separating lattice homomorphism, which seems to be on about the same level. --Deacon Vorbis (talk) 21:24, 4 November 2017 (UTC)

Copy editing needed
Forcing (mathematics) could use a once-over. It contains some odd phrasing with jumbled or missing words, such as "because it's the truth value at some point is defined by it's truth value." At the very least, one of those "it's" seems unnecessary/wrong, but this is not my area and I don't really understand the sense of the sentence as a whole. I do know it's not grammatical. There are also the incomplete (?) sentence "Such ordering is well founded to," the phrase "Define we forcing," and other oddities. Would someone versed in this area mind taking a look? Thank you. Jessicapierce (talk) 20:43, 4 November 2017 (UTC)
 * I've taken a quick look, but it needs a lot of work. power~enwiki ( π, ν ) 21:28, 4 November 2017 (UTC)

Hodge–Tate theory
One seldom sees a weaker attempt at a Wikipedia article that the one called Hodge–Tate theory in its current state. Can it be made into something worth keeping? Michael Hardy (talk) 16:29, 9 November 2017 (UTC)
 * Should it maybe just redirect to p-adic Hodge theory? XOR&#39;easter (talk) 16:46, 9 November 2017 (UTC)
 * If I'm not mistaken, these are separate theories (and so a redirect is inappropriate.) I agree the page needs to be improved. -- Taku (talk) 23:15, 9 November 2017 (UTC)
 * On the other hand, i’m pretty sure it and “Hodge–Tate module” discuss the same stuff (and so I have suggested a merger.) —- Taku (talk) 15:36, 12 November 2017 (UTC)


 * Ew. Reyk  YO!  15:38, 12 November 2017 (UTC)
 * I don't think there's anything to merge; redirecting would be best. XOR&#39;easter (talk) 17:26, 12 November 2017 (UTC)
 * It's of some interest to merge a historical remark like Tate curves. The module article is a bit terse and can use some expansion for instance by a merger. -- Taku (talk) 23:20, 12 November 2017 (UTC)
 * Sorry it seems the theory article discusses John Tate (not the theory) and so I simply redirected it to the module article. -- Taku (talk) 03:06, 13 November 2017 (UTC)

Requested move Module (disambiguation) to [[Module]]
Presently Module redirects to Modularity. I have requested to revert an old move, that is to move Module (disambiguation) to Module. As this concerns, among others, Module (mathematics), Modular arithmetic and various other mathematical articles, some members of this project may want to participate to the discussion at Talk:Module (disambiguation). D.Lazard (talk) 11:34, 15 November 2017 (UTC)

Requested move: Permutation representation (disambiguation) -> Permutation representation
Participation to the move discussion is welcome at Talk:Permutation representation (disambiguation). —- Taku (talk) 20:30, 15 November 2017 (UTC)

Animation in Hypersurface
A slow edit war has begun in Hypersurface since 2012. About an animation which, in my opinion, is not really related to the subject, and disturbs reading. As I recommended in my last revert, a discussion has started at Talk: Hypersurface, that requires third party opinions. D.Lazard (talk) 22:02, 15 November 2017 (UTC)

Self-publication on WP?
I would like to bring possible self-publication by Dominic Rochon and Pierre-Olivier Parisé to the attention of the more experienced editors in this group, since I'm not sure how this is most effectively managed. Please look at: Several observations seem to apply: Multiple IPs from the same general location that could be the same person have been used: I think the most egregious is edit warring at an established article to include a self-published fringe topic. The remainder may not pass the guidelines for inclusion in WP, but I leave that to the judgement of better-qualified Wikipedians. —Quondum 02:25, 15 November 2017 (UTC)
 * at Bicomplex number, including WP:3RR violation
 * Tricomplex numbers
 * Tricomplex multibrot set
 * Tetrabrot
 * 132.209.3.30 142.169.78.184 132.209.100.23 142.169.78.111 142.169.78.50 Mathopo
 * Associated websites appear to be http://mathopo.com/ and http://www.3dfractals.com/
 * I nominated a similar article for deletion, but that was years ago now and I don't remember if the content was similar. Looks to be cited to different "researchers" though. Could someone with the administrator tools check to see how similar these are? Reyk  YO!  11:42, 15 November 2017 (UTC)
 * All of this is about Parisé's PhD master thesis, or an older contribution of his master thesis advisor Rochon. The two web sites are those of these two authors. The account name of the author of Tricomplex numbers is the same a the name of the web page of Parisé. This I agree that this is self publication of WP:OR. This seems unrelated to the previous deleted article, as it is not cited in the new articles. I strongly suggest to delete the three new articles. D.Lazard (talk) 12:46, 15 November 2017 (UTC)
 * Yep, looks like self-promotion. XOR&#39;easter (talk) 17:35, 15 November 2017 (UTC)
 * They seem, refraining from engaging on talk or edit comment. —Quondum 03:32, 16 November 2017 (UTC)

I have nominated Tricomplex numbers, Tricomplex multibrot set, and Tetrabrot for deletion. SeeArticles for deletion/Tricomplex numbers D.Lazard (talk) 13:54, 16 November 2017 (UTC)

Getting to Philosophy game
Consider the essay Getting to Philosophy which describes a simple game of following wikipedia links, under a mild set of conditions. The claim is that 97% of the time one ends up at the Philosophy article. It is clear that by following the rules one must either end up at a sink (an article with no appropriate outgoing links) or in a loop. Stopping at Philosophy is a bit arbitrary as any such path could be continued to Education -> Learning before entering the Knowledge ↔ Facts loop. One of the reasons that the percentage is not higher is due to the Mathematics -> Quantity -> Counting -> Element (mathematics) -> Mathematics loop. It appears that some editors have taken up the task of increasing the percentage by trying to break up this mathematics loop. This has resulted in some very contorted rewriting of the first sentences in these particular articles (see this edit, and these edits). and I and some others have been reverting these mangled attempts but we are at a loss as to whether there is anything more proactive that we could do. Suggestions welcome.

In a related issue (actually more of a pet peeve of mine), I am distressed by the number of our articles that start with "In Mathematics, ...". This formulaic approach, meant to put the topic of the article into context, seems to not be as useful for readers, due to its generality, as the frequency of its use makes it appear. Sometimes it is the right way to start, but other times there are better approaches and there are even instances where it is inappropriate (Element (mathematics) being one case in my opinion). Could we have a discussion of a better set of guidelines to use in mathematics articles for the purpose of putting the topic into context? --Bill Cherowitzo (talk) 03:41, 17 November 2017 (UTC)
 * Meh. I just tried it now and got stuck in the Cardinal direction<->North loop. Reyk  YO!  07:41, 17 November 2017 (UTC)
 * I tend to concur with Bill. There are certain glitches in human nature, and sometimes it takes only a small persistent nudge to produce a large effect.  In politics this is becoming a science.  The existence of the Getting to Philosophy may be such a nudge; a "self-fulfilling prophesy" that some see as a challenge.  Perhaps including a section on the distorting effect of such patterns on the utility of WP might at least produce a balancing nudge: link patterns that tend to encourage editors to browse new articles rather than previously seen articles would result in readers becoming aware of far more material.  A mention of the disservice editors do when they amplify the observed effect might also help.  On the "In mathematics" issue, I agree: that is what categories are for.  —Quondum 12:40, 17 November 2017 (UTC)
 * Regarding the In mathematics, this sort of contextual link to the encompassing field is explicitly encouraged for technical articles in MOS:CONTEXTLINK. Our manual of style Manual_of_Style/Mathematics encourages the same thing. I am curious, what peeves you about it? The grammatical construction? The use of Mathematics instead of a more specific subfield? --Mark viking (talk) 13:06, 17 November 2017 (UTC)
 * IMO starting by "In mathematics" is useful, as, for many mathematics article, the title does not indicate clearly that they are about mathematics, and this introducing phrase is thus useful. However, everybody can understand this introducing phrase, and there is no need to follow the link or to know what is exactly mathematics, for knowing if one may be interested in the article. Therefore, IMO, "In mathematics," is overlinking.
 * On the other hand, it is often unsuitable to use a too specific subfield. For example, Ideal (ring theory) begins with "In ring theory, a branch of abstract algebra,". The first link is not useful, as it duplicates the disambiguation in the title. Both links are too restricted, since ideals are used in many areas of mathematics. Therefore, a reader interested, say, in algebraic geometry or algebraic geometry may think having followed a wrong link. Similarly, it is not clear from the title, that Flat module is about mathematics. This article begins with "In homological algebra and algebraic geometry". Again this is too restricted, as it is basically a concept in algebra that is used in various other areas of mathematics. Moreover, "flat module" may be encountered in various areas that have nothing to do with mathematics, and I am not sure that it is clear for every people interested in these areas that homological algebra and algebraic geometry are mathematics. Therefore, in these two cases, the best begin is "In mathematics", without link. There are a lot of similar examples. D.Lazard (talk) 15:37, 17 November 2017 (UTC)
 * My thanks to for providing examples and clarifying (for me) what was nagging me about this construction. The guidelines in MOS:CONTEXTLINK leave a lot of latitude for how contextualization is to be carried out (as they should, we don't want cookie-cutter articles) and all too often the simplest way to do it is to slap on an "In mathematics,..." clause. Sometimes this is the correct thing to do, but rarely is the link useful, so I agree that this is often a case of overlinking. At other times something narrower is called for, but this needs to be readily identified as a branch of mathematics (like geometry or algebra) or if needed with a little assist (say, topology a branch of mathematics). But this can be taken too far as in the Flat module example above. I don't know if it is possible to agree on a set of guidelines for arriving at the proper level of contextualization, but I do think it is something that should be discussed. --Bill Cherowitzo  (talk) 17:28, 17 November 2017 (UTC)
 * I overstated the "categories" bit above, so acknowledging what others have said. Maybe a guideline should stay with "don't overdo it, but disambiguate context as appropriate".  —Quondum 03:22, 18 November 2017 (UTC)

The reason for beginning with "In mathematics," is that the lay reader's unfamiliarity with the field may lead to confusion. Once there was an article titled "schismatic temperament," which I assumed, based on the title, was about a topic in psychiatry or the like, and I had to read several sentences before I found out it was about musical scales.

Alternatively, "In geometry," or "In algebra," etc. can serve, but "In category theory" or "In functional analysis" cannot since they don't tell the lay reader that's it's about mathematics.

If the title of the article is Mathematical induction or something that otherwise tells the lay reader that it's mathematics, then there's no need for the context-setting phrase and the phrase is probably just clutter then. Likewise often some other phrase in the opening sentence is sufficient and the "In" incipit can be omitted. Michael Hardy (talk) 22:17, 17 November 2017 (UTC)

User:Hesselp again
User:Hesselp has started nibbling at the edges of his topic ban from Series, at the article Cesaro summation, where he has some novel ideas of his own. The situation could use close monitoring. Sławomir Biały (talk) 11:27, 15 October 2017 (UTC)
 * It seems hard if not impossible to reason with him or explaining him how Wikipedia should approach a (math) topic. This issue has spread now over 3 Wikipedias, after starting out on the Dutch Wikipedia and being told off there, he moved to English Wikipedia and after the topic ban there on to the German Wikipedia. Now after his activities got largely stalled by other (math) editors in the German Wikipedia, he seems to be back in the English one.--Kmhkmh (talk) 14:23, 15 October 2017 (UTC)
 * This comment from seems like a good summary of the situation. --JBL (talk) 16:47, 15 October 2017 (UTC)
 * Maybe an even better summary is his own (just above and below my one cited). He acknowledges that, first, he is "genetically" different from most of mathematicians. Second, that his adamant position did not change even a little after that discussion ("you helped me to get my views on the subject even more concrete, and to find more compact and to-the-point wordings"), in contrast to my position. Third, that there is, indeed, a chance that sometimes he will do according to my guess. Boris Tsirelson (talk) 18:04, 15 October 2017 (UTC)

Just some comment from an outsider: this seems to be mainly of a terminology issue. Is 1+1 the same as 2? Numerically speaking, the answer is trivially (I suppose) yes while the former is a sum and the later isn't; so in that sense they are different. The case of series is similar; for the purpose of discussion, a numerical series converges to pi need to be somehow distinguished from pi, even writing down pi itself involves some infinite expression. I don't think the language in mathematics that is currently in use is able to take these nuances into account. I guess one mathematically rigorous way is to somehow encode the construction that is used to obtain the results; i.e., histories behind objects. I'm sure the resulting approach to calculus should be called motivic calculus. (In case you thought this is a joke, actually I'm 1 percent serious about this concept.) -- Taku (talk) 05:28, 16 October 2017 (UTC)


 * This is very close to User talk:Hesselp; I suggested, he rejected (as usual...). Boris Tsirelson (talk) 05:40, 16 October 2017 (UTC)


 * This is very similar to what I also tried to articulate, only to find my wording picked apart, talked around in circles. Engaging with this editor is a pure waste of time.   Sławomir Biały  (talk) 10:53, 16 October 2017 (UTC)


 * Just a comment on how the "language of mathematics take[s] these nuances into account": You seem to be discussing the difference between sense and reference, which appears in mathematics as the difference between intensional logic (as in Martin-Lof's intensional, intuitionistic type theory) and extensional logic. siddharthist (talk) 23:12, 17 November 2017 (UTC)


 * Or maybe it is about abstract data types. To my regret, these are not defined and used in mathematics. It would be very convenient to define series as an abstract data type, in the spirit of Equivalent definitions of mathematical structures. Boris Tsirelson (talk) 11:19, 18 November 2017 (UTC)
 * I don’t know enough philosophy to say how my early comment is related to logic. But Tsirel is correct: I was probably thinking of an abstract data type and such. In mathematics, we often casually compare two objects of different types: strictly speaking, series and number are incomparable but then I don’t know the best way to state/formulate geometric series, say. — Taku (talk) 18:56, 18 November 2017 (UTC)

An opinion
Some truth lurks behind his position.
 * We do not have a singe, universally accepted (and rigorous, of course) definition of "a series".
 * Sometimes $$\textstyle \sum_{n=1}^\infty a_n$$ denotes just a number (the sum of the series), but sometimes it denotes something much more informative ("the whole series") that determines uniquely each $$a_n.$$
 * The language of "series" should not be interpreted literally; the meaning depends on the context; some mathematical maturity is needed in order to understand it correctly.
 * This makes some troubles for teachers and students. Some students conclude that the series theory is non-rigorous, inconsistent etc.

However, whenever I try to elucidate such truth, he always disagrees: "but this is not my point". I fail to understand his point. In practice I observe that he attacks, here and there, an occurrence of the word "series" and insists on reformulating the text in order to remove this occurrence ("since this is consistent", or "more clear", or "less context-dependent", or "simpler", "more logical" etc). Maybe he hopes to gradually exterminate the word "series" this way. Anyway, he grossly exaggerates importance of all that. He believes that this is not just a pedagogical problem, but a mathematical problem, that mathematics is inconsistent (God forbid) because of that, etc.

Really, is it possible to reformulate everything (equivalently) in a "series-free" language? Yes, of course. Every mathematician can easily reformulate a statement accordingly. (And by the way, this is why consistency of mathematics is still safe.) Instead of a series one may use the sequence $$(a_n)_n$$ of its terms, or alternatively the sequence $$(s_n)_n$$ of its partial sums, or the pair $$\big((a_n)_n,(s_n)_n\big)$$ of these two (interrelated) sequences. Other possibilities are also available, of course.

The question is, does it makes our language more convenient, or less convenient. I tried to consider some examples ("User talk:Hesselp", near the end), but he missed my point completely.

As far as I see, it is possible to exterminate the word "series" from mathematics, but it is not worth to do, since ultimately it makes our language less convenient. This is not done for now, and I do not think this will happen in the (near) future.

Even if this seems helpful to do in textbooks, it is not. Textbooks should prepare a student to reading math literature. Thus, the word "series" (with all its intricacies) should be known to students. Boris Tsirelson (talk) 10:15, 19 October 2017 (UTC)


 * It is not up to Wikipedia editors no matter how knowledgeable or intelligent to reformulate mathematics in a more sensible or consistent way than is in current textbooks. They say series, we should say series. I really don't think there is very much more to it than that. As you pointed out right at the beginning of that very long discussion 'However, note a difference: on my courses I am the decision maker; here on Wikipedia I am not. Here a point of view cannot be presented until/unless it is widely used. And if it is, it must be presented with "due weight"'. Practically everything else there was irrelevant to improving the article which is the purpose of a talk page. The appropriate answer to him when he quoted Bourbaki and said though a definition was formally correct it was absurd is to say he needs a better source to say so than himself. No source was provided never mind a better one. Dmcq (talk) 11:27, 19 October 2017 (UTC)


 * I'm working on a reaction on the last two edits (19 October 2017). -- Hesselp (talk) 13:35, 20 October 2017 (UTC)


 * "They say series, we should say series." — Indeed: "There's no free will," says the philosopher; "To hang is most unjust." "There is no free will," assents the officer; "We hang because we must." Ambrose_Bierce  :-)   Boris Tsirelson (talk) 09:05, 21 October 2017 (UTC)


 * On 'An opinion' (Boris Tsirelson, Dmcq) Thanks to both of you for your efforts to explain your position, in a clear way.  I'll make remarks on six points.


 * On "Sometimes $$\textstyle \sum_{n=1}^\infty a_n$$ denotes ..." This symbolic form is used in three ways:  the sum number, the sum sequence and the 'series' of sequence (an).    Bourbaki has, in editions 1942 until 1971, the distinctive forms:  S $$\textstyle _{n=0}^{\ \infty} a_n$$,   $$\textstyle \sum_{n=0}^{\ \infty} a_n$$  and  $$\textstyle \left ( (a_n) \ ;  \sum_{n=0}^{\ \infty} a_n \right )$$.    The object symbolically denoted by  $$\textstyle \left ( (a_n) \ ;  \sum_{n=0}^{\ \infty} a_n \right )$$,  is verbally described by:  the series defined by the    sequence $$\textstyle(a_n)$$  or  the series whose general term is $$\textstyle a_n$$  [or simply  the series $$\textstyle (a_n)$$,  by abuse of language, if there is    no risk of confusion]. As is this capital-sigma form, the adjective ‘convergent’ is ambiguous as well:  "having a limit" and "having a sum".  This double meaning has a long history, at least untill  Euler and the Bernoullis. I cite (once more) Gauss, 18??:  Die Convergenz einer Reihe an sich ist also wohl zu unterscheiden von der Convergenz ihrer Summirung, Werke, Abt.I, Band X, S.400.  In all his publications Cauchy used the verb converger for limittable and the adjective convergente for summable, but this seems to be never adapted at large.


 * On "We do not have a single, universally accepted..." Is this really true? Or do we overlook Cauchy's observation? His famous Cours d'Analyse starts in CHAPITRE VI p.123 simply with: On appelle série une suite indéfinie de quantités ... . ("An infinite sequence of quantities is called series",   with  'quantity' = 'real number' as  declared in  PRÉLIMINAIRES p.2.)   Doesn't this fits with the (universal) practice: 'series' is used instead of 'sequence' in situations where it's essential that addition between terms is defined? And doesn't this fits with the contents of the chapters headed 'Sequences' and 'Series' in almost all textbooks on calculus? (Keep in mind that Cauchy used 'convergent' for 'converging partial sums' = 'summable',  not for 'converging terms'.) You are going to qualify this as being OR, not allowed in WP?  It's nothing else than the observation that Cauchy's terminology (with his 'convergente' replaced by 'sommable') still fits with actual practice.


 * On "Maybe he hopes..." . That’s your idea, Tsirel;   my comment: "Gedanken sind frei, wer kann sie erraten...".  Actually I'm quite convinced, and I wrote it several times, that a chapter "Series"  (and a chapter "Cesàro summability" connected with Fourier-expansion especially) would be much easier to understand by using 'sequence', 'summable' and 'absolutely summable'  instead of 'series', 'convergent' and 'absolutely convergent' (avoiding ambiguities).  On the other hand, the objective "prepare a student (and a WP-user) to reading existing math literature", is as important to me as it is to you. That’s beyond discussion.


 * On "he misses my point completely". I looked again at your questions of 9 October 2017 (18:16 and 19:54).  You varied the wordings of your two phrases in a way I never thought of. Combined with your puzzling "identify a series with...." I missed your point, yes indeed.


 * On "They say series, we should say series". They say series.   Literally yes, they use the word "series". But examining calculus textbooks you can find maybe a dozen different - non equivalent - attempts to describe its meaning. All of them pretending to present THE meaning; no one mentions Tsirel's "We do not have a single...". So what do you, Dmcq, mean with "we should say series"?   Should the WP article choose for just one description (out of the 'dozen')?  Bourbaki's? as in the renowned EoM. Or, current practice in WP, present a handful of non-equivalent descriptions, pretending their equivalence?  see: - a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after one, - a series, which is the operation of adding the ai  one after the other (line 21), -  a series is an infinite sum (Basic properties, line 1), - a series is the sum of the terms of an infinite sequence of numbers (line 1) - a series is, ... an expression of the form  Σundefined∞ an  or   a1 + a2 + ··· (section Series, line 1). Or, distinguish explicitely the different roles of the s-word in: series-expression, series-representation, series-expansion, and more?   And mention that 'sequence' and 'series' are synonyms (though sometimes one variant is more usual) in: alternating se..., Fibonacci-se..., Fourier-se..., geometric se..., harmonic-se..., power-se..., trigonometric-se..., et cetera.


 * On "Bourbaki’s definition is absurd".  I cannot provide sources that support the qualification 'absurd'. Nor sources that comment on 'series' defined as a   sequence - sum sequence pair. I can show circa 10 titles of calculus books with their exposition on 'series' based on this pair; so it seems to be important enough to be mentioned in WP Series (mathematics).  One more remark on this quite unusual definition:  Cauchy’s "sequence with real numbers as terms" implies that the partial sums are defined.  So "a sequence with additionable terms" is close to "a sequence with a sum sequence", and in this interpretation of Bourbaki there’s nothing 'absurd' left anymore. -- Hesselp (talk) 15:29, 22 October 2017 (UTC)


 * For goodness' sake. You just posted over 6000 bytes, and I have no idea what your point is, or if you even have one anymore.  You've been overwhelming these discussions with walls of text, and it's not productive.  Here's all you need to know: an (infinite) series is an expression $$a_1 + a_2 + a_3 + \cdots = \sum_{n=1}^\infty a_n.$$  When the $$a_n$$ are numbers, this notation can generally denote either the series itself as a formal object, or the (ordinary) sum of the series.  When the $$a_n$$ are functions (or operators, etc), there are often multiple common notions of convergence, so some care should be taken to indicate what's meant.  This is all pretty standard; can we just drop this all now?  --Deacon Vorbis (talk) 17:16, 22 October 2017 (UTC)


 * And not a single citation backing up whatever the view is. Ignore or revert on sight is my opinion. Dmcq (talk) 20:55, 23 October 2017 (UTC)


 * @Dmcq.  Your comment concerns Deacon Vorbis, 22 Oct., I suppose?   I agree, it wouldn't be possible to find reliable sources for his double cyclic:  An infinite series is an expression ....denoting either itself or its sum. In case you meant my text (22 Oct.), you probably missed Cauchy, Gauss, Bourbaki, EoM. -- Hesselp (talk) 08:42, 24 October 2017 (UTC)

Some response to all of the above: I think it is useful to remember calculus that is currently taught and is in use is not the only one and not even necessary an optimum one. An example: is 0.999... the same as 1? This is mainly of the language problem. The "standard" interpretation is that the former denotes the limit of the sequence 0.9, 0.99, ... and so (trivially??) is 1. But one might resonantly argue the former should mean a "number" that is arbitrary close to 1 but is less than 1; namely, 1 - infinitesimal. This is a matter of what calculus we are using. In some edge cases, the interpretations need not be obvious: the typical example is the "series" $$\sum_{-\infty}^{\infty} a_n$$. I think by that one typically means Cauchy's principal value of the series. But arguably the best approach is to study such a series in the context of distributional calculus. In other words, it is fallacy to assume there is one unique consistent approach to calculus; we search for it in vain (no?) -- Taku (talk) 04:00, 25 October 2017 (UTC)


 * Rather intriguing: what is $$\textstyle\sum_{-\infty}^{\infty} a_n$$ according to the distributional calculus? Boris Tsirelson (talk) 04:45, 25 October 2017 (UTC)


 * By the way $$a_n$$ there should be distributions or some other kind of generalized function. The example I had in mind was the formula like $$\sum_{-\infty}^{\infty} e^{2\pi i n \bullet} = \sum_{-\infty}^{\infty} \delta_n$$ where $$\delta_n[f] = f(n)$$ and $$e^{2\pi i n \bullet}[f] = \widehat{f}(n)$$, the Fourier transformation (the Poisson summation formula.) So here the sums/series denote particular distributions. My larger point was that the insistence on a unique interpretation seems unworkable not only atypical. For instance, I don't think there is a clean bright distinction between sum and series. The right-hand side in the above example seems better to be called sum than series. Likewise, any infinite sum involving partition of unity feels like sum than series. -- Taku (talk) 00:21, 27 October 2017 (UTC)


 * A sort of a corollary of the above is that a certain superfluous looseness between sum/series/infinite expression isn't because mathematicians are sloppy but because they are not completely distinct concepts. Trying to suggest there is a bright distinction is both a POV and misleading, I think (not only unsupported). -- Taku (talk) 21:07, 28 October 2017 (UTC)

G. Birkhoff's incorrect translation/interpretation of Cauchy
I invite everyone who criticizes my attempts to improve WP articles on 'series', to compare five sentences from Cauchy's text (1821) with Birkhoff's adapted (improved? modernized?) version (1973).

A. Birkhoff's adapted translation (see Garrett Birkhoff A Source Book in Classical Analysis 1973 page 3;  this adapted text is copied by J. Fauvel, J. Gray in The History of Mathematics: A Reader 1987, p.567, no digital version of this section) reads: A sequence is an infinite succession of quantities u0, u1, u2, u3, ... which succeed each other according to some fixed law. These quantities themselves are the different terms of the sequence considered. Let sn =  u0 + u1 + u2 + u3 + ··· + un-1  be the sum of the first n terms, where n is some integer. If the sum sn tends to a certain limit s for increasing values of n, then the series is said to be convergent, and the limit in question is called the sum of the series. [.....] By the principles established above, for the series u0 + u1 + u2 + ··· + un + un+1 + ··· to converge, it is necessary and sufficiant that the sums  s n = u0 + u1 + u2 + u3 + ··· + un-1  converge to a fixed limit s as n increases.

B. Birkhoff's translation without his adaptations (see Cauchy 1821 (French) and Bradley-Sandifer 2009 (English)) reads:  Series is used as name for (Cauchy: On appelle série) an infinite sequence (Cauchy: suite) of quantities u0, u1, u2, u3, ... which succeed each other according to some fixed law. These quantities themselves are the different terms of the series considered. Let sn =  u0 + u1 + u2 + u3 + ··· + un-1  be the sum of the first n terms, where n is some integer. If the sum sn tends to a certain limit s for increasing values of n, then the series is said to be convergent (Cauchy: convergente), and the limit in question is called the sum (Cauchy: somme) of the series. [.....] By the principles established above, in order that the series u0 , u1 ,  u2 ,  ···,  un ,  un+1 ,  ···    be convergent, it is necessary and sufficiant that the sums  sn =  u0 + u1 + u2 + u3 + ··· + un-1  converge to a fixed limit s as n increases.

Cauchy's nomenclature is consistent (although the adjective 'summable' instead of his adjective 'convergent' - close to the verb 'to converge' for 'tend to a limit' - could have avoided quite a lot of misunderstanding). In the adapted text, the word 'series' pops up in the fourth sentence without any explanation. Birkhoff remarks in a footnote "Cauchy uses the word 'series' for 'sequence' and 'series' alike, ...". This is incorrect: Cauchy uses série in all his works only for "an infinite sequence of reals". -- Hesselp (talk) 15:13, 30 October 2017 (UTC)


 * If you want to write an article on the history of the words "sequence" and "series" and submit it to a journal about the history of science, be my guest. None of this has anything to do with editing Wikipedia, so please stop spamming it here.  --JBL (talk) 15:24, 30 October 2017 (UTC)
 * Agreed. I can't figure out what Hesselp is trying to accomplish here, or how it relates to editing the encyclopedia. It seems to be a lot of long-winded rambling. Reyk  YO!  16:17, 30 October 2017 (UTC)
 * This editor is banned for editing Series (mathematics) and Talk:Series (mathematics). I suggest to extend the ban to all pages and discussions where series occur. D.Lazard (talk) 16:26, 30 October 2017 (UTC)


 * @JBL, @Reyk.  Isn't it desirable to inform WP readers that Cauchy's description is an alternative for no definition at all (or five contradictory)? -- Hesselp (talk) 17:25, 30 October 2017 (UTC)


 * None of your edits in the past couple of weeks relate in any identifiable way to the goal of informing WP readers about Cauchy's description of anything. Moreover, this is precisely the topic from which you are banned.  Knock it off.  --JBL (talk) 23:59, 30 October 2017 (UTC)


 * No one of the five attempts (in WP articles 'Series', 'Convergent series', 'Sequence') to describe the mathematical notion called 'series', is supported by any mentioned reliable and clear source. So Cauchy's (reworded by Bourbaki, used in the EoM) should be considered. That is my goal. -- Hesselp (talk) 15:33, 2 November 2017 (UTC)


 * "Cauchy's description" is already in use in the following sense (explained by me on Hessel's talk page, but apparently not understood). Mathematics works with notions rather than definitions. A notion is, effectively, an equivalence class of definitions. There is no gain in canonizing one definition and exterminating all others. It is better to know many equivalent definitions, and to understand their interplay (which needs mathematical maturity, sometimes missing). See Equivalent definitions of mathematical structures. For example, topological space has at least 7 definitions (which is good, not bad). Five (and more) equivalent (not at all "contradictory") definitions of a series is also a good, not bad, situation. One of these is "Cauchy's description" (which is just a historical fact of no special importance nowadays, I think so). Boris Tsirelson (talk) 05:53, 31 October 2017 (UTC)


 * @Boris Tsirelson.  Again, I agree with your general remarks on  "A notion is, effectively, an equivalence class of definitions." But (1):   How can you write "Five (and more) equivalent .... definitions of a series is also a good ... situation." ?  For that seems to say just the opposite of your "We do not have a single, universally accepted (and rigorous, of course) definition of  "a series" ". But (2):  The 'five' refers (yes ?) to five actual descriptions in WP, summed up above almost at the end of. How can you say that this five are 'not at all "contradictory"' ?  For: Don't you agree with me that an expression for a notion cannot define that notion itself ? Idem, that the notion in question cannot be defined by "the operation of adding the terms" as well as by "a description of the operation of adding...." ? Idem, that "the operation of adding the terms" comes much closer to the notion 'summing a series' than to the notion 'series' itself? -- Hesselp (talk) 10:03, 31 October 2017 (UTC)


 * Tsirel, on your judging "Cauchy's description" as a historical fact of no special importance nowadays: You think the same for Bourbaki's description (as in the Encyclopedia of Mathematics) ? And for which out of the cited 'five' as well? -- Hesselp (talk) 10:28, 31 October 2017 (UTC)


 * The mathematical notion usually named 'series' can be expressed/denoted by the symbolic form a1 + a2 + a3 + ··· .  But equally well by the symbolic form  a1,  a2 ,  a3 ,  ··· .  The comma's-notation can be found in: A.R. Forsyth Theory of functions of a Complex Variable, 1918 page 21.  Whatever the choice of symbolic notation, the denoted notion remains the same. The same applies for the name of this notion: whether one says 'series' or 'infinite sequence with addable terms' or 'sequence with sum sequence',  the notion does not change. -- Hesselp (talk) 20:21, 1 November 2017 (UTC)


 * I have asked for a ban extension at WP:ANI. D.Lazard (talk) 17:46, 30 October 2017 (UTC)

@ You use "There is an admin discussion." as argument for undoing a revision on a talk page. Please mention here where in WP's Policies and guidelines anything is said about the relevance of this argument. Or anything that touches this. I cannot find it; I suppose there's nothing of this kind. -- Hesselp (talk) 19:53, 2 November 2017 (UTC)
 * The admin discussion is currently looking like a pretty strong consensus that you should not be writing about sequences and series anywhere on Wikipedia. "Anywhere on Wikipedia" includes here (there is nothing in that discussion about limiting its restrictions to article space only). By continuing to do so anyway, and by demonstrating in your writing the same problems that previously caused you to be locked out from writing on those specific articles, you are only making it more likely that others will agree with the sense of that discussion. So, while your writing about this is not yet officially prohibited, it looks like it soon will be, and you are only hurting your own cause by doing it. —David Eppstein (talk) 01:26, 3 November 2017 (UTC)

User:Hesselp violation of topic ban
Please see WP:ANI. Sławomir Biały (talk) 23:10, 22 November 2017 (UTC)

Coauthor needed
Our "Space (mathematics)" is submitted to WikiJournal of Science and refereed there. In the second referee report I read:
 * The following sorts of spaces might be worth mentioning:
 * Schemes
 * Algebraic spaces
 * Algebraic and Deligne–Mumford stacks
 * Locales

I reply:
 * I would be glad to convey the intuition behind "pointless spaces", too, but I cannot. This is beyond my competence. I never used such spaces in my research. I would be happy to have a coauthor able to enlarge this survey accordingly.

Who is ready to take this challenge? Thanks in advance. Boris Tsirelson (talk) 18:45, 3 November 2017 (UTC)

And, by the way, that journal is Wikipedia-integrated: Appropriate material is integrated into Wikipedia for added reach and exposure. Boris Tsirelson (talk) 19:04, 3 November 2017 (UTC)

It may happen that you are ready to take this challenge, but your name is hidden behind your username and you do not want to disclose it. In this case, do not reply here (or reply anonymously), register on Wikiversity under your true name and edit there. Contact me there on v:User talk:Tsirel. Boris Tsirelson (talk) 20:18, 3 November 2017 (UTC)

I boldly notify some experts that maybe rarely visit this page: User:John Baez, User:R.e.b.. Boris Tsirelson (talk) 07:20, 4 November 2017 (UTC)

No volunteers? A pity. For now, I wrote something... A competent coauthor is still welcome, of course. Boris Tsirelson (talk) 09:18, 7 November 2017 (UTC) --- A lot of thanks to Ozob for Space (mathematics) and Space (mathematics). Wow! Boris Tsirelson (talk) 06:33, 24 November 2017 (UTC)
 * Very nice work! --Mark viking (talk) 19:04, 24 November 2017 (UTC)

viXra
Came across this article again for the first time in a while. Current article gives the impression that it is part of the scientific enterprise in a meaningful way and almost entirely avoids the fact that it is mostly just a nicely formatted crank magnet. Perhaps it could use some attention. --JBL (talk) 13:10, 28 November 2017 (UTC)
 * The problem is finding a Reliable Source (in the Wikipedia definition of the term) that says in print what every physicist knows about it. I'll look around. XOR&#39;easter (talk) 15:06, 28 November 2017 (UTC)
 * (from Jesus Christ himself)//// (co-authored with the ever-wonderful Florentin Smarandache), etc... should tell you all you need to know about viXra. Headbomb {t · c · p · b} 15:15, 28 November 2017 (UTC)
 * It's easy to find chatter on blogs and Reddit and such, but maybe there's something out there which is more suitable for our purposes. XOR&#39;easter (talk) 15:17, 28 November 2017 (UTC)
 * Here's one which notes that viXra is full of people who don't like relativity. XOR&#39;easter (talk) 15:21, 28 November 2017 (UTC)
 * There's also, which might pass as an expert's blog. Don't know who Briggs is though, so maybe not. Headbomb {t · c · p · b} 15:21, 28 November 2017 (UTC)
 * Well, he's the author of a book that's been reviewed at least twice. XOR&#39;easter (talk) 15:29, 28 November 2017 (UTC)
 * might be useful, although it's quite dated now. Headbomb {t · c · p · b} 15:35, 28 November 2017 (UTC)
 * Gerard 't Hooft: "When a paper is published in viXra, it is usually a sign that it is not likely to contain acceptable results. It may, but the odds against that are considerable" . XOR&#39;easter (talk) 16:53, 28 November 2017 (UTC)
 * It reminds me of the Journal of Irreproducible Results, with the difference is that JIR already knows it isn't to be taken seriously. ~Anachronist (talk) 17:46, 28 November 2017 (UTC)
 * your edits are a definite improvement, thanks. --JBL (talk) 18:25, 28 November 2017 (UTC)

Polynomial mapping
Hi all. I noticed polynomial mapping is a red link. Is this topic covered somewhere? I think it would be unhelpful to just redirect it to polynomial or polynomial function. So I’m planning to start the article if there is no good redirect target. (The definition in the finite-dimensional case appears in Jacobian conjecture.) —- Taku (talk) 21:12, 29 November 2017 (UTC)
 * Looking at Special:WhatLinksHere/Polynomial_mapping there is one incoming link from Polynomial functor. There is a brief definition there (a vector-valued polynomial in linear forms).--Salix alba (talk): 21:55, 29 November 2017 (UTC)
 * Yes in fact that's how I discovered this red link. The google search with ""polynomial mapping" site:wikipedia.org" revels many potential link targets (so the topic is notable enough). -- Taku (talk) 22:57, 29 November 2017 (UTC)
 * As far as I know, a polynomial mapping is a regular function between affine spaces. See the first sentence of Regular function. Also, a regular function on an affine algebraic variety is often called "polynomial function on the variety". Therefore, I suggest to redirect polynomial mapping there, and to adapt regular function for clarifying the redirect. D.Lazard (talk) 08:44, 30 November 2017 (UTC)
 * I agree with the definition. But shouldn’t the notion make sense outside algebraic geometry? Since morphism of algebraic varieties concerns a more general topic, I still think it makes sense to have a standalone article that doesn’t presuppose the readers know algebraic varieties. -- Taku (talk) 09:31, 30 November 2017 (UTC)

Proposed move: Tannakian category -> Tannakian formalism
I have proposed the move of the section title at Talk:Tannakian category. Opinions on the move are very welcome. -- Taku (talk) 23:03, 30 November 2017 (UTC)