User talk:D.Lazard/Archive 2

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Blackboard bold

Hello. Using "blackboard bold" in print is apparently a bad style that originated from using "bold" symbols on ... well ... blackboards and then trying to mimic their appearance in printed texts. You may check some early texts by specialists in the subject about R, Q, H. Of course, anyone is free to represent bold symbols the way they like, but Wikipedia need not list all possible styles. In any case, the article is about quaternions and not about the appearance of bold symbols in mathematics, this would be a different subject. Please restore my clean-up. --Alexey Muranov (talk) 10:00, 1 October 2016 (UTC)

To editor Alexey Muranov: You say Using "blackboard bold" in print is apparently a bad style. This is your opinion. As far as I know, this notation has been introduced around 1960 by Bourbaki, and, since them it is widely used in mathematics for the basic structures ($\mathbb {N} ,\mathbb {Z} ,\mathbb {Q} ,\mathbb {R} ,\mathbb {C}$). This success comes probably from the fact that this provides an unambiguous notation for constants which are structured sets, while standard bold may be ambiguous. As quaternion is less used than above structures, blackboard bold is less used for quaternions, but there are many textbooks which use it. Thus you are asserting that most mathematicians have a bad style. You have the right to have this opinion, but not to try imposing it to others. Note that it is not said in the article that this notation is a standard, but that it is often used, which is the truth. Choosing among several widely used notations would be against Wikipedia policy of neutral point of view (see WP:NPOV for details). D.Lazard (talk) 14:34, 1 October 2016 (UTC)

This would be a good (and unexpected to me) argument that blackboard bold had been used by Bourbaki, except that I do not find it: https://books.google.fr/books?redir_esc=y&id=STS9aZ6F204C&q=rational#v=snippet&q=rational&f=false. Could you give me a precise reference, please? Also, could you give me an example, please, of a well respected mathematician using both bold and blackboard bold to differentiate between a structure and its underlying set (as you seemed to imply)? --Alexey Muranov (talk) 11:14, 2 October 2016 (UTC)

In any case, i believe that a bold "H" and a bbbold "H" is the same symbol, otherwise how would you suggest to differentiate between them on a blackboard? Exact typography IMO should be out of scope of an article about a mathematical structure. Anyone who knows that a bold capital "H", or even just a capital "H", is commonly used for quaternions, should be able to recognize a "blackboard bold" capital "H" as such. --Alexey Muranov (talk) 11:31, 2 October 2016 (UTC)

To editor Alexey Muranov: OK, I did a mistake in crediting Bourbaki of the use of blackboard bold. I agree with you that bold and blackboard bold are equivalent in the sense that, normally, in a mathematical text, the same character must not appear in both fonts. The possible ambiguity appear clearly in a sentence such as "Let $P$ and $Q$ be polynomials in $\mathbb {Q} [x].$" If ordinary bold would be used then the author would need to clarify that Q is the field of the rational, as this symbol may have other usages. Moreover the rather small difference between italic and bold italic makes confusion possible for a non-careful reader.

However WP is not the place for discussing the advantages and the drawbacks of both notation. The fact is that both notations are used, and this must not be hidden for the reader of Wikipedia. D.Lazard (talk) 09:50, 3 October 2016 (UTC)

ArbCom Elections 2016: Voting now open!

Hello, D.Lazard. Voting in the 2016 Arbitration Committee elections is open from Monday, 00:00, 21 November through Sunday, 23:59, 4 December to all unblocked users who have registered an account before Wednesday, 00:00, 28 October 2016 and have made at least 150 mainspace edits before Sunday, 00:00, 1 November 2016.

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attempt to communicate with M. D.Lazard

Hello D.Lazard,

I am new to Wikipedia and am already very impressed with the great organization that makes it available to the public free of charge.

You reverted an edit of mine in the Quintic Function and I thanked you for it, hoping that I would be able to include a small comment with my thanks. Unfortunately, the addition of a comment was not available.

This is an attempt to communicate with you. If you can suggest a better method, that would be appreciated.

Thanks, MegaKlhc. MegaKlhc (talk) 23:06, 22 December 2016 (UTC)

To editor MegaKlhc: You have chosen the right method for communicating with other wikipedians. Sincerely. D.Lazard (talk) 08:52, 23 December 2016 (UTC)

On Hilbert polynomial

Hello!

I disagree with your assessment of my section in Hilbert polynomial article. First, I don't think the name "In scheme theory" suits it well. It's technically true, but, if anything, it should be "In algebraic geometry". Indeed, most textbooks on algebraic geometry which are not specifically dedicated to computational algebraic geometry give only the "geometric" definition for coherent sheaves, and don't mention Hilbert polynomials of graded modules at all. This is true, for example, for Hartshorne's Algebraic Geometry, Ravi Vakil's "Foundations of Algebraic Geometry", Qing Liu's "Algebraic Geometry and Arithmetic Curves", "Grothendieck's FGA Explained" by several authors. This definition is used for varieties as well as schemes. And personally I think that for an algebraic object "Geometric definition" is a better title than "In algebraic geometry", but they mean essentially the same thing in modern mathematics. For the same reason (ubiquity in algebraic geometry) I don't think this definition should be called "highly technical". It's just as technical as the subject itself, and really fundamental (e.g. for Hilbert schemes). For all those reasons I'll revert your change to the article, but I'm open to discussion if you wish. Dpirozhkov (talk) 20:50, 1 January 2017 (UTC)

{{to:Dpirozhkov}} There are several distinct points behind your post:

Geometry or scheme theory? It is an error to reduce, as you do, algebraic geometry to scheme theory: many subareas of algebraic theory do not use, or rarely use the language of schemes. You cite computational algebraic geometry, but you omit real algebraic geometry, singularity theory, invariant theory, ... All these areas use Hilbert series and Hilbert polynomial, and many specialists of these areas are not accustomed with scheme language. It is therefore misleading to suggest that the content that you have added is standard in (algebraic) geometry. It is also an error to say, as you do, that geometry and algebraic geometry are essentially the same in modern mathematics.

Definition: I disagree with your use of the word "definition". The polynomial that is considered in the content that you have added cannot be credited to Hilbert, as coherent sheaves have been introduced a long time after his death. What you call a definition is a generalisation or an extension.

Reader's point of view: May I recall you that Wikipedia is not a textbook, but an encyclopaedia. This means that expected readers may come from any area of mathematics. This implies that technicalities that belong to a specific area must appear after the sections that may be understood by a widerer audience, and that a point of view that is perfectly adapted for the specialized audience of a textbook may be not convenient for a wider audience. See WP:NPOV for details.

I see that you have reverted my edit of the article. For above reasons, I'll revert this again. I'll do this in two steps for distinguishing the question of the place of the new section from the question of its name. I'll also start a discussion in the talk page of the article. Please, follow WP:BRD policy, and do not revert again before reaching a consensus in the talk page. D.Lazard (talk) 10:47, 2 January 2017 (UTC)

On Radical form, sin and cos of π / Fermat_prime_products

This is related to the section about: Radical form, sin and cos of ⁠π/(2^2m-1) × 2ⁿ⁠ for Fermat prime products.

You reverted (deleted) the entire section with this comment - Too much unnecessary square roots: for example, for the simplest case, 1/15=2/5-1/3 gives a simpler formula.

You missed the entire point of that section. It is about the simplicity of a pattern in the sin and cos formulae that applies to all the products of Fermat primes. The pattern becomes simple because of the mathematical properties of Fermat primes. You are right about the one-off simpler formula in the simplest case of 15, but then you over-generalized your comment which absolutely does not apply to the entire rest of the section (including other Fermat prime products) and esp. beyond that very specific example that you mention in your comment.

It is important to note the bigger picture and not get over-influenced by the simplest case of 15 and delete the entire rest of the section. A more responsible edit would have been to update / modify the simplest case of 15, showing that a little deviation from the pattern can further simplify this very specific case.

Please revert the delete and then you or I can update the section to incorporate your suggestion.

(Also please note that in addition to the above there are other additional insights in the content of the section (e.g. the largest known odd denominator beyond which the radical form is not known to exist and then some more insights that I can elaborate upon if / as needed)).— Preceding unsigned comment added by 67.170.74.174 (talk • contribs) 08:44, 17 January 2017 (UTC)

Please, sign your posts in talk page with four tildes (~~~~)

You are wrong in asserting that you consider all product of Fermat prime (there are 26 such products). You consider only the four products of the first Fermat primes.

You are wrong in asserting that I am influenced by the simplest case.

This is true that for each of the 26 products of Fermat primes, the sine and the cosine of π/n may be expressed without any other square root than those needed for the Fermat primes that are factor of the considered product. This is an easy consequence of Bézout's identity. Thus, in each case that you consider, there are unnecessary square roots.

In any case, this section is WP:OR, as you are unable to provide any published reference. As such, it has not its place in Wikipedia. D.Lazard (talk) 13:01, 17 January 2017 (UTC)

Möbius transformation

I did some (not all good) edits on Möbius transformation and you reversed them, and I would like to discuss how we together can improve the article. (hope you argee with this not sure if you wanrt to discuss it here or on talk:Möbius transformation but we can always move it to where you want it.

my edits were mostly mentioned in Schwerdtfeger's "Geometry of complex numbers"

$f(z)={\frac {az+b}{cz+d}}{\text{ or }}f(z)={\frac {a}{c}}-{\frac {ad-bc}{c(cz+d)}}$ the second part is formula (6.3) page 43

Maybe it was at the wrong place it would be better under the c /not = 0 section

${\frac {-d}{c}}{\text{ and }}{\frac {a}{c}}$ are the pole and the inversive pole of the transformation. are on page 41 for pole and page 62 for inverse pole.

I also wanted to enlarge this section a bit with the formula's of the fixed points of the mobius transformation and the formula that the midpoint of the fixed points is the midpoint of the poles (8.21 , page 62)

I liked my edit on the cross ratio:

If m(z) is a Möbius transformation ${\frac {az+b}{cz+d}}$ that maps $z_{1},z_{2}$ to $w_{1},w_{2},$ respectively, then

$w_{1}-w_{2}={\frac {(ad-bc)(z_{1}-z_{2})}{(cz_{1}+d)(cz_{2}+d)}}$

This identity means that the Cross-ratios are invariant under Möbius transformations. That is, if a Möbius transformation maps four distinct points $z_{1},z_{2},z_{3},z_{4}$ to four distinct points $w_{1},w_{2},w_{3},w_{4}$ respectively, then

It is a nice and basic proof that the cross ratio follows from the mobius transformation. I have not found a citation of if i guess because most books first explain the cross ratio first and the mobius transformation later

I was wondering about the section on classification

I think that this section presumes that (ad - bc) = 1 or c=1 or something else but it is nowhere mentioned ( I guess the section needs this notion because otherwise the trace (a+d) makes no sense multiplying a,b,c,and d with k does not change the transformation but it does multiply the trace.

hoping on your comments WillemienH (talk) 21:23, 17 January 2017 (UTC)

The formulation

$f(z)={\frac {az+b}{cz+d}}{\text{ or }}f(z)={\frac {a}{c}}-{\frac {ad-bc}{c(cz+d)}}$

is highly confusing, as the reader may ask why there are two non-equivalent definitions for a single object.

The formulation

$f(z)={\frac {az+b}{cz+d}}={\frac {a}{c}}-{\frac {ad-bc}{c(cz+d)}}$

would thus be better if it were true. Unfortunately it is wrong if c = 0 (the same error is repeated in section "Decomposition"). In any case, this formula rewriting belongs to this section "Decomposition", which should better begin with

If c ≠ 0, one has

${\frac {az+b}{cz+d}}={\frac {a}{c}}-{\frac {A}{z-d/c}},$

where A = (ad-bc)/c².

This shows that, if c ≠ 0, a Möbius transformation may be decomposed into a translation, followed by an inversion, followed by a homothety, followed by another translation. More precisely ...

Take care that the article has already a section on fixed points. For a good reference for the relation between homographies of the projective line and cross ratio, look at Berger's book Geometry. This book is more about the real case than about the complex case, but many of the properties considered in Möbius transformation are more general and should appear in an article Homography of a line. Also, the homographies of the real line deserve to have a specific article, because lenses and mirrors realize these homographies (note that poles are called focuses in optics).

For continuing this discussion, it is better to go to the talk page of the concerned article. D.Lazard (talk) 01:33, 18 January 2017 (UTC)

Reverting of my edits on the Logarithm pages

Why did you do that under the pretence of "unsourced assertions" ? they were sourced and the historical reference cited.

I will re-instate them back and also refer to the particular pages. Maybe you'd have the grace to understand and not be racially or religiously biased or motivated in your future edits. — Preceding unsigned comment added by أحمد الآلوسي (talk • contribs) 11:33, 19 January 2017 (UTC)

The reasons of my revert are explained in details in WP:OR. In particular, the first paragraph of WP:SECONDARY explains clearly that your analysis of the content of Al Khowarizmi book must be referenced to a secondary source. Your etymology for "logarithm" is not only original research, but is also blatantly wrong. D.Lazard (talk) 14:12, 19 January 2017 (UTC)

Gaussian elimination

Hi, D. Lazard!

Thank you for your edit reverting my use of piped links to sections of the Gaussian elimination article.

Since receiving notification of your edit, I've studied the relevant portions of the Manual of Style, including MOS:NOPIPE and also WP:NOPIPE, to try to understand the purpose of their rules. However, I'm still somewhat mystified by what they're supposed to achieve! :-(

Meanwhile, I discovered the {{section link}}, which I believe meets my objective perfectly: to link directly to the relevant sections of an article, rather than just to the article itself, so that the interested reader will find the most appropriate information immediately.

Please tell me whether you foresee any problem arising if I were to use elementary matrix § elementary row operations to refer the reader directly to that section. yoyo (talk) 04:27, 21 January 2017 (UTC)

{{to:Yahya Abdal-Aziz}} Both links that you have edited are links to sections, through redirects, which fits exactly the text that should appear in the article. For getting a direct link to a section, with the same displayed text, one needs a pipe, which provides, for the reader, exactly the same result. However Wikipedia evolves every day, and nobody can predict if a section, that is the target of one, or many redirects, will or not be split in a separate article. It may also be the case that the topic described in this section is better described in another article. When such things occur, a single edit of the redirect page will fix the problem, while, if pipes are used, all the pages where the pipe occurs must be edited.

In summary, for readers there is no difference, while, for editors, maintenance is much easier. D.Lazard (talk) 08:47, 21 January 2017 (UTC)

Factoriangular number

Why did you put a COI tag on the page I created? How can I possibly have a conflict of interest over an integer sequence? I created this page because it was at the top of Wikipedia:Requested_articles/Mathematics and you can take a look at my contribs before making baseless accusations that frankly don't make much sense. Thanks. Laurdecl ^talk 08:13, 22 January 2017 (UTC)

Revision of Comma After "i.e.," on Integers Article

Thanks for your work improving Wikipedia.

I think that you'd find these articles on commas after "i.e" and "e.g." informative: https://en.m.wiktionary.org/wiki/i.e. http://writingexplained.org/chicago-style/ie-and-eg Steven Carter (talk) 17:47, 9 February 2017 (UTC)

Coversine on page Trigonometric Functions

I beg your pardon, sir. Was there an issue with the instation of "coversine" on the page Trigonometric functions? If not, I think it probably should be reinstated. But if so, I only wish to know what the issue was. Either way, it is wisest that I don't start an edit war. Thank you.LakeKayak (talk) 21:50, 17 February 2017 (UTC)

To editor LakeKayak: The main point is that coversine is not commonly used, and is not known by most mathematicians. Per WP:NOR, to have its place in Wikipedia, it needs to be sourced, that is, a reliable publication must be provided, for showing that the topic is notable. The second point is that mentioning coversine in one of the definitions of trigonometric functions and not in the others, and giving it the same importance as sine and cosine is confusing for readers. If there would be a consensus for mentioning the coversine in this article, this should be done in a specific section entitled "Secondary trigonometric functions". D.Lazard (talk) 08:48, 18 February 2017 (UTC)

Fair enough. Thanks for the explanation.LakeKayak (talk) 16:26, 18 February 2017 (UTC)

Root of unity talk page

Hey, thanx, man! [kiss] Verdana♥Bold 07:26, 10 March 2017 (UTC) — Preceding unsigned comment added by Verdana Bold (talk • contribs)

Perfect Cuboid

I've long been interested in this problem, so I want to thank you for bringing to my attention that someone has submitted a proof.

However, even though one person has reviewed it on a list server, I am still unsure as to who else has peer reviewed this proof and whether it has been published in a mathematics journal.

I think we should not list it as solved until the proof is reviewed.

Your thoughts?

TheRingess (talk) 20:56, 12 March 2017 (UTC)

re: Order (mathematics)

Check out the categories that are populated with {{disambiguation|math}} and {{mathdab}}. The former puts it into Category:Disambiguation pages with (qualified) titles which lists all of the disambiguation pages with potential WP:INCOMPDAB issues. The latter does not. I can't see any advantages to using {{mathdab}}, do you know of any? -- Tavix ^(talk) 13:19, 17 March 2017 (UTC)

To editor Tavix: WP:DCAT says "If a disambiguation page consists exclusively of items in one of the more specific classes, then a specific template should be used instead of {{disambig}}". If the specific template does a wrong (or incomplete) categorisation, then this should be fixed by improving the template, not by editing the article where it appears (otherwise, you should edit many articles, not only this particular one). Note also that {{disambiguation|math}} categorizes to a soft redirect, and {{mathdab}} does not. D.Lazard (talk) 14:35, 17 March 2017 (UTC)

Reversion of my edits

Hi Lazard.

You recently reverted my edits on the page Operator_(mathematics). Could we discuss the changes to see if we can resolve the problem? (Sorry I don't know the best way to discuss like this on here)

Thanks David — Preceding unsigned comment added by 82.69.43.178 (talk) 09:42, 19 March 2017 (UTC)

Hi Lazard

I noted your comment with your reversion of my latest update to Operation_(mathematics). I agree that the inner product can be considered an operation, and it does not follow the rule I cited. However, I think this is a fairly uncommon exception. It was noted in the text that this rule is not universal.

The introductory definition as it currently stands does not distinguish at all from a regular mapping as far as I can see. I feel this addition adds significant value to someone new to the term. I did cite it with an authoritative source. There is also text already in the body of the article saying what you have disagreed with: "Often, use of the term operation implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain),[1] although this is by no means universal, as in the example of multiplying a vector by a scalar."

I believe it makes sense to keep the text I added. I would be interested to hear your point of view though, maybe we can work together to improve this article? I think it is not quite up to the standard we would like for a fundamental concept.

Thanks David — Preceding unsigned comment added by 82.69.43.178 (talk) 14:37, 19 March 2017 (UTC)

Field (mathematics)

Hello I would like to point out that while you simply reverted my initial edit, I took your criticisms into account in my subsequent edits. I removed the term "algebraic structure" and I kept to the "1/a" notation. I reverted your second revert only because it made no attempt at reaching a consensus. If you make 'constructive' edits, I will not simply revert them. Let's not start an edit war and please remember that reaching consensus is also Wikipedia policy. Rgds Vincent (talk) 16:56, 4 April 2017 (UTC)

Parallel projection, axonometry

I want to thank You for Your support. But SharkD is drawing the discussion to the village pump and doesn't stop spilling me with "clarify" marks at Axonometry. I give up and stop my contributions on "descriptive geometry". Thank You ! --Ag2gaeh (talk) 14:11, 24 April 2017 (UTC)

ANI notice

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Sławomir Biały (talk) 11:59, 6 May 2017 (UTC)

Affine manifold (disambiguation)

Hello - I'm writing because you are an editor of Algebraic variety that might be able to help. Could you take a look at Affine manifold (disambiguation) please? It's a WP:2DABS page trying to disambiguate 2 subjects that look to me the same, but might not be! Are the 2 entries the same thing? Shhhnotsoloud (talk) 12:21, 9 May 2017 (UTC)

To editor Shhhnotsoloud: The 2 subjects are not the same. I have changed the hatnote of Affine manifold for clarifying this (the new hatnote has more blue links than recommended by WP:HATEXTRA, but, in this case, this seems unavoidable). I have also nominated the dab page for speedy deletion (db-g6). D.Lazard (talk) 13:37, 9 May 2017 (UTC)

Thank you. The dab page is not strictly eligible for CSD because that would need only one (or zero) entries, but sometimes it works. If speedy is declined I'll PROD it. Regards. Shhhnotsoloud (talk) 13:55, 9 May 2017 (UTC)

Proposed deletion of Affine manifold (disambiguation)

The article Affine manifold (disambiguation) has been proposed for deletion because of the following concern:

Disambiguation not required. Primary topic has necessary hatnote

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Shhhnotsoloud (talk) 10:57, 23 May 2017 (UTC)

Division algorithm

I noticed you undid my edits on the article Division algorithm for improper publishing. I was hoping you could help me know how I should publish appropriately. Thanks. Warnerjon12 (talk) 16:58, 13 June 2017 (UTC)

Hello Warnerjon12. Regarding your contribution here, please see WP:No original research. Wikipedia is not intended to be a venue for first publication of novel ideas. From a practical standpoint, your method is still far from proving its usefulness. When you claim cubic convergence, you do no analysis of how the algorithm will behave on typical floating-point hardware. Also, any new method would have to be implemented in code and the code would have to be tested. EdJohnston (talk) 17:13, 13 June 2017 (UTC)

Okay, great. Warnerjon12 (talk) 22:03, 13 June 2017 (UTC)

Edits by 114.205.211.151

This IP 114.205.211.151 (talk · contribs · deleted contribs · logs · filter log · block user · block log) has/have (I don't know the number of users) made a number of edits to math articles. Some have been made to other articles, but the anon has returned to math articles. A number of them have been undone for various reasons. The IP adds unsourced, opinion, and/or rants to articles such as Yahoo! GeoCites and Algerian Arabic. I am unqualified to validate edits to math articles. Would you please take a look? Thanks Jim1138 (talk) 07:27, 15 June 2017 (UTC)

To editor Jim1138: I have looked to their math edits. They are not I'm my main area of competence, but the few ones that have not been reverted seem not really problematic. Can you be more specific on doubtful edits that have not been reverted? D.Lazard (talk) 09:03, 15 June 2017 (UTC)

Given the anon's problematic edits on many non-math articles, I was rather concerned with the math-related articles. I was worried something had fallen through the gaps. Thank you for checking. Cheers Jim1138 (talk) 10:53, 15 June 2017 (UTC)

Joel Moses

Pls explain why you reverted my edit. I thought bullet format highlights his various roles better.--K81944 (talk) 17:34, 22 June 2017 (UTC)

To editor K81944: I have reverted your edit because of the manual of style (MOS:LISTBULLET), which says "Do not use lists if a passage is read easily as plain paragraphs." D.Lazard (talk) 19:12, 22 June 2017 (UTC)

OK, thanx for enlightening.. --K81944 (talk) 21:02, 22 June 2017 (UTC)

Algebraic Geometry Talk

I added a talk section to the Algebraic Geometry page. — Preceding unsigned comment added by 128.138.65.70 (talk) 22:38, 10 July 2017 (UTC)

Real number too technical?

I question this edit. Here I sympathize slightly with the view that we should not give the cranks any room for ambiguity. By specifying "real number" in the first sentence of the article, we make the context completely unambiguous. It's a frequent argument that the article is prejudiced in the treatment of real numbers as the (capital-R) Real numbers, and I fear that eliminating the qualifier and link only further muddies the water. Sławomir Biały (talk) 15:55, 28 July 2017 (UTC)

MOS:MATH#Article introduction: The lead should as far as possible be accessible to a general reader, so specialized terminology and symbols should be avoided as much as possible (boldface is mine)

MOS:INTRO: ... avoid difficult-to-understand terminology and symbols

The concept of "real number" is surely difficult to understand for most readers of this article, and this is for this reason that the proponents of the algebraic pseudo proof insist for keeping them. Therefore, as "number" is sufficient for accurately stating the definition as least upper bound, I see no reason for confusing the reader by using a terminology, which he may not master. Moreover, if one replaces "real number" by "rational number" everything in the article remains correct (if it was already correct). Therefore, I am against linking to Real number in the lead. D.Lazard (talk) 17:41, 28 July 2017 (UTC)

You may be right at least as far as first paragraph of the lead goes, but I still feel like real numbers should be mentioned particularly in connection with the absence of infinitesimals. Does that seem more reasonable? Also, I think hyperreals should not be singled out specifically for attention in the lead of the article. Sławomir Biały (talk) 18:13, 28 July 2017 (UTC)

OK, I have linked Real number in the paragraph of the lead about infinitesimals. D.Lazard (talk) 19:06, 28 July 2017 (UTC)

Variable (mathematics)--Genesis and evolution of the concept

This is literally the first time I've ever corresponded with anyone on Wikipedia (honestly I don't even know if there is some mechanism to simply email you) and I apologize if this is not the correct forum or if I use incorrect etiquette; please correct me if I do.

First, I can tell you have made a myriad of mathematics contributions to Wikipedia and I greatly appreciate your work for it!

I have some questions, but first let me explain where I am looking. The edit made to the Variable (mathematics) page at 18:03, 20 November 2013. (I think this was the edit where the section "Genesis and evolution of the concept" was created.) Toward the end of the edit, the following statement was made: "Weierstrass replaced this sentence by the formula [epsilon-delta definition given] in which none of the five variables is considered as varying." There is an epsilon-delta definition Wikipedia page (#REDIRECT (ε,_δ)-definition_of_limit) that states the formal definition was first given by Bolzano and the "definitive modern statement was ultimately provided by Weierstrass;" furthermore, it suggests both were "credited with providing a rigorous footing...". When I read the edit, I was under the impression Weierstrass was solely responsible so I would suggest a redirect to the epsilon-delta definition page, a citation, or a rewording that included Bolzano.

Finally, I do not understand the last part of the edit "in which none of the five variables is considered as varying." I assume the variables in question are: epsilon, eta, x, a, and l? Why are epsilon and x not varying? In addition, is eta not a dependent variable that depends on epsilon?

Thanks NCarter1 (talk) 05:55, 24 July 2017 (UTC)

Normally, this kind of discussion should appear in the talk page of the article (Talk:Variable (mathematics)). This allows other users interested in the article to know of and to participate to the discussion.

I am not an expert in history of math. Therefore, when I wrote the section "Genesis and evolution of the concept" I was more interested by the trends than by the complete crediting. IMO, the important fact is that it is Weierstrass who has made a standard from this new formalism. Nevertheless I agree that the section deserves to be edited for a better historical accuracy. Could you be bold and try to fix this.

About the last part: eta is not really dependent on epsilon (in the sense of a dependant variable), as it is not uniquely defined as a function of epsilon. The phrase "in which none of the five variables is considered as varying" has been introduced for emphasising that the epsilon-delta formulation has introduced a new way of thinking: Instead of working with moving things ("limit", "tends", "variable"), statements are based on purely static formulas. This is important and could explain why continuity and limits are difficult to teach, as students have to understand that the static formalism is equivalent with the dynamic intuition. However, my formulation may be to short, and deserves probably to be expanded for clarification. Again, could you propose better formulation? D.Lazard (talk) 08:19, 24 July 2017 (UTC)

Hello! Thanks for your time and your response. I'm taking a course right now, but I will consider at least talking on the page to see if there is some consensus before making edits.

Thanks again NCarter1 (talk) 00:23, 31 July 2017 (UTC) NCarter1 (talk) 00:23, 31 July 2017 (UTC)

Decimal number

Can you please explain why you removed the redirect and did this? Noting your edit summary, it doesn't make sense that you'd put an under construction/in-use tag and remove the redirect. ^{Atsme📞📧} 02:09, 7 August 2017 (UTC)

I have explained this at Talk:Decimal fraction D.Lazard (talk) 09:22, 7 August 2017 (UTC)

Borel measure and the Dirac delta function

Hello D.Lazard,

I've decided to talk to you because apparently you reverted my recent contribution. I am extremely new to the Wikipedia and I haven't had enough time yet to get used to how things work here.

You wrote in the edit summary of your revert that "The article was not wrong" and that "the edit summary is mathematically wrong". I assume that the latter refers to the edit summary of my contribution. I think it would have been a good idea if you had left a note on the article's Talk page explaining the reason why you think my edit summary "is mathematically wrong" before actually reverting my contribution, exactly as Wikipedia recommends.

Because the contribution is already reverted by you, I'd still -- even more so -- apprecite a note from you on the article's Talk page explaining the reason why you think my edit summary is "mathematically wrong". This way you'd give me an opportunity to respond to your concern, so we could reach an editing consensus.

Thank you, I hope to talk to you soon. Konstantin Pavlovskii (talk) 10:16, 10 August 2017 (UTC)

To editor Konstantin.pavlovskii: The Dirac delta function is not a function, as clearly stated in the article about it. This fact is sufficiently known and accepted by all mathematicians, for not needing any discussion here. Thus, this is your assertion in the edit summary that is wrong, not the result of your edit. I apologise for not having done the distinction in my own edit summary. Nevertheless the revert was justified, because it is always useful to recall that the Dirac function is not a function, despite its name. As the point is not the distinction between a function and a distribution, I have edited the sentence for less emphasizing on this point. D.Lazard (talk) 12:42, 10 August 2017 (UTC)

To editor D.Lazard: Hello D.Lazard, what makes you think that a Dirac delta function that is a distribution, is not at the same time a function? Any distribution is a linear functional, so any distribution is a real-valued map. By definition any real-valued map is a function. I've already pointed it out in the Dirac delta function talk page the corresponding article that you refer to has been recently edited by the community to remove the incrorrect statement that the Dirac delta function is not a function. You could have a look at the new Dirac delta article yourself. I'd appreaciate if you undid the harmful reverts of my contributions, please. And could please discuss my contributions on the corresponding talk pages first before reverting them. And thanks for that prompt reponse. Konstantin Pavlovskii (talk) 13:34, 10 August 2017 (UTC)

I think Konstantin's perspective is reasonable. I don't claim to fully agree with it, but I'm inclined to tone down the "not a function" aspect at least. Russian mathematicians even call it a "generalized function" ;-) I think we should clarify both the sense in which it is and is not a function, rather than relying on possibly hidden meanings of the word "function". Sławomir Biały (talk) 13:43, 10 August 2017 (UTC)

Rational number edit

Somehow I misread "a=0" as "n=0", sorry about that. GiovanniSidwell (talk) 13:02, 11 August 2017 (UTC)

Gaussian integer: your dispute

Quotation: For all Gaussian primes except $p_{1}:=1+i$, there is one and only one associate, which fulfils the congruence $p\equiv 1{\pmod {2+2i}}$

disputed inline|reason= wrong: a+bi and -a–bi are congruent mod 2+2i and associated|date=August 2017

Your statement is wrong. What makes you think, that for an arbitrary Gaussian integer z=a+ib holds $z\equiv -z{\pmod {2+2i}}$? The definition (see chapter Congruences and residue classes below) says, that there must exist a Gaussian factor $q$, with $z-(-z)=2z\;{\stackrel {!}{=}}\;q(2+2i)=2q(1+i)$, i.e. $z\;{\stackrel {!}{=}}\;q(1+i)$ This is only the case, if $(1+i)|z$. That again only holds for even Gaussian integers (defined in same chapter, see example 1), which are never primes, except the noted $p_{1}=1+i$, because they are divisible by $1+i$. Please remove your dispute

kind regards --Wolfk.wk (talk) 17:32, 13 August 2017 (UTC)

I have followed your query and have given a complete reference of the questioned definition of primary associates.

I have even added a translation of the relevant paragraph of Gauss' paper into English.

What more could I do to convince you, that my edits are correct and originated by Gauss himself?

Please remove your dispute, to clear this topic.

--Wolfk.wk (talk) 21:29, 14 August 2017 (UTC)

You have posed an inline query with wrong statements. I have explained it to you, and you have accepted, that you have been wrong.

Then you changed its state to 'citation needed'.

I gave a citation of Gauss himself, even as translation into English, and asked you to remove your tag, with no reaction.

Please remove your tag, or tell me what is the problem.

--Wolfk.wk (talk) 21:15, 16 August 2017 (UTC)

Primary Decomposition Edit

Hi D.Lazard,

You claimed that the ideal intersection and product do not agree. Although this is true in general, for the example I gave, it holds. You can check the following example using http://habanero.math.cornell.edu:3690/

R = QQ[x,y,z]
I = ideal(y*z - x^2, x-z)
J = ideal(x^3 + y^3 + z^3)
intersect(I,J) == (I*J)

If you want more information, check out proposition 3.11 on page 98 of Eisenbud's book on commutative algebra. You can also look at page 103 for more about the geometric interpretation. Also, in the future, can you please edit changes that you may think are wrong instead of just outright revoking them? Wikipedia desperately needs more examples and motivation for its mathematics pages. — Preceding unsigned comment added by 70.59.20.131 (talk) 00:22, 28 August 2017 (UTC)

Computations

I think there should be explicit computations on the wiki page for primary decomposition. In addition, there should be a (sub)section dedicated to doing computations with macaulay2. This will help newcomers to commutative algebra to get a better hold of the subject. I have started a discussion on the commutative algebra talk page, but figured I may send a message directly to you. — Preceding unsigned comment added by 128.138.65.151 (talk) 21:44, 28 August 2017 (UTC)

This should have been posted on the talk page of the article. Also, please, sign your posts in talk pages with four tildes (~~~~).

I agree that a section about algorithms for primary decomposition would be useful, as well as a list of the computer algebra systems that have an implementation (Macaulay2, Maple, Singular, probably Mathematica and Macsyma), but it is not Wikipedia policy to discuss specific implementations outside the articles about them. Moreover, writing the section on algorithms would need the verify the assertion of the introduction about G. Hermann paper (see the talk page of the article).

Where is this policy for wikipedia? I think it is more helpful to show people how to use a specific implementation so that they can experiment on some platform. 70.59.20.131 (talk) 01:08, 4 September 2017 (UTC)VeryConfused70.59.20.131 (talk) 01:08, 4 September 2017 (UTC)

See MOS:CODE and MOS:MATH#Algorithms. In the case of this specific article, it would be much more useful and much more encyclopedic, before giving code samples, to produce some non-trivial examples (that is with embedded components), to give an idea of the main existing algorithms, to explain for which kind of problems the computation of primary decomposition is useful, to list the main implementations, etc. When this will be done, examples in a specific software will become totally useless, as the only specificity is the syntax of the function "PrimaryDecomposition". D.Lazard (talk) 09:23, 4 September 2017 (UTC)

Plot of Bring radical

Hi, D.Lazard,

Back in October 2015 at Talk:Bring radical#Would like to see the usual investigations an editor made a comment of which this is an excerpt:

$\operatorname {BR} (a)$ looks like a function: $\operatorname {BR} (a)=x$ such that $x^{5}+x+a=0.$

Someone must have done to the Bring radical function all of the things that are done to every other function:

• Show a table and/or graph of the function. (And then of its derivative, integral, etc.)
• Show expressions for $\operatorname {BR} (a+b)$, $\operatorname {BR} (ab)$, $\operatorname {BR} (a^{b})$, etc., or the impossibility thereof.

I particularly like the idea of having a graph of the real branches of BR(a), for some range of real values of a. Has this been done or could you construct it? Also, the properties of BR(a+b) and BR(ab) would be nice to see, if any are known. Loraof (talk) 23:13, 13 September 2017 (UTC)

As $a=-x^{5}-x,$ the Bring radical is the inverse function of the function $x\to -x^{5}-x.$ As the derivative $-(5x^{4}+1)$ of this quintic function is always negative, BR(a) is defined and real for every real a, and always decreasing. The graph of BR(a) is obtained from that of $x\to -x^{5}-x$ by symmetry around the diagonal y = x. The derivative of BR(a) is ${\frac {-1}{5BR(a)^{4}+1}}$ (formula for the derivative of an inverse function). For the behavior under arithmetic operations, I believe that there is no useful formula. D.Lazard (talk) 02:10, 14 September 2017 (UTC)

Gaussian integer: your edits

I am writing this final remark as consequence of the dispute with you on the Talk:Gaussian integer page, which lingered for nearly one month. Therefore, I think to know, what I'm talking about. You have deleted and rewritten all my edits on Gaussian integer based on claims, which always turned out to be wrong. But this did not stop you in any way. Instead, you continued to rewrite the whole page in your very personal manner (which apparently is the only right one, others are 'old fashioned'), no matter if eg. the context of figures was lost by using other symbols, etc. Of course, I have no problem with extensions and corrections of my edits, that is usual practice and generally improves pages. But what you are doing is unacceptable. For me, you act as if you were the owner of the page.

Probably, you think that your edits are a great support for WP. I believe, the opposite is true: because you show no respect for the work of other voluntary editors (like me), they are discouraged to contribute to WP. Personally, I will never again write anything on any page, which you seemingly 'own'.

BTW: I am writing this comment not in the hope, to change your behaviour, but as benefit for other editors, which have to struggle with you, too.

--Wolfk.wk (talk) 07:41, 22 September 2017 (UTC)

Cube (algebra)

Special:Diff/802466739. Where is x=0 here? --ㅂㄱㅇ (talk) (Bieup Giyeok Ieung) 10:37, 26 September 2017 (UTC)

Using Graded Free Resolutions

I saw you deleted my section on graded free resolutions for the Hilbert polynomial page. Your comment said "deleting the recently added section, before moving, renaming and rewriting it: free resolutions are not useful for computing Hilbert series and Hilbert polynomials". This is in fact not the case since you can compute the Hilbert polynomial from the graded free resolution. We are using this in slightly different language when discussing the usage of the Euler characteristic. Can you please put this section back? — Preceding unsigned comment added by 75.166.193.229 (talk) 03:15, 20 September 2017 (UTC)

This should be discussed in the talk page of the article (Hilbert series and Hilbert polynomial).

This is true that "you can compute the Hilbert polynomial from the graded free resolution", if you know a free resolution. But, as said in the present version of the article, free resolutions are never used for computing Hilbert polynomials, because free resolutions are more difficult (or, at less not easier) to compute than Hilbert polynomials. This for this reason that I have moved the relevant content of your edit in the (new) section Hilbert series and Hilbert polynomial#Relation with free resolutions. If you think that this new section is incomplete or wrong, please, discuss it on the article talk page, but, for the moment, I do not see any reason to prefer your version to mine. D.Lazard (talk) 09:54, 20 September 2017 (UTC)

I have added numerous examples demonstrating the power and ease of computability for free resolutions. Username6330 (talk) 06:00, 29 September 2017 (UTC)

October 2017

Your recent editing history at Muhammad ibn Musa al-Khwarizmi shows that you are currently engaged in an edit war. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See BRD for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

Being involved in an edit war can result in your being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.
- LouisAragon (talk) 11:40, 8 October 2017 (UTC)

Gaussian integer: your edits

I see, that you have moved my last comment on this talk page to the archive. Since it was posted only 2 weeks ago, and your talk page is not overloaded, I do not agree with this action; probably you did it for only one reason: other editors should not see it anymore. Therefore, I post it here in the following again:

---

I am writing this final remark as consequence of the dispute with you on the Talk:Gaussian integer page, which lingered for nearly one month. Therefore, I think to know, what I'm talking about. You have deleted and rewritten all my edits on Gaussian integer based on claims, which always turned out to be wrong. But this did not stop you in any way. Instead, you continued to rewrite the whole page in your very personal manner (which apparently is the only right one, others are 'old fashioned'), no matter if eg. the context of figures was lost by using other symbols, etc. Of course, I have no problem with extensions and corrections of my edits, that is usual practice and generally improves pages. But what you are doing is unacceptable. For me, you act as if you were the owner of the page.

Probably, you think that your edits are a great support for WP. I believe, the opposite is true: because you show no respect for the work of other voluntary editors (like me), they are discouraged to contribute to WP. Personally, I will never again write anything on any page, which you seemingly 'own'.

BTW: I am writing this comment not in the hope, to change your behaviour, but as benefit for other editors, which have to struggle with you, too.

--Wolfk.wk (talk) 13:32, 10 October 2017 (UTC)

It is not me who have archived your comments. This is a bot who has been programmed, a long time ago, for archiving threads (not single posts) after 10 days without edits. The archive can be read by anybody by simply clicking on the box "Archive" on the top of this page.

In any case, your comments are misplaced here. It should have been posted on Talk: Gaussian integer, for. being accessible to everybody interested on this subject.

Since our edits four different editors have edited the article, and none has complained about my edits. One has reverted your last edit. This suggests that there is a WP:Consensus that was I have done is far for being "unacceptable".

Finally your assertion "the context of figures was lost by using other symbols" is definitively wrong, since, in my last version, I have kept your notations, although there are not coherent with the remainder of the article. D.Lazard (talk) 15:14, 10 October 2017 (UTC)

Log scale

Hi, I see you reverted my edit on the log scale in Number line. Let me clarify: as the ticks on a log scale are by factors of 10 apart: 1, 10, 100, 1000, ..., there is no 0. The continuation to the left is 0.1, 0.01, 0.001, ... never reaching 0. Now the logarithms of these ticks are, of course, ..., -3, -2, -1, 0, 1, 2, 3, ... but these are not written next to the scale. (Which is why the term "log scale" is unfortunate, it should be called "exponential scale".) The "log scale" has an origin, but its place corresponds to the number $1=10^{0}$, not its logarithm 0.

--Benzh (talk) 14:00, 24 October 2017 (UTC)

To editor Benzh: We are both partially right: In both cases the text is confusing, as it is never said that this "logarithmic number line" is aimed to represent only positive real numbers, and, for this reason, it is 1 instead of 0 that is placed at the origin. I have reverted your edit, because I have misunderstood both versions. I'll try to fix the problem. D.Lazard (talk) 14:30, 24 October 2017 (UTC)

Thanks and a question

Hi, D.Lazard,

Thanks for all the work you’ve put in on the math articles! And thanks for your recent answer at Talk:System of polynomial equations.

I have a question on that topic that I’ll ask here because it probably could not lead to any additions or clarifications in the article. If we have a system of polynomial equations in n variables, and we know one solution $(x_{0},y_{0},\dots ),$ is there some way to “divide out” the solution to obtain a lower-dimensional system, as we would for a single equation in a single unknown? Loraof (talk) 23:56, 1 November 2017 (UTC)

As asked, the answer is clearly no. However, if one knows that some component of the algebraic set of the solutions belong to an hypersurface, one may divide them out by saturation. This is widely used for eliminating the degenerate solutions that occur frequently in applications. D.Lazard (talk) 09:31, 2 November 2017 (UTC)

Thanks !

I just saw your edit on the Continuous function page and I wanted to thanks you for it as I was going to make a similar edit. Pyrrhonist05 (talk) 17:07, 9 November 2017 (UTC)

Hypersurface

Daniel, please respond to my talk entry to the Hypersurface article. Meilleurs vœux! Simiprof (talk) 20:17, 15 November 2017 (UTC)

Thank you and a question

Thank you for checking and reverting my mistaken edit of the Sylvester matrix article.  I was going to revert it myself as $p_{m-n}^{m}\neq p_{n}^{m}$, assuming your $p$ symbol meant number of permutations of m-n objects selected from a set of m objects.  Please forgive my ignorance.  What does your $p_{m}^{m-n}$ symbol stand for?  If not number of permutations, then what?  May I suggest that you add an explanation for ignorant people like me?  Perhaps you meant the {m-n}th power of the highest coefficient, $p_{m}$, of the first polynomial?  If so, it would help readers like me not to see $p_{m}^{m-n}$ as a permutation symbol, if you could add a couple of words.  Howard McCay (talk) 19:59, 20 November 2017 (UTC)  (Sorry, forgot to sign.)

———————————————————————————————————————————————————————————————————————————————————————————————— — Preceding unsigned comment added by Howard McCay (talk • contribs) 18:20, 20 November 2017 (UTC)

To editor Howard McCay: $p_{m}^{m-n}$ is the standard notation for $p_{m}$ to the power $m-n.$ The use of the notation $p_{m}^{m-n}$ for counting permutations is standard only in combinatorics, and, even there, must be defined before its first use. D.Lazard (talk) 18:45, 20 November 2017 (UTC)

———————————————————————————————————————————————————————————————————————————————————————————————— Thank you again for the clarification.  Thank you for teaching me how to read a math article.  Sorry for all the trouble.  Howard McCay (talk) 19:59, 20 November 2017 (UTC)

Thank you

Thank you for your last three edits of the article Field extension.  Each of them has made that article easier to read.  Your edit of 05:22, 21 November 2017 replaced the example (which used the symbol $\mathbb {Q}$ instead of explaining to the novice that the example was an extension of the rational number field) with the better example of the complex number field as an extension of the real number field.  Your superior example made my attempted edit unnecessary.  It is my desire that mathematics articles by accessible to beginners (like me), so I am tempted to add links for unexplained math symbols and terms at their first occurrence in an article.  Your edits improve that article in that it now explains everything as it appears and does not introduce any unexplained symbols with which a beginner might not be familiar.  Thank you.  Howard McCay (talk) 06:39, 21 November 2017 (UTC)

Hilbert Polynomial

Hi D. Lazard,

I have written up a rebuttle for the hilbert polynomial page. Let's try and figure out how to incorporate the material I've written about using free resolutions since this they are the categorification of the hilbert polynomial (and are important for living in the derived world...)

Username6330 (talk) 21:22, 1 December 2017 (UTC)

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From PBadali

Dear Professor Daniel Lazard, I am Alireza Badali Sarebangholi from Iran, once you said me if I have a question I can come to your page and I thank you for your attention and help to me.

Yours Sincerely, Alireza Badali Sarebangholi Alireza Badali (talk) 09:58, 5 December 2017 (UTC)

Question $1$: Let $r:\mathbb {N} \to (0,1)$ is a function given by $r(n)$ is obtained as put a point at the beginning of $n$ like $r(34880)=0.34880$ and similarly consider $\forall k\in \mathbb {N} \cup \{0\}$ $r_{k}:\mathbb {N} \to (0,1)$ by $r_{k}(n)=10^{-k}\cdot r(n)$ and $\mathbb {P}$ is the set prime numbers now is $\{t^{i}\,|\,t\in r(\mathbb {P} )\}$ dense in the $\{z\in \mathbb {C} \,|\,|z|=1\}$ and is $\{s\cdot t^{i}\,|\,s,t\in \bigcup _{k\in \mathbb {N} \cup \{0\}}r_{k}(\mathbb {P} )\}$ dense in the $\{z\in \mathbb {C} \,|\,0.1\leq |z|\leq 1\}$. Alireza Badali (talk) 18:04, 6 December 2017 (UTC)

I know that there is a wide literature about the density of sequences based on prime number, but I do not really know this subject, and, so, I am unable to answer to this kind of questions.

Sincerely. D.Lazard (talk) 18:30, 6 December 2017 (UTC)

Anyway, thank you so much, but am not I annoying in your page? Alireza Badali (talk) 18:50, 6 December 2017 (UTC)

No problem. D.Lazard (talk) 18:57, 6 December 2017 (UTC)

Thank you. Alireza Badali (talk) 13:05, 7 December 2017 (UTC)

Sorry Professor Daniel Lazard I thought this question is a spam in your page please forgive me for this careless. Alireza Badali (talk) 18:33, 7 December 2017 (UTC)

Question: What is rule of this sequence: $2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,...,k,k,k,...,k,...$ that $k$ repeats $k-1$ times. Thanks in advance. Alireza Badali (talk) 14:55, 10 December 2017 (UTC)

What is your definition of a rule? Your definition of the sequence is a rule. I guess that you mean a function f(n) expressed in the language of elementary mathematics, but there is no workable definition of such a function. For example a recurrence relation is a function where f(n) is defined by using the values of f(k) for k < n. Although I guess that you want avoid this, this is a perfect rule for defining a sequence. In my opinion, the simplest definition for a rule is "a computer program that computes f(n) for the input n". This has been formalized (a long time before computers) by the concept of primitive recursive function; your sequence is clearly a primitive recursive function.

On the other hand, I guess that, from your point of view, the best answer for your question is

$f(n)=k,$ where k is the smallest integer such that $k(k-1)/2\geq n.$

This may be rewritten, using the ceil function,

$f(n)=\left\lceil {\frac {1+{\sqrt {1+8n}}}{2}}\right\rceil .$

IMO, none of these formulas is useful, as they hide the main properties of the sequence. D.Lazard (talk) 15:58, 10 December 2017 (UTC)

Thank you so much this function is very good, and I mean was function by rule (My English isn't good unfortunately). Alireza Badali (talk) 17:54, 10 December 2017 (UTC)

Question: What is love to mathematics? what does math mean? is love to math love to knowing? does mathematics include all other sciences? and finally what is love to knowing? when I see your relation by $f(n)=\left\lceil {\frac {1+{\sqrt {1+8n}}}{2}}\right\rceil$ I enjoy math when I see $8n$ and $1+8n,$ though I can't understand how you wrote it. why should I love math? what is this feeling in me? Alireza Badali (talk) 16:30, 11 December 2017 (UTC)

I will answer to "What is love to mathematics?" and to "what is love to knowing?", when you will be able to give a commonly accepted answer to "What is love?" For "does mathematics include all other sciences?", the answer is definitively no. For "what does math mean?", I doubt that you will find two mathematicians that will give you the same answer. For all these questions, the best that you have to do is to learn philosophy. However, I doubt that it is easy in Iran, because of the religious laws. D.Lazard (talk) 16:58, 11 December 2017 (UTC)

I asked you because I think you love math and hence your answer is philosophy! I don't know exact meaning of philosophy from your viewpoint or philosophers of course I believe without philosophy thinking on mathematics is impossible and skill in mathematics is dependent to skill in philosophy. Alireza Badali (talk) 18:39, 11 December 2017 (UTC)

As for me, love of math is best expressed in "Jonathan Livingston Seagull"; and aversion to math – in "The Snow Queen". 77.126.123.111 (talk) —Preceding undated comment added 09:57, 14 December 2017 (UTC)

Thank you, I shall read these novels of course I like novel. Alireza Badali (talk) 18:14, 14 December 2017 (UTC)

I read the book Jonathan Livingston Seagull, and it is a good book but I didn't understand you mean. (and I don't need to read the latter book.) Alireza Badali (talk) 19:40, 23 December 2017 (UTC)

Assume $\forall m,n\in \mathbb {N}$

${\begin{cases}n\star 1=n\\(2n)\star (2n+1)=1\\(2n)\star (2m)=2n+2m\\(2n+1)\star (2m+1)=2n+2m+1\\(2n)\star (2m+1)={\begin{cases}2m-2n+1&2m+1>2n\\2n-2m&2n>2m+1\end{cases}}\end{cases}}$

clearly $(\mathbb {N} ,\star )$ is a cyclic group, $\langle 2\rangle =(\mathbb {N} ,\star )\cong (\mathbb {Z} ,+).$

and let $Q_{1}=\left\{{m \over n}\,|\,m,n\in \mathbb {N} \right\}$, it is clear $(Q_{1},\star _{1})$ is an Abelian group with:

${\begin{cases}\forall m,n,u,v\in \mathbb {N} \\({m \over n})\star _{1}1={m \over n}\\({m \over n})^{-1}={m^{-1} \over n^{-1}}\qquad m\star m^{-1}=1=n\star n^{-1}\\{m \over n}\star _{1}{u \over v}={m_{1} \over n_{1}}\star _{1}{u_{1} \over v_{1}}={{m_{1}\star u_{1}} \over {n_{1}\star v_{1}}}\quad {\text{if}}\,\,{\begin{cases}{m \over n}={m_{1} \over n_{1}},\,\,{u \over v}={u_{1} \over v_{1}},\,\,{mu \over nv}={m_{1}u_{1} \over n_{1}v_{1}}\\\gcd(m_{1},n_{1})=\gcd(m_{1},v_{1})=1\\\gcd(u_{1},n_{1})=\gcd(u_{1},v_{1})=1\end{cases}}\end{cases}}$

I mean is first simplification of fractions and then calculation like ${44 \over 12}$ that gets ${11 \over 3}$.

Question: does $(Q_{1},\star _{1})\cong (\mathbb {Q} ,+)$?

Problem: Suppose $N_{1}=\{(m,n)\,|\,m,n\in \mathbb {N} ,\,\gcd(m,n)=1\}$, make a group on $N_{1}$ correspondence to $(Q_{1},\star _{1})$ in terms of members production and isomorph to $(Q_{1},\star _{1})$.

Thanks in advance. Alireza Badali (talk) 12:06, 27 December 2017 (UTC)

Am not I welcome here?! Alireza Badali (talk) 22:01, 28 December 2017 (UTC)

You are welcome, but I am not here to solve at your demand any problem that you imagine, nor for decoding what you are trying to do. Here, you start by encoding (that is representing) the integers by their rank in the sequence (0, 1, -1, 2, -2, ...), and your operation $\star$ is simply the translation of the addition of the integers on this encoding. In the second part of the question you try to define the addition of rational numbers represented as a pair of encoded integers. For this, it does not suffice to have the addition of encoded integers, but you need also the multiplication of encoded integers (needed for testing the equality of fractions). Thus your real question is: how computing the basic operations on the rational numbers from the basic operations on the encoded integers? The answer is: start from the description of the operations on rationals in terms of operations on integers, and replace every operation on integers by the corresponding operation on encoded integers.

Please, avoid unnecessary formalism, or, at least, explain in words what the formalism is supposed to formalize. Also, I am not willing to solve any problem that you want to solve. Nevertheless, if you are blocked because you lack some knowledge, I am ready to tell you where getting the missing information. D.Lazard (talk) 23:09, 28 December 2017 (UTC)

Thank you so much for your attention and help to me, yes of course you are right. Alireza Badali (talk) 11:11, 29 December 2017 (UTC)

Notification

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. — Preceding unsigned comment added by Karjam (talk • contribs) 09:54, 1 January 2018 (UTC)

User Badaly again

What has gone wrong about me?! Alireza Badali (talk) 17:51, 1 January 2018 (UTC)

To editor PBadali: Too vague question for being answered. Maybe you believed that the preceding notification was addressed to you, while, being on my talk page, it was clearly addressed to me. D.Lazard (talk) 19:10, 1 January 2018 (UTC)

Sorry, my mistake, I saw that message in the From PBadali so I thought might my presence in your talk page has made a bug! I didn't have another purpose! Alireza Badali (talk) 22:36, 1 January 2018 (UTC)

Possibly I am annoying here! Alireza Badali (talk) 23:04, 1 January 2018 (UTC)

No problem. However, I have to recall you the guidelines for user talk pages, which says Wikipedia is not a social networking site, and all discussion should ultimately be directed solely toward the improvement of the encyclopedia. So, it is possible that another user will send warnings about this. Also, if I do not answer to some question, this does not mean any problem, this means either that I am busy for some other work, or that, for any reason, I am not willing to answer to this specific question. You can also use Wikipedia:Reference desk/Mathematics, where other editors use answering questions like yours. D.Lazard (talk) 13:53, 2 January 2018 (UTC)

Thank you so much for your attention and help to me, yes and I am learning about wikipedia further though I still have some defects. Alireza Badali (talk) 16:09, 2 January 2018 (UTC)

A little advice that is valuable in an occidental environment, but maybe not in your country (different cultures have different behavioral rule): Everybody "still has some defects", but the person to whom you are talking may have not remarked them. Thus, it is counterproductive to insist on them or to apologize for them. So, avoid to be negative about yourself. D.Lazard (talk) 16:59, 2 January 2018 (UTC)

Thank you for your guidance, you delivered good advice and I agree with it (though when I focus on a issue I do feat.), but Iranian people are very better than me because they are sage and unique and number one in the world (although apparently isn't such and maybe it is a secret yet.) and I live into a dreamy world hence obviously I don't know many social behaviors, but generally when I do an incorrect behavior I know an obligation for me to apologize honestly. Alireza Badali (talk) 17:48, 3 January 2018 (UTC)

Zeros and poles

Hello D. Lazard, I agreed at Talk:Zero of a function#Merge Zero (complex analysis) with your plan to create an article Zeros and poles and merge the existing information and links accordingly. How about if we do this together? How can we split up the work? Since you are more familiar with the subject, I am fine with ceding the driver's seat to you. — Sebastian 13:28, 11 January 2018 (UTC)

I have just finished to put Multiset in an acceptable shape. I'll look to these articles in a few days. D.Lazard (talk) 18:31, 12 January 2018 (UTC)

To editor SebastianHelm: I have proceeded. Please, verify that everything is correct. D.Lazard (talk) 15:40, 15 January 2018 (UTC)

Thank you! I will look at it in the next couple days. — Sebastian 17:35, 15 January 2018 (UTC)

Now I found the time to look at it. There isn't much I changed in the article; most of what I did was create incoming links. One thing I realized, though, was that there is another symmetry of terms that is not yet expressed in the article: That of multiplicity [of zeros] and degree [of poles]. For instance the lede of Valuation (algebra) currently has three links in "consideration of the degree of a [[pole (complex analysis)|pole]] or [[Multiplicity (mathematics)|multiplicity]] of a [[zero (complex analysis)|zero]] in complex analysis". Currently, "multiplicity" is defined in Zeros and poles § Definitions, while we don't have a definition for "degree". To make matters worse, "degree" is used interchangeably with "order". (Similar case at Argument principle, where only "order" is used instead of "degree".) Please also note my comments on the article talk page. — Sebastian 16:42, 17 January 2018 (UTC)

Geometric Algebra Page

Your edit has been reverted by 2 independent editors, you may not just rerevert because you happen to think you are right and we are wrong; if you wish to make further edits in the same space then I suggest you raise the matter up in the talk pages and explain precisely why you think you are right and we are wrong and we will do likewise.Selfstudier (talk) 13:18, 16 February 2018 (UTC)

Division is anticommutative

Your revert of the fact that division is anti-commutative is not backed up by any evidence.

The statements as follows are correct;

Given that $1$ is the right identity for division

$x\div 1=x$

then

$x\div y=1\div (y\div x)$

or in fraction form

${\frac {x}{y}}={\frac {1}{\frac {y}{x}}}$

You are claiming otherwise? — Preceding unsigned comment added by 147.147.104.5 (talk) 11:38, 9 March 2018 (UTC)

Reason of delete my material

i do not know why you delete my material. I agree the first two attempt to modify it have copyright issue. but I do not think the last revision has anything inappropriate. Please do not abuse your authority and please give me the reason Jianguopku (talk) 15:13, 17 March 2018 (UTC)

To editor Jianguopku: I have given the reasons of my last revert in the edit summary which was "Per as WP:OR and WP:COI". If you follow the first link, you will see that original research is forbidden in Wikipedia, and that your addition is original research as appearing in a single article, which is not referred to by any secondary source. Moreover, this article is not a reliable source, as not being peer reviewed (the journal has not any scientific committee, nor scientific editors that can organize the referee process). The second link provided in my revert summary is related to your conflict of interest: it is clear that you are the author of the article you want cite in Wikipedia. In such a case, you must not edit the article yourself, but you must request an edit on the talk page, with the template {{edit request}}.

By the way, if there were not problems of original research and conflict of interest, I would have also reverted your edit, for several reasons. It is misplaced: the section is about the nature of plane sections, and not about the way of computing them. It is too specific for an encyclopedia as it supposes a specific way for representing ellipsoids (not the most widely used). It is confusing, as not distinguishing between the problem of computing a plane section, and the problem of, given an ellipse, to compute its axes (the latter belonging to ellipse). D.Lazard (talk) 16:17, 17 March 2018 (UTC)

Euclidean Algorithm for Greatest Common Divisor

Sorry, but you don't have any scientific arguments. Please test our work and you will see that it is faster than Knutn's realizations in all cases.

This is completely new way for realization of Euclidean algorithm and it will reflect to many books in algebra, number theory and discrete mathematics.

Gruyio (talk) 16:36, 17 March 2018 (UTC)

Several scientific argument have been given in the edit summaries of the reverts. Here is a deeper argument: In your paper, you show only that, on a specific visual C compiler, derecursiving half of the recursive calls save 30% of the computing time. This does not show that your algorithm is better. This shows only that, on this specific implementation, most of the time is spent on recursive calls. Apparently, this is because tail-recursion is not recognized by the compiler or is badly implemented. Your claim of having improved the algorithm would be scientifically valid, if you would have tested this on various computers and in various languages, and if you had searched why tail-recursion does not work. As it is, your article is of no scientific value. D.Lazard (talk) 17:11, 17 March 2018 (UTC)

You can see that pseudocode is optimized and it is independent of compiler. So you can write solutions on different languages to see that result is the same. You are editor in Wikipedia. You obviously do not understand this task moreover you cannot perceive the many different solutions that exist. Your work is to test what contributors make.Gruyio (talk) 17:52, 17 March 2018 (UTC)

No, Wikipedia is not a scientific publisher. The role of Wikipedia editors and contributors (they are the same people) is to built an encyclopedia. They have not to review sources. They have only to verify that added content is sourced and has been verified and validated by secondary reliable sources. D.Lazard (talk) 18:13, 17 March 2018 (UTC)

The cited source also apparently does not exist. Sławomir Biały (talk) 20:28, 17 March 2018 (UTC)

For the record, the above Google page shows that the cited source should appear in March 2018. That is, it does not exist yet. Also, my above comments are about a paper cited in an edit summary, paper that is published, but would never pass any serious referring procedure. D.Lazard (talk) 09:17, 18 March 2018 (UTC)

Factorization

In factorization, the factors are always simpler than the product by some measure. In the case of $x^{n}-1=(x-1)(x^{n-1}+x^{n-2}+\cdots +x+1)$, the factors are of lower degree. — Preceding unsigned comment added by Magyar25 (talk • contribs) 15:53, 18 March 2018 (UTC)

Slider-crank linkage

Please help with the Slider-crank linkage article as well. Thank you. — Preceding unsigned comment added by 97.98.78.51 (talk) 17:12, 18 March 2018 (UTC)

Edits at Integer

Hey. I'm assuming that this edit where you changed "Moreover, Z is a principal ring" to "Moreover, Z is a principal ideal" was inadvertent? See the recent two edits here and here. Paul August ☎ 15:41, 23 March 2018 (UTC)

OOOPS, I intended to remove the right part of the pipe, and I removed the left part. Reading this, it appears that this sentence is essentially duplicated by the last sentence of the section. I'll fix this. D.Lazard (talk) 16:22, 23 March 2018 (UTC)

Yeah that's what I thought. Paul August ☎ 20:03, 23 March 2018 (UTC)

About polynomial function

I strongly disagree with your decision to redo my changes to Polynomial function. As said in the article, this is not a content fork, the concept of polynomial and polynomial function are NOT the same thing (the polynomial X(X-1) is non zero in Z/2Z but the associated polynomial function is). Notice also that there are specific articles about polynomial functions in a lot of other languages.

I know the article is lacking sources right now, I am working on it. But I don't think redo my changes (decided by yourself alone) without discussing it first is a clever way to do things on Wikipedia.

Valvino (talk) 09:10, 8 April 2018 (UTC)

Not the right place for this discussion. I'll answer on the talk page of the article. D.Lazard (talk) 09:24, 8 April 2018 (UTC)

"as explained below"

makes life difficult for readers (it is unexplanatory and vague; it also suggests information is being presented in the wrong order), and two in one sentence is really over the top! --JBL (talk) 10:34, 9 May 2018 (UTC)

Square-free integer

I appreciate the work you've done on this article. Please try to cite your sources, as many Wikipedia math articles are quite paltry when it comes to verifiable, inline sources. Wqwt (talk) 08:37, 16 June 2018 (UTC)

To editor Wqwt: I agree that sources are important, but content (understandability, context, ...) is also important. It appears that, in mathematics, editors who are good for writing articles and editors that are good for finding sources are not always the same. In my case, after a long mathematical career, I am generally unable to remember where I have learnt things that I know. It is thus difficult for me to provide sources. In the case of my edits in this article, one may think of them as aimed for making WP:CALC applicable to it. In fact, as soon as the content is expressed in terms of the prime factorization, everything becomes trivial. This is probably the reason why square-free integers are not widely considered in textbooks. As far as I know, the concept has been introduced for integers only by analogy with the more important concept of square-free polynomial. This is the reason for having expanded the comparison with polynomials at the end of the section. D.Lazard (talk) 09:17, 16 June 2018 (UTC)

I find most of my sources by Google, in particular Google Scholar. I don't trust my memory and it is always nice to have a source to back up my beliefs. There is also more info to be learned from looking over these papers. I'm not concerned with WP:CALC stuff like factoring 54, but with higher level math claims (like those about time complexity) which aren't obvious at all. Wqwt (talk) 09:27, 16 June 2018 (UTC)

3RR warning

Hi! I have been discussing the changes to the e page on its Talk page. It seems that a couple of people really really want the table I edited to end with the Wozniak entry. Wozniak is definitely a cool guy and that seems to be the impetus for some to undo my addition; I have, can, and will defend my position, however, and wish you had read the thread before undoing my entry. (Some find the addition acceptable.) Since I rarely edit Wikipedia pages, I do not know how to move this dispute up the chain. If you could let me know, I'd be most grateful. Thanks. Owlice1 (talk) 18:01, 7 July 2018 (UTC)

To editor Owlice1: When you have been reverted by six different editors, this means that there is a strong WP:Consensus against your edit. So, continuing this dispute is WP:disruptive editing. The best you have to do is to give up. D.Lazard (talk) 18:11, 7 July 2018 (UTC)

There is not strong consensus, however. There does seem to be vicious protection of the Wozniak entry. I like Wozniak a great deal, but liking him is a silly reason to prevent someone from editing the page to present a useful addition; it appears a few people really want his entry to stand as last and have banded together to make that happen. There's no clique like a Wikepedian clique, alas. Owlice1 (talk) 18:48, 7 July 2018 (UTC)

Chinese remainder theorem

You ring please. I should have written about it. I would correct the changes. I will surely think over soy a mistake. Best regards, Alpha-Gamma (talk) 17:26, 23 July 2018 (UTC)

• Million, Million apologies!!

I slept badly now, wanted to solve a problem. I understand - it is silly, but there is a wish to bring a question to the logical termination. How to you this primitive option?

${\begin{aligned}x&\equiv a_{1}{\pmod {n_{1}}}\\&\ \ \vdots \\x&\equiv a_{k}{\pmod {n_{k}}},\end{aligned}}$

Alpha-Gamma (talk) 13:29, 25 July 2018 (UTC)

This version (with 2 spaces for aligning the \vdots) renders well on my browser. However this kind of manual alignment is generally not recommended, as not being robust on all browsers. I am not sure that improving the alignment of \vdots is useful, but, if you do it, I'll not revert you. D.Lazard (talk) 14:40, 25 July 2018 (UTC)

• Thanks. With the best, Alpha-Gamma (talk) 18:56, 25 July 2018 (UTC)

Residue number system

1. Thanks a lot for remarks. This information for me new. Is over what to think. On the other hand, if not to make mistakes, then there will be no progress also. You first who pointed to me to it. It is important for me. Thanks a lot.
2. I did not begin to edit article Chinese remainder theorem more. I seem because of the persistence overstepped the limits of ethics a little. But I recognize what from "small is under construction big". When I only began to work in LaTEX (about 20 years ago) for me there was a big problem to put a point symbol in the right place. Also there was nobody to help (none of my acquaintances in LaTEX worked). It is a shame to me before User:Magidin, it could think that I am some "easy rider". I am not a mathematician, but I work in the field of applied mathematics. And I have a habit — to bring the matter to the logical end, whether it be big business or small. It can sometimes be perceived as violation of norms of ethics. But it not so.
3. I very badly know English and did not begin to do to a pm other changes. In particular I very much do not like the example taken out of a context: "(3) decimal = (3 | 1) _{RNS(4 | 2)} (7) decimal = (3 | 1) _{RNS(4 | 2)} ". What is RNS(4 | 2)? Me is clear, and to the reader — no. I will try to change it, I do not promise good English.
4. Do you consider that the paragraph "Associated mixed radix system" should be deleted from article? The matter is that it is very important method for RNS. I am an expert in this area.
5. And the last. For me there was "riddle" a question: why it is not necessary to draw a brace "{" before the system of congruences? Why User:Magidin objects to it?

I try to study on the mistakes and I do not hesitate to speak about it.

With the best ... Alpha-Gamma (talk) 10:54, 29 July 2018 (UTC)

To editor Alpha-Gamma:

Item 5: In my opinion, brace or not brace is a question individual preference. As far as understand, braces are mainly used in education and elementary mathematics, while they are less used in advanced and professional mathematics.

About the section "Associated mixed radix system": I removed it because this is WP:OR, and also because its content is wrong. If fact, the AMRS representation of an integer depends on the order of the moduli, while the RNS representation is independent of this order. Thus the AMRS (as defined in this section) is not well defined, and represents integers that have nothing to do with the integer represented by the RNS.

About the remainder of the article: it has multiple issues, which I will discuss in article's talk page. D.Lazard (talk) 12:52, 29 July 2018 (UTC)

Cantor and transfinite numbers

Hi D.,

you made this edit with an edit summary that said Cantor revolutionized the way of thinking of infinite sets, but did not introduced infinite or transfinite numbers.

I don't object to the edit itself, as the new sentence you removed was awkwardly connected to the paragraph. But I can't figure out what you meant by the edit summary. Cantor did indeed introduce the notion of transfinite ordinal and cardinal numbers, and invented the "aleph" notation for the latter. --Trovatore (talk) 18:20, 2 August 2018 (UTC)

To editor Trovatore: Ok; I wrote the edit summary before reading more on the subject. Otherwise, I would have written an other summary. Nevertheless, I am not sure whether Cantor considered transfinite cardinals and ordinals as numbers or as tools for studying infinite sets. In any case, this is the way of thinking of infinite sets that has been revolutionized. The way of thinking about infinite numbers was not revolutionized, because, before Cantor, infinite numbers did not exist, and nobody was thinking about them. D.Lazard (talk) 19:57, 2 August 2018 (UTC)

Well, he called them numbers, or at least his translator, Philippe Jourdain, did. I spent a little time trying to find the original-language Beiträge to see if he used the word Zahl, but I have not succeeded (it's weird — you can find that issue of Annalen online in scanned-PDF form, but Cantor's contribution seems to be missing from it).

I agree that the sentence you removed was less than ideal. I'm undecided on whether we ought to mention Cantor at that location in the article. It wouldn't strike me as out of place to do so, but I'm also not sure it's necessary, as the concept has been sufficiently internalized by mathematics that it no longer seems Cantor-specific. --Trovatore (talk) 20:23, 2 August 2018 (UTC)

To editor Trovatore: IMO, a sentence on the historical context would be useful, something like: Ordinal and cardinal numbers have been introduces at the end of 19th century by Georg Cantor, when he initiated the study and the classification of infinite sets. — Preceding unsigned comment added by D.Lazard (talk • contribs) 21:06, 2 August 2018 (UTC)

Derivative and the mentioning of differentiability classes

Hello D.Lazard, you recently undid my edit on the page Derivative, where I removed what I believe to be a redundant link to the page Differentiability classes. My reason was that differentiability classes had been mentioned and linked to just above next to the C^k in the same sentence. In your edit summary you argued that the link is to an example of a differentiability class, which I don't understand considering it was just a link to Differentiability classes, not anywhere specific on the page, such as Smoothness#Examples. I understand the importance of linking to examples, especially on a page where readers may be learning, but the linking to the same page so close seems a little over the top for me, if the mention of differentiability classes could be combined into one more coherent sentence that would be fine enough for me, if you feel it would make more sense to remove the first link and restructure the second half I would also support that. —The Editor's Apprentice (talk) 22:56, 24 August 2018 (UTC)

To editor The Editor's Apprentice: The sentence was "For an example [that the condition is stronger] see ...". This means that this is not the concept that is linked, but the article of the same name. Thus this is not redundant. However, such a link to an example should be more specific and should mention the article title, not a redirect. I have edited the article for fixing this. Note that Smoothness is linked 3 times in the paragraph, and that none of the links is redundant. D.Lazard (talk) 09:50, 25 August 2018 (UTC)

Cool! I agree with the current revision thanks for working this out with me! —The Editor's Apprentice (talk) (contribs) 15:24, 25 August 2018 (UTC)

Function

Sorry, I don't know if this is the right place to lead discussion about entries on Wikipedia. You reverted back a change I (MBachtold) did on the function entry, saying "this is standard" terminology. Could you back that up please? Because it makes absolutely no sense to me to say that a modern function, like the one that squares its input is a function of x. On the other hand it is very well standard terminology to say that x^2 is a function of x and I could back that up with basically every calculus textbook since Euler to Peano. — Preceding unsigned comment added by Mbachtold (talk • contribs) 06:33, 29 August 2018 (UTC)

To editor Mbachtold: Normally this discussion should be placed at the end of the talk page of the article (Talk:Function (mathematics)) The sentence that you have edited is in a paragraph about a named function of a named variable. This does not apply to "the function that squares its input", as, this function and its variable are not named by this sentence. Many people say that $x^{2}$ is a function of x, but this is a wrong formulation as $x^{2}$ is not a function, but an expression. The correct formulation would be "the function $x\mapsto x^{2}$ is a function of x". Apparently, you seem to make a distinction between "modern functions" and the concept of function that was used "since Euler to Peano". Such a distinction does not exist, and the "old" terminology is still in use, at elementary level as well as at advanced level. Therefore, Wikipedia should reflect this common use. D.Lazard (talk) 08:55, 29 August 2018 (UTC)

To editor D.Lazard: Thanks for your reply here, I continued the discussion on the talk page of function. Let me just mention here that your phrase "the function $x\mapsto x^{2}$ is a function of x" is meaningless by all current standards of logic I'm aware of, since x is bound in the expression $x\mapsto x^{2}$. I tried to explain that over at the talk page of function.Mbachtold (talk) 09:00, 29 August 2018 (UTC)

To editor D.Lazard: Also, could you please point me to a standard reference on what it means for a function to have a named variable. I have never heard of that. Further you claim that a distinction between modern function and how the word function was used since Euler to Peano does not exist. I beg to disagree, and would point you to these discussions Who first considered the f in f(x) as an object in itself and who decided to call it a function and Formalizations of the idea that something is a function of something else.Mbachtold (talk) 09:26, 29 August 2018 (UTC)

To editor D.Lazard: Claiming "$x\mapsto x^{2}$ is a function of x" is like claiming "The truth value of $\forall x\in \mathbb {R} :x^{2}\geq 0$ depends on x". It makes no sense. Since you are not responding to my comments, I'll assume you have realized your confusion. In such a case I would kindly ask you to not only stop spreading this nonsense on Wikipedia, but to actively work against any further divulgation of it. Mbachtold (talk) 06:24, 31 August 2018 (UTC)

This discussion does not belong to this talk page, as related to a specific article, and duplicating a discussion at Talk:Function (mathematics). Therefore, this is the last time I'll reply here.

You are wrong when you write that "$x\mapsto x^{2}$ is a function of x" is a claim (that is a theorem). A sentence like "<something> is a function of x" is not a claim but a declaration, meaning that <something> must be viewed (interpreted) as a function of one variable (argument), which is named x for convenience. There is nothing mathematically wrong here.

Also, you are also wrong in distinguishing between ancient and modern definitions of function. Your error is to confuse the mathematical concept (here function) and the way people think of it (the intuitive view of it). The same function may be viewed as a process (old view), as a static object, as a relationship, as an element of a Hilbert space, ... None of these interpretations is a part of the mathematical definition of a function, and they are all compatible. D.Lazard (talk) 08:20, 31 August 2018 (UTC)

To editor D.Lazard: I pity your students. Again: What does it mean to view a function like the one that squares it’s input “as a function of x”, even as a ‘declaration’? You’re idea that maybe x\mapsto x^2 could be declared to be a function of x does not make any sense, since (x \mapsto x^2)=(y \mapsto y^2). In fact, x\mapsto x^2 is the SAME OBJECT as the function that squares its input, they are indistinguishable mathematical objects, just like 2/4 and 1/2 are! (If you don’t understand the difference between a free and a bound variable, you might want to catch up on that and stop considering yourself a expert on computer science in the mean time.) You’re error is to confuse the mathematical object (the function x \mapsto x^2) with its syntactic representation. I am not confused about the mathematical object f and the way people think of it, as you claim, because I have understood that for more than 200 years people did not call f the function, they called f(x) a function of x and often dropped the “of x” out of convenience (I doubt you read the links I provided, otherwise you would understand this). My change on the WP article was pertaining the the mathematical object f(x), not f (it would be a low point in this discussion if now I have to explain that f and f(x) are different mathematical objects.) It is f(x) that is ‘dynamic’, since it changes with x, it dependes on x, it is a function of x. The mathematical object f on the other hand is NOT a dynamical process in any reasonable sense. The second sentence of the WP article says ‘the position of a planet is a function of time.’ It might come as a surprise to you, but that poistion is NOT the function f, that position is f(t) and is being called a function of t. Finally, there was no consensus in the talk page where you reverted my last change, because only purgy tried to adress some of my points. But he did’t directly answer any of my questions or address my objections, he only tried to explain the strange point of view people hold around here, but didn’t succed. Neither have you. I’m copying this discussion on the TP of function, but I will also not write anything else, as I have given up hope that the people reverting my changes have understood anything of what I’m saying. Mbachtold (talk) 05:39, 1 September 2018 (UTC)

Your reversion at Sequence has been reverted

You reverted to a formula in error (signs), forcing me to repair your repair. You don't throw the baby out with the bathwater.

What's with the hasty drive-by press-the-magic-button wholesale revert? Do you read edit summaries? According to Sloane, N. J. A. (ed.). "Sequence A005132 (Recamán's sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation., the signs, to progress or regress were in error, which is why I had also added verbiage as a highlighter. I'll trust you to take the time to ammend the text to more closely conform with the formula. WurmWoode^T 20:52, 8 September 2018 (UTC)

Nobody is saying that Apostol's book is a bible.

Don't put words in my mouth, or apply Straw man. In what I wrote I never presented Apostol's definitions as the unique treatment of the subject. Actually, I explicitly added a sentence saying that it is common to use function to refer to mapping. — Preceding unsigned comment added by Cactus0192837465 (talk • contribs) 13:44, 9 September 2018 (UTC)

Once again, don't put words in my mouth

"In this case the name affine function is used ..." doesn't imply "always". You should really learn what straw man fallacy is. Cactus0192837465 (talk) 12:53, 11 September 2018 (UTC)

To editor Cactus0192837465: The problem is not what you wrote, but what can be understood by readers. As it was written, it was normally understood as a general rule, which it is certainly not. In other words, the previous formulation is likely to be interpreted as always by non-specialists, and that is what was meant by my edit summary.

By the way, you have introduced mathematical analysis in the second concept of linear function, but left "calculus and related areas" in the first concept. This is confusing, as calculus is the elementary part of mathematical analysis.

I apologize having been too rude, by talking of Bible. But some of your edits and posts in talk pages give the impression that you consider that Apostol's terminology is a standard that cannot be a subject of a discussion. Even if Apostol's book is an excellent reference, not all its terminology is universally used by mathematicians. Thus, WP:NPOV implies to present Apostol's terminology as a standard only when this is effectively the case. Your reference to straw man is irrelevant, as an edit summary are not a place for a discussion, and my edit summaries are not written for discussing. An edit summaries is aimed for explaining briefly the reasons of the edit. There should not be arguments there, and their content may be qualified as "fallacies" only if the edit itself introduces a fallacy. D.Lazard (talk) 13:35, 11 September 2018 (UTC)

As I said, that is your imagination, your own impression. I know very well what I am talking about when I write about mathematics. You can avoid all your mistaken interpretations by only describing in the edit summary your own edit. I understand that you have a need to being heard, having got to the end of your career and soon your life and being left to having to "write your own Wikipedia page". But you can express yourself, without having to smear others. Cactus0192837465 (talk) 21:20, 11 September 2018 (UTC)

Textbooks and citation

Hi, you just reverted my citation of a textbook. I’d probably edit the citation anyway as it does not source the sentence actually that there is a requirement that such a non controversial fact has to be sourced by published material. There probably is actually, but as far as I know we have to use our judgement in citing, and « reliable » (academic material) and well written are good reason to cite something. Actually, per https://en.wikipedia.org/wiki/Wikipedia:Verifiability#Reliable_sources it seems that university level textbooks are explicitly cited as citable, even if it’s not externally published material. Even blogs if they are written by competent people in the matter, on the same document, so … should this revert be reverted ? It does not seem very Wikipedish spirit to refuse good material just by principle. « Be bold » … TomT0m (talk) 15:05, 19 September 2018 (UTC)

To editor TomT0m: This is an external link to a personal website. As such, it can hardly be used, even in the "external link" section (see WP:ELNO). This could be accepted as a source only if there were no regularly published textbooks discussing this matter. For Hamel bases, they are plenty. Thus it would be much better to cite one of them. D.Lazard (talk) 15:18, 19 September 2018 (UTC)

I don’t really understand why you are referring to external links as it is not an external link … Anyway I think I’ll never quite understand very strict reading of the rules when their is really no obvious problem and the pages you cite are full of « one should generally avoid ». If you have a good reference please insert it but in my opinion it’s a shame avoiding a good one because of a (too, as it’s a university textbook so it pass the test) firm reading of the rules. As far as I understand, citations rules does not enforce the usage of the most existing source in the world, according to their own definition. TomT0m (talk) 15:49, 19 September 2018 (UTC)

Need some advice

I am contacting you because of your comments in Wikipedia:Verifiability/2012 RfC:

Strong support but move the note into the text. Rationale for moving the note: firstly, notes should be avoided in a lead. Secondly "verifiability, not truth" is a sufficiently longstanding and notable slogan for deserving to be clearly apparent in the lead. Otherwise this version is clear, simple and is the one which best resolves the following ambiguity. In a scientific context, especially in mathematics, "verifiability" and "truth" have not the same meaning as in Wikipedia: A theorem is true if and only if it has been proved, and a proof is correct if and only if it is verifiable by anybody. This ambiguity makes, sometimes, content discussions very difficult with unexperienced editors and also with some experienced editors with insufficient mathematical knowledge. A policy is aimed to make discussions easier, not harder. This version is the one that best resolves this ambiguity. D.Lazard (talk) 12:29, 3 July 2012 (UTC)

Recently, an article I rewrote a few years ago, Georg Cantor's first set theory article, was nominated for Good Article (see Talk:Georg Cantor's first set theory article/GA2). With feedback from the GA reviewer, I made improvements and the article achieved GA status. I did have some minor difficulties over my use of proofs, but I made an improvement and successfully cited WP:Scientific citation guidelines#Examples, derivations and restatements.

Next, the article was nominated for "Did you know?". The DYK editor has problems with at least two simple proofs that Cantor failed to give because he was communicating with his fellow research mathematicians. Since Cantor did not give these proofs, I provided them. I know that Wikipedia appeals to a wide audience, I wanted to make sure readers had a complete proof rather than expecting them to finish it. Currently, we are dealing with:

1. Proof of Cantor's uncountability theorem: I state that "Cantor does not explicitly prove his uncountability theorem, which follows easily from his second theorem." Then I supply a simple derivation of his uncountability theorem, which uses his second theorem.
2. The development of Cantor's ideas: I state "2. The proof by contradiction used to prove the existence of transcendental numbers from the countability of the real algebraic numbers and the uncountability of real numbers. Cantor's December 2nd letter mentions this existence proof but does not contain it." Then I supply a simple derivation (or proof) of the existence of transcendental numbers given the countability of the real algebraic numbers and the uncountability of real numbers.

I justify my derivations or proofs by the scientific citation guidelines, which not only permits the use of "simple derivations" but even allows an editor a further option: "it is often necessary … to provide a different derivation". I guess it could be said that I may be using a different derivation since Cantor gave no derivation.

I am currently involved in a discussion with this editor and would appreciate any advice you have. The DYK discussion is at Talk:Georg Cantor's first set theory article#Did you know nomination.

By the way, how did that RfC go? Also, I just checked WP:Good Article and found that there are only 63 good articles in mathematics. This is by far the least of any subject. Could be this caused at least partly by what you bring up in the RfC? Namely, "This ambiguity makes, sometimes, content discussions very difficult with unexperienced editors and also with some experienced editors with insufficient mathematical knowledge."

My plan is not to give up on GAs and DYKs. I think that mathematics needs more GAs. I didn't do the current GA nomination—the editor who wrote the first version of the article did. However, next summer I plan to nominate an article that I recently rewrote. Thank you, RJGray (talk) 17:44, 23 September 2018 (UTC)

I am not really interested in GAs and DYKs. My point is rather the number of articles that are among the most viewed ones and are (or should be) rated C. See my user page for having examples of what I mean. Generally I push such articles toward level B or A, but not higher as it is difficult for me to find sources that I consider as belonging to the common knowledge. Nevertheless, I try to add only sourcable content. When I know that sources are difficult to find for some reasons, I use WP:CALC (after all, a source is a computation), and provide a proof for insuring verifiability (for an example, see my edits on the relations between monomorphisms and epimorphisms one a one side, and injections and surjections on the other side, in Homomorphism: as this concerns many kinds of homomorphisms, it is difficult to find a source covering all of them).

On the other hand, I have often difficulties with articles on mathematical logic and their editors: As they like formal treatment, the intuitive interpretation is often laking, even if it has motivated the inventors of the theory. When I try to add some intuitive explanation, I am generally reverted, as an intuitive explanation is always formally wrong.

Otherwise, I am unable to give general advices. If you have specific point of discussion, I am ready to give my advice on them, but I need a specific link. D.Lazard (talk) 21:00, 23 September 2018 (UTC)

Arithmetic

I tried to expand the intro section of the article on Arithmetic with a Summarized version of the History Section. May I know what went wrong? Arman ^(Talk) 06:30, 24 September 2018 (UTC)

As the "History" section follows immediately the lead, this is not useful to repeat its content in the lead. Moreover, your addition is confusing, as it is not immediately clear for the reader that it is a summary of the section that follows. Moreover, devoting more than half of the lead to history is against WP:NPOV. D.Lazard (talk) 06:39, 24 September 2018 (UTC)

A thank you

Dr. Lazard,

I don't know if this is the place for such things, but I feel obligated nonetheless. I'm familiar with your work both on Wikipedia and in mathematics, but have never made the connection that the two people were one and the same until now. I want to thank you for all that you've done in my undergraduate and graduate studies and for your general contributions. Thank you. P.s. If this violates some WP policy, I apologize and ask for it to be deleted. — Preceding unsigned comment added by 2605:6000:FFC0:65:5C9D:6BCD:5A45:438A (talk) 08:53, 6 October 2018 (UTC)

Algebra revert

You were right: it was a more major edit than I anticipated, and I should have gotten consensus first; with that in mind, could you please look over my talk page post and lend me your opinion for the change? Thank you IntegralPython (talk) 16:14, 24 October 2018 (UTC)

typo in polynomials

Hi, I fixed some typos in the article on polynomial, these were mainly cosmetic, but nevertheless meaningful to comply with wikipedia mandated rules for math typesetting. The former html version, which you reverted, had many variables in roman when italic is the standard. In order to fix this I used latex math as I have no familiarity with html math typesetting. I hope this is reason enough to rerevert the changes I made. I didn't have time to do this everywhere, but I was hoping that by setting the example other contributors might help. cerniagigante (talk) 10:34, 1 November 2018 (UTC)

To editor Cerniagigante: I did not remarked that so many variables were in upside roman. I have fixed this. Note that for doing this, it suffices to put them between double quote (for example ''a''). If your edits were limited to polynomials, I would not have revert them. But, for inline simple formulas, html is generally preferred because of a better vertical alignment (the bad vertical alignment of inline latex is less visible when there are indices of exponents). In any case, thank you for pointing out this formatting error. D.Lazard (talk) 12:10, 1 November 2018 (UTC)

To editor D.Lazard:Thank you for your reply. I agree that vertical alignment is not great with mathjax, I just find the font difference between inline and displayed math distracting. Let's hope they fix this in the future. cerniagigante (talk) 07:19, 3 November 2018 (UTC)

To editor Cerniagigante: I, and most math editors also, agree with you for formulas written in simple html (sanserif font), such as abcdefgh. But the rendering with {{math}} template (abcdefgh) is acceptable and the differences with mathjax are, in general, not distracting. Moreover it is very easy to pass from abcdefgh to abcdefgh: it suffices to select the formula and to click on the button {{math}} in the menu "Math and logic" at the bottom of the edit window. Care should be taken that if "=" appears in the formula, one must add "1=" just before the formula (because of the general template syntax). D.Lazard (talk) 09:49, 3 November 2018 (UTC)

why don't you include material in talk page into article, it is relevant

You should probably review the material I have put into the talk page and include it in the article.

It is relevant and is understandable. You can read Dickson's reference to convince yourself it is actually math from Euler, and you can follow the mathematica example to show that the math can factor a 3 mod 4 semiprime.

Endo999 (talk) 11:47, 4 November 2018 (UTC)

This is for the Euler factorization article.

Endo999 (talk) 11:49, 4 November 2018 (UTC)

To editor Endo999: I agree that this method may deserve to appear in this article, but

• The English wording is poor, and I cannot understand what "at times" means in this context
• Per MOS:LEAD, the lead must be a summary of the content of the article. Thus, mentioning this method in the lead would be pertinent only if the details are given in the body of the article
• Per WP:LINKDD, talk pages must not be linked from articles
• The link to the talk page that you have provided is your original research, and cannot be accepted per WP:NOR
• I have no opinion whether this method is notable enough for having its place in Wikipedia, because you do not provide enough information. In particular, you do not mention clearly in which case it works, and in which case(s) it is useful (when it is faster than other known algorithms).

D.Lazard (talk) 12:56, 4 November 2018 (UTC)

You're welcome to read the Dickson reference if you wish. It's online. And McKee (in article references) [[1]] implemented the algorithm and said it was Big O(N^(1/3)). I have an example that shows it factors 3 mod 4 semiprimes, and is therefore more general than the more well known algorithm. Therefore, it is topical on that note alone. Endo999 (talk) 04:44, 5 November 2018 (UTC)

To editor Endo999: I could read these papers, but this would be useful only if I were willing to adding myself their content in Wikipedia, which is not the case. You may do that yourself, but you must fix the issues of your first tentative, and typically those that I have listed in my previous post. D.Lazard (talk) 09:30, 5 November 2018 (UTC)

A barnstar for you!

		The Tireless Contributor Barnstar
		For your many significant contributions to math articles. I would give you a math barnstar if one existed. Wqwt (talk) 03:59, 9 November 2018 (UTC)

ArbCom 2018 election voter message

Hello, D.Lazard. Voting in the 2018 Arbitration Committee elections is now open until 23.59 on Sunday, 3 December. All users who registered an account before Sunday, 28 October 2018, made at least 150 mainspace edits before Thursday, 1 November 2018 and are not currently blocked are eligible to vote. Users with alternate accounts may only vote once.

The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.

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Hello, D.Lazard. Voting in the 2018 Arbitration Committee elections is now open until 23.59 on Sunday, 3 December. All users who registered an account before Sunday, 28 October 2018, made at least 150 mainspace edits before Thursday, 1 November 2018 and are not currently blocked are eligible to vote. Users with alternate accounts may only vote once.

The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.

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hey why did you delete my add to the dimensions page

This is explained in the edit summary that appears when displaying the history of the page. D.Lazard (talk) 08:36, 6 December 2018 (UTC)

Primary source

hey James MacCullagh died in 1847, so an 1849 paper cannot possible be a "primary source" as you rushed to wrongfully claim and act! — Preceding unsigned comment added by 83.149.239.125 (talk • contribs) 14:25, 13 December 2018 (UTC)

A posthumous paper may clearly be a primary source, and this is the case here. D.Lazard (talk) 14:59, 13 December 2018 (UTC)

No it is NOT the case here Talk:MacCullagh ellipsoid and Galois axis. 83.149.239.125 is absolutely correct and you must look at that paper before you further embarrass yourself. That paper is NOT a primary source. It is NOT authored by James MacCullagh. You were and still is wrong, so do the homework which was already assigned to you and learn. You are not obliged to edit topics you do not understand. Cocorrector (talk) 13:54, 14 December 2018 (UTC)

For me, "An account of the late Professor Mac Cullagh's Lectures on that subject, compiled by the Rev. Samuel Haughton" means that this is a posthumous work of Mac Cullagh edited by Haughton. In any case, for Wikipedia, this is not a secondary source. Nevertheless, some other editors have provided reliable secondary sources and clarified the difference between MacCullagh ellipsoid, and the AfD discussion has been closed by a consensus for keeping. So there is not need to harass me about this. D.Lazard (talk) 14:22, 14 December 2018 (UTC)

A page you started (Parametrization) has been reviewed!

Thanks for creating Parametrization.

I have just reviewed the page, as a part of our page curation process and note that:-

This has been tagged for one issue.

To reply, leave a comment here and prepend it with {{Re|Boleyn}}. And, don't forget to sign your reply with ~~~~ .

Message delivered via the Page Curation tool, on behalf of the reviewer.

Boleyn (talk) 11:14, 23 December 2018 (UTC)

Metaphor

For you education. [2] Cactus0192837465 (talk) 22:18, 26 December 2018 (UTC) You can change 'representing' if you like. But that is certainly not a 'metaphor', it is 'diagram' [3] Cactus0192837465 (talk) 22:22, 26 December 2018 (UTC)

WP:3RR warning

Your recent editing history at function (mathematics) shows that you are currently engaged in an edit war; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See BRD for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

Being involved in an edit war can result in you being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.

On January 10, you did four times the same revert. It is possible that, before this warning, you ignored the WP:3RR rule of Wikipedia. Now this rule has been notified to you. So, the next time you will break it, I'll report your behavior to WP:ANI for an edit block. D.Lazard (talk) 19:29, 10 January 2019 (UTC)

You are the one engaging in edit war. I reverted and immediately added the section in the talk page to discuss what is wrong with what you wrote. You are the one reverting without going there to read the explanation of your lack of understanding of proper grammar. Cactus0192837465 (talk) 20:10, 10 January 2019 (UTC)

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. ---- Dlohcierekim (talk) 23:02, 10 January 2019 (UTC)

On invariance under change of polynomials

Hi! You've added $\deg C\leq \deg A-\deg B$ restriction for ${\text{res}}(A-CB,B)={\text{res}}(A,B)$. Although I think it's true for arbitrary $C$... What do you think on it? Adamant.pwn (talk) 14:52, 13 January 2019 (UTC)

To editor Adamant.pwn: If $\deg C>\deg A-\deg B$, the degree of the first polynomial changes, and this changes the value of the resultant if B is not monic, because of the coefficient $b_{0}^{d}$ in the formula

$\operatorname {res} (A,B)=b_{0}^{d}\prod _{j=1}^{e}A(\mu _{j}),$

where the $\mu _{j}$ are the roots of B. D.Lazard (talk) 17:04, 13 January 2019 (UTC)

To editor D.Lazard: Hmm, indeed. But it changes as well if $\deg C=\deg A-\deg B$ and $c_{0}=a_{0}/b_{0}$ which is the case in Euclidean algorithm because it reduces degree of $A$! So, formula still has to undergo some fixes. Adamant.pwn (talk) 20:25, 13 January 2019 (UTC)

To editor Adamant.pwn: Good point. Although your edits of the article are good, I have changed the presentation for making this clearer for non-experts, by making all cases explicit. If you disagree with my edits, it is better to continue the discussion on the talk page of the article. D.Lazard (talk) 11:55, 14 January 2019 (UTC)

I'm fine with current version, thanks! :) Adamant.pwn (talk) 17:21, 14 January 2019 (UTC)

Definition of the real number power

I define integer power as:

$a^{n}=a\cdot \quad \dots \quad \cdot a\quad (n\,{\textrm {times}})$

Now I want to define real number power via logarithms:

$a^{r}=e^{r\cdot ln(a)},\quad r\in R$

I can calculate $x=r\cdot ln(a)$, but the resulting x is again a real number, so I still don't know how to calculate $e^{x}$. You said the way of defining exp(x) —using integer powers— does not matter here. Thus far I can calculate integer power and rational power. How do I calculate $e^{x}$ according to the alternative definition? ale (talk) 11:30, 15 February 2019 (UTC)

To editor Ale2006: The alternative definition supposes the knowledge of the exponential function and the natural logarithm, and is better written as

$a^{r}=\exp(r\ln a).$

If one puts a = e in this formula, one gets

$e^{r}=\exp(r),$

if one knows that $\ln e=1.$ This explains why $e^{x}$ is commonly used for denoting $\exp(x).$

So, the alternative definition does not depend of any exponentiation, and this is why I wrote "the way of defining exp(x) does not matter here". The definition of the exponential function in terms of a power series is fine, but I do not like it, as it involves the non-elementary concept of convergence of a series, and does not explains the choice of particular coefficients. This is the reason for which I prefer to define the exponential as the unique function that equals its derivative and takes the value 1 for $x=0,$ and the natural logarithm as the antiderivative of $1/x$ that takes the value 0 for $x=1.$ Either of these two functions is inverse of the other because of the differentiation rule for inverse functions. As e is defined as $\exp(1),$ this shows $\ln e=1.$

Above considerations may be summarized as follow: For giving a definition, it is always useful to examine the other definitions that are hidden behind the used terminology. This is fundamental for avoiding circular definitions and for avoiding definitions that are unnecessary complicated or technical. D.Lazard (talk) 12:24, 15 February 2019 (UTC)

The current text only says that The natural logarithm ln(x) is the inverse of the exponential function. That defines the logarithm, not the exponential. If it were a definition of exp(x), it would have spelled The exponential function exp(x) is the inverse of the natural logarithm. That would indeed be circular, since most definitions of the natural logarithm suppose the knowledge of the exponential function.

Supposing the knowledge of exp(x) to define real number power sound circular to me, unless you somehow recall that exp(x) can be defined without knowing real number power. You preferred definition of exp(x) via derivatives is good, but it also implies the convergence of a Taylor series. And anyway it is missing from that subsection either... Heck! Right now I noticed that the previous subsection gives a definition of exp(x) in terms of a limit of integer powers. I hadn't seen it yesterday. That's why the definition seemed circular to me.

Perhaps, the convergence of a limit is easier than that of a power series? Let me try recalling it. If you still dislike my edit revert it again and I won't try any more times. Just try to read that paragraph ignoring the previous one. ale (talk) 17:39, 15 February 2019 (UTC)

rogue bot?

Hello,

As I understand it, your javascript bot undid the edit I happened to make yesterday on Angle trisection

I strongly suggest you give your bot some insights on mathematics, semantics and image analysis so that it doesn't invalidate valuable information such as the one I posted.

Please _read_ and _analyze_ personally (that means don't let the bot do the job) the content of the paper posted on wikimedia commons _before_ you (or your bot) decide to invalidate modifications on this article.

Once the proof I have provided has been validated by mathematicians of international reputation (which, by providing the paper on wikimedia commons, was a way of providing these mathematicians the opportunity to view and validate my proof), your bot will look foolish. Since you're the one operating the bot, it seems obvious you will by then have made a total fool of yourself.

I have once already been faced with a wikipedia "moderator" (or should I say "censor") that tried to revert some first-hand information I gave about swiss electrical outlets. He finally changed his mind. I sure hope what now seems a standard "you plebs have no authority to edit wikipedia" will quickly come back to a true, collaborative encyclopedia.

Regards. — Preceding unsigned comment added by Petaflot (talk • contribs) 20:40, 20 February 2019 (UTC)

To editor Petaflot: I am not a bot, and I do not use any bot. I assume to have reverted you edit, because it does not follows any Wikipedia rule. Firstly, Wikipedia does not accept any original research (see WP:OR), and your edit is blatant original research. Secondly, every possibly controversial or disputed assertion must be supported by reliable source (see WP:Reliable sources), and your source is clearly not reliable, as not regularly published, and not supported by any secondary source (see WP:SECONDARY). Finally, as your result contradicts a well know and well studied theorem dated from 1837, if your result would be true, this would logically imply that all modern mathematics would be wrong.

So your edit cannot be accepted without breaking the main policies of Wikipedia. D.Lazard (talk) 21:22, 20 February 2019 (UTC)

Comment

You left a comment on my talk page: "I have the (possibly wrong) impression that you are not yet fully aware of the Wikipedia guidelines on this subject". I was wondering what gave you that impression. Thanks. Latex-yow (talk) 22:22, 25 February 2019 (UTC)

To editor Latex-yow: Normally, discussions should not be split into several talk page. This is why I answer here with a template insuring notification, instead replying on your talk page,

Sorry, my post was caused by an edit by another user, who changed ℤ into $\mathbb {Z}$ instead of ℤ, including in a section header. My error come from several of your edits, such as this one where you have changed many (not all) formulas, sometimes reduced to a single letter, from html to latex. Apparently, your most recent edits follow the guidelines that I have tried to summarize, so my post was probably not useful, and you may ignore it. D.Lazard (talk) 10:46, 27 February 2019 (UTC)

Thanks for responding. With respect to the edit you link to, I changed ƒ to LaTeX because that character should not be used per guidelines, while f and f have readability and spacing issues. I switched C to $\mathbb {C}$ because the article also used both and I was aiming for a uniform notation. When an article uses a consistent notation for $\mathbb {N} ,\mathbb {Z} ,\mathbb {Q} ,\mathbb {R} ,\mathbb {C}$ I don't convert it, say, from \mathbb to \mathbf. Finally in LaTeX formulas "\ldots" is preferable to "...". Latex-yow (talk) 11:24, 27 February 2019 (UTC)

Edit of the infobox of Paul Erdős

Hello, you reverted my edit for as you said, because I didn't summarize, I consider my goal is not only to summarize but also to unify as much information as possible on the main page with the associated pages, but also to keep it comprehensive, i.e. "summarized". As far as my conception of "known for" is concerned, I don't have a narrow minded approach towards the concept of 'known for" that I presume you have, a mathematically ignorant person may or may not "know" a person or his name because of his direct "contributions" to knowledge.

Also, to back up my argument, I'll also mention you 3 few "good","protected" and a "featured" article that have the same format of representation of "known for" field that I tried to edit in my editing of Paul Erdős' article.
Please have a look at the following articles: Richard Feynman, John von Neumann and Paul Dirac. The 3 aforementioned articles are rated "featured, "good" and "semi-protected" respectively also have a lengthy collapsible list.

Also, to avoid a super-lengthy infobox, I added a collapsible list, as it'd hence, be intuitively understandable to the reader that the associated field may contain a long/medium sized information.

My request to you would be not to revert the article and to allow my previous edit, as it'll both unify and summarize the article's infobox. — Preceding unsigned comment added by Debaditya2000 (talk • contribs) 17:05, 18 March 2019 (UTC)

To editor Debaditya2000: The edits of an article must be discussed in the talk page of this article, not on my page. Edits on multiple articles of mathematics must be discussed in the talk page of the project. Here WT:WPM, where a thread has already been open about your edits (WT:WPM#Infobox edits (thankfully not about FLT). I repeat here what I have already written on your talk page. When you (or anybody else) are reverted, and you disagree with the revert, you have to follow the procedure that is detailed in WP:BRD. You must not try to restrict the discussion to you and the editor who has reverted you, as all editors who watch the article must be involved if they want. Also, at least two other editors have reverted your edits of the infoboxes. So, if you want to continue this discussion this must be done in WT:WPM#Infobox edits (thankfully not about FLT). This is why I do not discuss your arguments here. D.Lazard (talk) 17:38, 18 March 2019 (UTC)

To editor D.Lazard: I have written it on the page you posted the link of.

Stable?

Thanks for your edit to the topology article. In the first sentence you wrote, shouldn't the word be "closed" rather than "stable"? Jrheller1 (talk) 17:11, 31 March 2019 (UTC)

To editor Jrheller: in mathematical jargon, this is the same. However "closed" is better because it may be linked. D.Lazard (talk) 17:30, 31 March 2019 (UTC)

Elliptic curve

Would you be able to take a look at my creation q:Elliptic curve and answer a query of mine (I don't understand the math involved)? Our article Faltings's theorem seems to imply that from the POV of algebraic geometry elliptic curves with genus 1 are the hardest i.e. harder than genus g=0 or >1 whereas Michael Harris says they are the "simplest class of polynomial equations for which there is no simple way to decide whether the number of solutions is finite or infinite". Solomon7968 13:10, 16 April 2019 (UTC)

reversion feels bad

Hi, D.Lazard--

Your advice to another editor on this talk page helped me understand Wikipedia's BRD cycle. So your demonstrated interest in effective communication gives optimism that you may care about the slapped-in-the-face feeling that I got from your speedy reversion of [my attempt to improve] the solutions/ roots/ zeros sentence in the Quadratic_equation article.

The content of the attempt is small potatoes. Beyond the typo that you and I agree warranted correction, the vocabulary of "zeros of an equation" is unlikely to confuse anyone. I'm happy to leave it the way you preferred it.

If you are interested in the inter-personal impact, however, I can recommend Wikipedia:Revert_only_when_necessary. That page does a better job than I can of those considerations.

Respectfully, --DavidHolmes0 (talk) 23:10, 19 April 2019 (UTC)

To editor DavidHolmes0: OK, I was too fast for reverting. I have almost restored your version, except that I have removed the usage of "expression" that is not necessary and is too technical for this elementary article. The rationale for this is the following (I give details because other people may come here, by following the link in my edit summary)

Originally and properly speaking, one should talk of root of a polynomial (extension of the concept of nth root), zero of a function, and solution of an equation. Presently, the terms zero and root are almost equivalent, except that root is generally preferred for univariate polynomials (algebra and number theory), while zero is generally preferred for the other cases (the unit circle is the set of zeros of $x^{2}+y^{2}-1;$ using "root" here would sound strange).

On the other hand, talking of zero or root of an equation is almost nonsensical: what is zero in a solution of the equation $ax^{2}+bx=-c?$ --D.Lazard (talk) 08:28, 20 April 2019 (UTC)

To editor D.Lazard: Thank you for...

• the kind words above
• the further improvement in the sentence in the article, which is now clearly better than the way I left it
• and most of all, for the language lesson on the solution / root / zero choice, which has bothered me for a while. That education is valuable to me because I'm employed at a New York City high school to introduce students to computer science. The quadratic formula provides a motivating example of expressing math they know in a computer language they don't yet know. So you can appreciate that I want to use the language precisely. That's where your response is so helpful to me. I think I have been clear on the phrase solution of an equation. But thanks to your note I now have some insight into the use of root, which I have previously avoided because it made no sense to me. Now, if I understand you correctly, mathematicians talk about the root of a general univariate polynomial as an extension to the idea of the $n^{th}$ root of a number, $k$, since the root of the number, ${\sqrt[{n}]{k}}$, is a solution to the special polynomial equation $x^{n}=k$.

Mixing in here — the essay mentioned by DavidHolmes0 is, well, basically completely wrong. Edits need to be justified. If an edit is not an active improvement, it should be reverted completely, and then any good parts re-added.

There are two main reasons for this. The first is that there should be a bias to stability. There is a benefit to being able to expect article content to remain constant except when it improves, and the improvements need to be actual improvements.

The other is a sort of general "best practice" in controlled-versioning systems, which WP articles are an example of. When editors make complicated changes quickly, it is hard for watchers to keep track of exactly what has happened. If a large set of changes, either in one edit or in a quick succession of edits, has problematic elements, then it is best to revert to a known state and add from there, with the reasons for each specific change being clear.

As for "feels bad" — yes, this is possible, but this is more something to "get over" than to accommodate. Sure, I feel my hindbrain triggering my — is it sympathetic or parasympathetic nervous system, I can never remember? — when I am reverted, but this is a response to subject to rational challenge and figure out a way to work with the other editor, not a reason for the other editor not to revert in the first place. --Trovatore (talk) 20:50, 20 April 2019 (UTC)

My recent edit to the short description of Polynomial

Hello D.Lazard, you reverted my removal of the phrase 'In mathematics," from the short description of Polynomial citing that it exists for readers who ignore context and that not everyone may know the 'polynomial' is a mathematical term. I would contest that for three reasons, the first is that 'polynomial' has only two definitions in English, and the other meaning which is about scientific species naming conventions which is much less likely to be familiar to a reader than a topic in algebra. The second is that even if a reader was wholly unaware of what the context of the article "sum of products of variables, power of variables, and coefficients" would probably make them think of mathematics. Finally, the fact that there do not exist any hatnote templates at the top of the page linking to similarly named articles indicates to me that current consensus regards it unnecessary to link other similarly named pages because most readers are likely to be looking for Polynomial or that there does not exist any pages that are similarly enough named to be linked to in a hatnote.—T.E.A. (Talk•Edits) 22:38, 18 May 2019 (UTC)

Short descriptions in a menu of suggested articles

To editor The Editor's Apprentice: In WP:Short description one can read The short description will be the first point of contact for many readers, so it should be readily comprehensible. In the figure on the right, you can see that many reader can see the short description without opening the article. So it must be comprehensible even for people who do not know anything to mathematics. Removing "In mathematics" means in fact asking such readers to infer something such as "As I do not understand anything, it should be mathematics". It is not the image of mathematics that I want to give. In WP:Short description one can read also The short description is not required to provide an adequate definition of the article subject. These two quotations suggest that "Mathematical object" or "Mathematical concept" could be a better description, as the present explanation, although correct, is not useful for helping threader to decide whether he want open the article: Either he has absolutely no idea of what is a polynomial, and the explanation is too technical for being readily comprehensible, or he has a vague idea, and the explanation is not sufficient for avoiding opening the article. In both cases, the shorter descriptions that I suggest are convenient. D.Lazard (talk) 09:07, 19 May 2019 (UTC)

@D.Lazard: I disagree with your assessment that the short description for this article, or for any article related to mathematics, "must be comprehensible even for people who do not know anything to mathematics" since a great number of mathematical concepts, including polynomials, cannot be explained with out background knowledge and so applying such as rule would relegate those many articles to to one of the two descriptions that you mentioned "Mathematical concept" or "Mathematical object" which although communicating to a read that the article is about mathematics provides them no further information about what specifically the subject is. I see that the article on short descriptions says that short descriptions "are not required to provide an adequate definition of the article subject" but I would say that that doing so concisely should still be a goal. The point I was trying to make about if a reader was wholly unaware of the context was that if you were to ask a large number of people what they thought was being described I would guess that a vast majority of them would correctly identify mathematics. I do see the general danger of people associating mathematics with things they don't understand but I think that in this case even though a reader may not gain a complete understanding of what a polynomial is they almost definitely would gain a basic grasp of the concept.—T.E.A. (Talk•Edits) 16:49, 19 May 2019 (UTC)

Euclidean domain

In your most recent edit, you changed < to ≤ in several places. Is this what you wanted? My textbook indicates f (r) < f (b) for a Euclidean valuation.—Anita5192 (talk) 16:44, 22 May 2019 (UTC)

To editor Anita5192: Oops, I was confused by &lt ;. I'll fix this. D.Lazard (talk) 17:09, 22 May 2019 (UTC)

Thank you! —Anita5192 (talk) 17:27, 22 May 2019 (UTC)

Vandermonde matrix (reverted edit)

Hello, what was wrong with the link I added? I am new to wiki editing. Thanks for explaining. — Preceding unsigned comment added by Martin.patil (talk • contribs) 21:30, 1 June 2019 (UTC)

To editor Martin.patil: I have linked my edit summary to WP:ELNO, which lists the types of external links that must be avoided in Wikipedia. The first item is Any site that does not provide a unique resource beyond what the article would contain if it became a featured article. In other words, the site should not merely repeat information that is already or should be in the article. The eleventh item is Blogs, personal web pages and most fansites (negative ones included), except those written by a recognized authority. (This exception for blogs, etc., controlled by recognized authorities is meant to be very limited; as a minimum standard, recognized authorities who are individuals always meet Wikipedia's notability criteria for people.) As "MathDoctorBob" does not verifies the notability criteria for people, both items provide a valid reason for not accepting this external link. D.Lazard (talk) 10:10, 2 June 2019 (UTC)

Resultant (reverted edit)

Hello,

I have to disagree here. For one, the existence of algebraic closures requires (some weaker version of) AC, so what you claim to be equivalent assertions is in fact not equivalent in ZF (OTOH, the existence of splitting fields doesn't require any choice). Second, even if we put foundational issues aside then it's unnecessary to bring the algebraic closure (which may be some very messy infinite extension of the base field) in the picture when all the computations are happening in some finite extension. I really don't see how that is supposed to be clearer for most readers.

Regards, GreenKeeper17 (talk) 14:15, 8 June 2019 (UTC)

This article is not only for specialists of number theory. More readers are interested in polynomials with real or complex coefficients, and have no idea of what is a splitting field, but know the fundamental theorem of algebra. Probably, it would be worth to add after "algebraically closed field" something like "in particular, if the coefficients are real or complex, one generally takes the complex numbers for such an algebraically closed field".

If, after having read WP:TECHNICAL, you continue to disagree, the best is to open a discussion in the talk page of the article. Then you will see if there is a consensus for one of the formulations. D.Lazard (talk) 15:11, 8 June 2019 (UTC)

OK, how about this: "... in any algebraically closed field (or more generally any field in which A and B split) containing the integral domain." ? GreenKeeper17 (talk) 15:58, 8 June 2019 (UTC)

Multivalued function

Hi, may I ask you for help with issues about binary relation and multivalued function:

1. In the lead of multivalued function, I found the text "a multivalued function ... is a another term for binary relation" (I'll abbreviate this as "mvf ⇔ br"). I changed it to "a multivalued function ... is a left-total relation" (abbreviated as "mvf ⇔ lt ∧ br"), since (1) "function" means "total function", and (2) binary relation#Special types of binary relations contained the text "[a relation] R is left-total when it is ... multivalued function", which amounts to "mvf ⇒ lt ∧ br". However, I encountered another occurrence of "mvf ⇔ br" in binary relation#Definition which reads: "A binary relation is also called a multivalued function". So, I got uncertain whether my changes were ok, and I'd like to hear your opinion on that (i.e. on "mvf ⇔ br" vs. "mvf ⇔ lt ∧ br").
2. I saw that you restored in the lead of multivalued function the link to left-total. This is fine (provided my changes described unter 1. were ok), except that it is a link from an article into a section. Usually, one would expect in the item "Left-total" of binary relation#Special types of binary relations a tag like {{main|multivalued function}}, that is, a link from the section to the article.

Many thanks in advance for your comments. Best regards - Jochen Burghardt (talk) 13:17, 17 June 2019 (UTC)

Point 2: most links aim to provide a definition to the reader and do not need a back link in the target article. Here, a {{main}} would be more confusing than useful. I am not sure that it is useful to edit the target. At most a mention such as {{tq|In some contexts, typically in complex analysis, a left-total function is called a multivalued function.

The first point is more complicated. Firstly, the equality "function = total function" is not valid in all mathematics. Typically, it is not the common standard in mathematical analysis and computation theory, where the determination of the domain of a function can be difficult, and even not computable. IMO, the two different definitions of multivalued functions are are similar. On the other hand, one must recall that the term "multivalued function" has been introduced in mathematical analysis. One of the first multivalued function that students encounter is complex logarithm, which is certainly not a total function.

By the way, in mathematical analysis, a function is generally not viewed as a relation. Therefore, it would be better to not relying this article too heavily to binary relation. I'll change the first sentence of the article accordingly, hoping that you will agree with the new version. D.Lazard (talk) 14:37, 17 June 2019 (UTC)

Degree or degrees?

I surrender, I promise. But you keep speaking of a degree of certainty, while I keep thinking multiple degrees (which could only reasonably be those of certainty, never backward). For what it's worth (if anything), the current header is the plural version. As long as you're aware of and cool with that, so am I. InedibleHulk (talk) 08:44, July 8, 2019 (UTC)

To editor InedibleHulk: I can accept the plural, although WP:MOS would certainly recommend singular, as a given event has only one degree of certainty. D.Lazard (talk) 17:14, 8 July 2019 (UTC)

Absolutely. But this section doesn't mention a given event. Just covers the general range for every theoretical case, and all ranges have multiple levels (even True or False are two). InedibleHulk (talk) 19:12, July 8, 2019 (UTC)

Chain Integration by Parts

Yes, Petaflot is entirely correct. You, D.Lazard and Deacon Vorbis, among many others, seem to want to revert (e.g. my contributions) something merely because they appear disagreeable with you. On this note, you should not tell me what you think edit warring is, because I already know what that is. In fact, I had already mentioned this to Deacon Vorbis as a warning. Also, perhaps, you think I am playing victim, but who is the victim may be subjectively assigned.

Yes, there are indeed no cited sources. In fact my proofs rely solely on the content within the collapsible templates, which in turn reference the respective Wikipedia pages (yes, I am playing your game by saying Wikipedia is a source - why don't you humor me and take all those sources from those other Wikipedia pages and cite them in my sections in Chain rule and Integration by parts?). Yes, the notation is unconventional, but that is necessary (you are at total liberty to revise the notation at your own discretion, but I cannot allow you to revert or police my contributions - replace with you own version for your own sake, delete, copy, etc.). I contribute with Chain Integrals and higher-order integrals because of what they are and not what mathematical role they will play with respect to Deacon Vorbis or your opinions. That is for mathematical society to decide.

Indeed, my claim here may appear outrageous to you. I apologize for any animosity this may cause you, but I stand by it. Thanks for you consideration. Harry Princeton (talk) 18:33, 19 July 2019 (UTC)

Just a couple quick notes. First, Harry Princeton, you copied another editor's comment here and kept their signature without any sort of explanation. This was confusing, and it inappropriately added a signed comment to a section that a user didn't make, so I've removed it (sorry for the excessive messages, DL). Second, please stop preemptively pinging me during your edit summaries; there's no need to do that.

Now then, if you find yourself in a content dispute, the place to discuss it is on the article talk page(s), not on user talk pages. This gives other editors a chance to weigh in, and it gives you the chance to build a wider consensus, which is what you generally need if material that you wish to add is being reverted (see WP:BRD) – especially when it's unsourced WP:OR. I'd also advise you to stop with the accusatory tone, and focus on the content (see WP:BATTLEGROUND); you'll generally be a lot more successful in disputes that way. I won't say any more here, but if you wish to discuss the content dispute on the article talk page(s), then I think that would help.

And just as a postscript, the editor you were trying to quote from above was someone who was trying to insert a common bit of mathematical crankery – that he had solved the problem of angle trisection with compass and straightedge, despite it being proved impossible. That's probably not a good case to cite in your favor. –Deacon Vorbis (carbon • videos) 18:57, 19 July 2019 (UTC)

Sorry for the secondary dispute with Deacon Vorbis, D.Lazard. Harry Princeton (talk) 19:11, 19 July 2019 (UTC)

Deacon Vorbis: (1) It was not you who I was talking to, but another person. So you should not reply. The situation already escalated to the point where I "could not reason with you," so I wanted a moderator to look at my case, hence D.Lazard. (2) No, I did not copy another editor's comment, but quoted it. You are more than welcome to instruct me how to quote another editor rather than copy him, but not point fingers at me the instant you see something disagreeable. Here, it is evident that you do not take my revision comments seriously as an editor's. (3) NO! It's urgent. This is exactly the point - I don't believe you are instructing me in good faith, so I need a third opinion. Better more urgent than less urgent, at least in my own interest, lest you take my edits not seriously. (4) Thanks for the explanation. But there is a point to be made with the very existence of that mathematical anecdote; you are acting like one of them. Again, I want D.Lazard to moderate my case, and not take this case into your own hands. Thanks! Harry Princeton (talk) 19:11, 19 July 2019 (UTC)

See User talk:Harry Princeton#Original research and reliable sources. - DVdm (talk) 19:13, 19 July 2019 (UTC)

Finally, an admin. Thanks so much :). Harry Princeton (talk) 19:20, 19 July 2019 (UTC)

No admin. - DVdm (talk) 19:25, 19 July 2019 (UTC)

(edit conflict) HP, as far as quoting, you can take a look at {{tq}} or {{talkquote}} and see what's appropriate for you (or find another one). I'm confused by your comment; you pinged me here, so I replied. Even if you didn't ping me, discussions are open for all to see, so there's no reason why I shouldn't be able to chime in. I'm also confused because DL reverted you also for essentially the same reason as I did...maybe you want a fourth opinion instead? Nothing about this is urgent; the articles will still be here tomorrow. Also, Wikipedia doesn't have moderators (it does have admins, aka sysops, with some advanced permissions, but those don't really apply here). I'm also confused when you say the situation escalated. I reverted your additions twice; that's about the barest minimum of a dispute; I can see no escalation here. Anyway, as I said, I'd advise you to take your concerns to the appropriate article talk pages. That's your best bet moving forward. There's no guarantee that you'll get your way. You may find that a compromise can be reached, but you may find that there's overwhelming opposition to what you want to do. That's just the way Wikipedia works. –Deacon Vorbis (carbon • videos) 19:29, 19 July 2019 (UTC)

Plane Algebraic Curves

Some comments on your undo. I think you are right that I wrote too hastily. However I think some things need to be fixed:

> many non-singular algebraic curves are not birationally equivalent to any non-singular algebraic plane curve (this is the case of all curves of positive genus).

You mean genus g > 1, since elliptic curves are smooth plane curves of genus 1. It is a crucial fact that smooth g > 1 curves are not embeddable in the plane, and should be featured more prominently, not just in a parenthesis at the end.

> a skew curve is a curve that is not embedded in a plane, it is not a curve that cannot be embedded in a plane

OK, but your version says "non-plane curves (often called space curves or skew curves)", which leads to the same confusion. Again: feature the distinction between a non-plane-embeddable curve and a plane curve.

> introduction of unnecessary notation in the lead

Are ten words really clearer than one equation? Will a naive reader, puzzled by an equation like p(x,y) = h(x,y,1), be helped by a long sentence summarizing the equation? -Magyar25 (talk) 14:02, 22 July 2019 (UTC)

About your first point: The previous version was written too hastily (I remember I was its author). I am not sure that the sentence is correct for g > 1. The true assertion that is relevant in this context is that a nonsingular curve of genus 0 and degree ≥ 3 cannot be mapped to a nonsingular plane curve by a projective transformation.

Second point: There are several sorts of morphisms (and thus of isomorphisms} for algebraic curves (as well as for any algebraic variety). At least, rational mappings, polynomial mappings, and, for projective curves, polynomial transformations. The concept of "plane-embeddable curve" is non-sensical without specifying the sort of allowed mappings. Thus, it is too technical for the lead. However, I agree that the definition of space and skew curves deserve a specific paragraph.

Third point: I agree that dehomogenization is better explained with a formula. Nevertheless the notation for this must not be introduced several sentences before.

I'll try to fix these points. D.Lazard (talk) 16:24, 22 July 2019 (UTC)

Your revert

About this revert: are you saying that PG(3,2) has an incorrect title? If you're correct, that article should be moved, and a whole bunch of spaces should be added all over that article. However, sources I've looked at, such as one from the Annals of Discrete Mathematics, do not use a space. MANdARAX • XAЯAbИAM 07:44, 5 August 2019 (UTC)

To editor Mandarax: This is a valid source. I'll revert myself. D.Lazard (talk) 08:00, 5 August 2019 (UTC)

Thanks. I wasn't familiar with the terminology, and thought maybe you were more knowledgeable on the subject. MANdARAX • XAЯAbИAM 08:14, 5 August 2019 (UTC)

the revert of Quartic function

Hello， since this topic "Quartic function" is filled with long formulas, I added a small section to summarize the pattern of roots in short. If the pattern is wrong, could you give some criticism here? According to the rule of "good faith" reads "When a disagreement occurs, try the best to explain and resolve the problem".

You also tag this edit as "NOR", however, the pattern is not new nor original discovery. The formula of roots is there for several hundred years. Best regards. Lingwanjae (talk)

To editor Lingwanjae: If you read WP:NOR, you will see that, in Wikipedia, "original research" does not means new, but means "result of the work of a single person, that is not validated by WP:secondary sources". This is definitely the case of the section that you added, as there is no source giving this pattern, at least for degree four. In fact, the formula for the roots, given in this article, does not follows your pattern when the term of degree three is zero. Moreover, for being significant, such a pattern must include information on the nature of the operands of the nth roots; this is not the case of your edit. D.Lazard (talk) 13:07, 10 August 2019 (UTC)

To editor D.Lazard: Thank you for your kindly response so quickly. Firstly, let me explain some mathematic symbol:

$j_{1}{\sqrt[{4}]{A}}+j_{2}{\sqrt[{4}]{B}}+j_{3}{\sqrt[{4}]{C}}$ ,where $j\in \{h^{0},h^{1},h^{2},h^{3}\},\ \ h^{4}=1$

serves as a general pattern covering specific examples such as

$h={\sqrt {-1}},$

and $(j_{1},j_{2},j_{3})=(h^{0},h^{0},h^{0})$,

or $(h^{0},h^{2},h^{2})$,

or $(h^{2},h^{0},h^{2})$,

or $(h^{2},h^{2},h^{0})$.

Or equivalently:$(j_{1},j_{2},j_{3})=(1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1)$.

Or roots =$({\sqrt[{4}]{A}}+{\sqrt[{4}]{B}}+{\sqrt[{4}]{C}}),\ ({\sqrt[{4}]{A}}-{\sqrt[{4}]{B}}-{\sqrt[{4}]{C}}),\ (-{\sqrt[{4}]{A}}+{\sqrt[{4}]{B}}-{\sqrt[{4}]{C}}),\ (-{\sqrt[{4}]{A}}-{\sqrt[{4}]{B}}+{\sqrt[{4}]{C}}),\$

which serves as a pattern covering the formula in section 4.4.4 Euler's soulution, which reads root $r_{1}=({\sqrt {\alpha }}+{\sqrt {\beta }}+{\sqrt {\gamma }})/2,r_{2}=...$

Secondly, wiki policy. Wiki insists on giving references so to protect the correctness of wiki, but it gives no policies on editing the topic in a comprehensive manner. So I try to give a short section about patterns, which is nothing new but might be comprehensive as I thought. Anyway, I will add some references in my section. I wish new edition will match your criterion as I respect you are a kindly senior wiki editor. Best regards. Lingwanjae (talk)

To editor Lingwanjae: Firstly, I have edited your post for an indentation that is conform to the manual of style.

WP:COMPREHENSIVE is a policy that asserts that article must be comprehensives. Sorry for saying that, but your edit and your post are not written in a "comprehensive manner". Although being a specialist of this subject, I have great difficulties for understanding what you are trying to explain. This resemble to an introduction to Lagrange resolvents, but I an quite sure that you do not know of them.

Anyway, this subject is an old one, and a lot of work has been done on it. So, for adding a new section on "patterns", you must have a textbook that explain them. Writing something, and then searching references is not the right way to do. You must have a reliably published source before starting to write something in Wikipedia. D.Lazard (talk) 17:05, 10 August 2019 (UTC)

To editor D.Lazard: Hello, it's nice to talk about math. Am I clear to explain that Euler's solution matches the form of $({\sqrt[{4}]{A}}+{\sqrt[{4}]{B}}+{\sqrt[{4}]{C}})$ ? Or more explanation is necessary? Best Regards. Lingwanjae (talk)

My talk page, and more generally Wikipedia are not the place for discussing your thoughts. Euler's solution is a linear combination of three square roots, not fourth roots. Again, this does not deserve any discussion here, unless you can provide a textbook that present and discuss this. Please stop using Wikipedia as a forum. D.Lazard (talk) 08:19, 11 August 2019 (UTC)

Angle trisection

Hello,

thank you for your answer ; somehow I got two different ones and that confuses me.

I have, in the mean time, sent my papers to "real" mathematicians and have already started debating the validity of the procedure.

I feel flattered that you see this as original research ; I don't believe it is because it's only the application of a known algorithm to a known problem.

You may, however, also be aware that Gallileo's work was considered to be correct until Newton came along, whose work was also considered to be correct until a guy who went by the name of Einstein proved him wrong. In the meantime, generations of mathematicians and physicists blindly accepted what eventually turned out to be flawed proofs. In fact, I don't really care if _you_ believe or not that Wanzel (and others) could be wrong : the method works and that's a fact, measurable _and_ computable.

In a short time I shall also provide an explanation of how and why George Cantor was mislead when he stated his "diagonal" theory. That theory, in particular, is one of the biggest frauds I'm aware of in the history of mathematics. I'm also aware this will definitely not please the majority of mathematicians who have built an extensive system on flaky grounds and will need to reconsider quite a lot of the things they believe they have proven on top of this fraudulent theory : it's actually gonna hurt way more than proving Wanzel was wrong. Shit happens.

Wikipedia is not a place for "religious" considerations dictated by a small elite that has a clear interest in the conservation of their monopoly of "truth". It is a place for people to share their knowledge. In this regard, this edit was clearly _not_ an act of vandalism.

If you are not a "competent mathematician" as you say, then it should not be _your_ decision to edit a post such as mine to purely and simply suppress that information ; instead, you should make sure such mathematicians have access the subject so they can give prove or disprove it, and at the very most edit the page in such a way that it would say something like "An amateur mathematician based in La Chaux-de-Fonds believes he's formalized a method to trisect the angle with straight-edge and compass but this has not yet been cross-proved nor dissmissed".

Additionally, the method I propose solely uses a straight-edge and compass ; this fits the antique definition of the problem (which says nothing about not using recursive procedures) and hence should be considered as valid. I hereby invite you to try this method on any scale and see for yourself if it works. : if you do it right, I guarantee it will. — Preceding unsigned comment added by Petaflot (talk • contribs) 00:08, 21 February 2019 (UTC)

See next edit

The edit summary in [4] is nonsensical – in no circumstances can you be sure which edit will come next. If you want something based on a revision other than current, then open the base revision for editing and save changes as usual. Don’t pollute recent changes with edits making no sense in isolation. Incnis Mrsi (talk) 09:43, 21 August 2019 (UTC)

My Mistaken Edit of "Parametric Equations" Article

Thank you for correcting my mistake/misunderstanding (67.34.80.221). — Preceding unsigned comment added by 67.34.80.221 (talk) 17:12, 25 August 2019 (UTC)

Euler's formula

Dear D, My derivation for Euler's formula has not been published but has been read, not formally reviewed, by several professional mathematicians.

I published it on the Duth pages. There it was not wiped, but clarification was asked which I added. I can share the pdf containing the more detailed derivation if you want.

I did not want to clutter the page with a detailed derivation.

Cheers, Bart vanderbeke (talk) 16:52, 3 September 2019 (UTC)

To editor Bart vanderbeke: Unfortunately (for you), this is what Wikipedia calls original research, and the policy WP:NOR forbids adding original research to Wikipedia. D.Lazard (talk) 18:09, 3 September 2019 (UTC)

So why waste my time?

I asked politely a while ago at the talkpage. NO ANSWER. Don't be so frigging lazy. Tony (talk) 09:08, 5 September 2019 (UTC)

... and why waste my time to answer to questions whose answer can be found in the guidelines? D.Lazard (talk) 09:33, 5 September 2019 (UTC)

No, you've got it wrong. My time is far more important than yours. Let's leave your rank rudeness at that. Tony (talk) 11:14, 5 September 2019 (UTC)

A doubtful edit from you

Hi, D.Lazard! I want to say that those written at talk:sequence are a proposed addition to that article, not a forum intention as you supposed.--109.166.129.57 (talk) 16:05, 10 September 2019 (UTC)

Geometry edits

Thank you, that will make things much easier. Are there any particular sections you could point out to me to use? Because you've done so much of the work recently, you know what kind of errors need to be corrected in these pages, so I could use your advice! Brirush (talk) 16:22, 14 September 2019 (UTC)

Ah, never mind, I see your edits in the history. Thanks! Brirush (talk) 16:33, 14 September 2019 (UTC)

To editor Brirush: Also, I have explain my edits in the talk page. D.Lazard (talk) 17:36, 14 September 2019 (UTC)

Involute

Hi, I think a user is just demolishing the article involute,(see Talk:Involute, too) . Please could You check ? Thanks !--Ag2gaeh (talk) 15:55, 29 September 2019 (UTC)

Expressions vs. formulas

Hi! The motivation for my recent edit at expression (mathematics) was that in first-order logic, authors usually distinguish terms from formulas. I naively thought, that "term" and "expression" has the same meaning (this is supported by the examples in the article), and based my edit on this. On the other hand, I agree to your responding edit: the distinction term/formula is mostly an unnecessary sophistication (except that requiring true≠false usually is necessary even in an otherwise purely equational setting that considers junctors as particular function symbols).

So, if you know better than my naive opinion, I'd no objection if you edit the text accordingly.

It would be fine, however, if the article would say what expressions are good for ("denoting objects rather than / including truth values"), and not just how they are built ("according to some syntax rules"). At term (logic), I found the analogy "term"/"formula" to "noun phrase"/"sentence" a good introduction. - Jochen Burghardt (talk) 09:32, 1 October 2019 (UTC)

To editor Jochen Burghardt: Some comments:

• An equation involving variables is not a "sentence". For being a sentence, quantifiers must added. More generally, one must distinguish between an equality of objects, which is a statement, and an equality that appears in a formula, which is an operator. Clearly $ax^{2}+bx+c=0$ is not a statement, but an expression. These are the rules for manipulating expressions that are used for transforming it into the quadratic formula. By the way, the word algebra comes from the title of al-Khwarizmi's book, where it denotes a rule for manipulating expressions. So (this is my own WP:OR) al-Khwarizmi was the first to distinguish equality of objects from equality as an operator in an expression. This was the foundation of algebra. IMO, this is this rather subtle distinction between two meanings of equality that makes so difficult to give a correct shape to the article Equality (mathematics).
• As far as I know, the term expression has been introduced by the need of computer algebra (before learning computer algebra, I never heard the term of expression in mathematics). As far as I know, the word term is preferred for the same notion in logic and some parts of computer science such as lambda calculus.
• For explaining the difference between an object and an expression that represent it, a good example is undecidable problems: for example Richardson's theorem asserts that deciding whether an expression represents zero is undecidable.

This being said I agree to add some explanation, but, just now, I have othre priorities. D.Lazard (talk) 11:14, 1 October 2019 (UTC)

Reverted 1 edit by Bob K: \triangleq is not a standard notation in mathematics (in more than 40 years of professional mathematician, I have never seen it be used in mathematical papers

And you  have  seen  ${\overset {\underset {\mathrm {def} }{}}{=}}$  ??

$\triangleq$ shows up in Google searches for "mathmatical symbol for equal by definition":

https://www.google.com/search?q=mathematical+symbol+for+%22equal+by+definition%22&oq=mathematical+symbol+for+%22equal+by+definition%22

https://books.google.com/books?id=-WC_AAAAQBAJ&pg=PA3&dq=equal+by+definition&hl=en&sa=X&ved=2ahUKEwjg4YbJ6pvlAhVGmuAKHSRwCgkQ6AEwBXoECAYQAg#v=onepage&q=equal%20by%20definition&f=false

And as you can see here: https://en.wikipedia.org/wiki/List_of_mathematical_symbols,
Wikipedia is not limited to the symbols preferred by professional mathematicians.

--Bob K (talk) 13:37, 14 October 2019 (UTC)

To editor Bob K: The question is not whether some people use this definition. The true question is wheter the intended audience of the article is aware of this notation. As this article is about an advanced concept in mathematics and physics, the audience is certainly restricted to people with some experience in mathematics or physics, that is with the level of an undergraduate student or, maybe, a good college student. I am quite sure that most of them do not know this notation. Certainly := is better known, and its usage is explicitly discouraged by WP:MOS. I guess that \triangleq is essentially used in US educational mathematics only. If my guess is true, this is a further reason for avoiding this symbol, as English Wikipedia must not be restricted to any regional audience. D.Lazard (talk) 16:04, 14 October 2019 (UTC)

About ${\overset {\underset {\mathrm {def} }{}}{=}},$ I do not like it either, but everybody can understand it without explanation. So, contrarily tp \triangleq there is no harm to keep it. D.Lazard (talk) 16:04, 14 October 2019 (UTC)

Fundamental mathematical operation

Discussion removed due to lack of support. You can keep your comments. Thanks.

— Preceding unsigned comment added by 24.190.8.215 (talk) 09:03, 18 October 2019 (UTC)

To editor 24.190.8.215: Your edit is not a post per as WP:Wikipedia is not a blog. Moreover I have not removed it, as you can see it in the history of the page. I have reverted it for the following reasons:

• Misplaced: the discussion whether it is fundamental or not must not occur before the description of the addition.
• Poorly written: incomplete sentences, grammatically incorrect, ...
• Entirely based on your personal opinion, which is strictly forbidden in Wikipedia, see WP:OR
• Wrong, as multiplication of real numbers cannot be deduced from addition only
• Wrong also because your definition of fundamental is not the common one
• Wrong with your definition of fundamental, as ignoring Peano arithmetic, which defines all operations of arithmetics from the successor function only.

D.Lazard (talk) 09:31, 18 October 2019 (UTC)

Infinity edit physics

Your edit on physics infinity is wrong. In _physics math_ there are two infinitys; 1/∞=infinitesimal is the axiomatic idealization of a specific though indeterminate arbitrarily large number thus effectively an arbitrary large number A, thus effectively finite. The other ∞s are just arbitrarily large numbers (again axiomatically idealized) thus effectively finite. However in their world they are considered infinite by language. If you told them the number of cubes in a sphere per an argument on the derivation of an equation for volume of sphere's from radius is not ∞ they'd disagree even though the number is related to the precision. When precision is unspecified to simplify they assume ∞ precision.

Your contribution Annoys me. As a perfect pattern going a finite number of orders of magnitude rules change. The rules of physics for the inside of a particle are different for the rules for the inside of a sugar cube. So no rule seems to apply literally ∞ly except in religion-of-atheism physics which is effectively science fiction even though believed.

However their is an ∞ that is ∞ in math. Proof ∞ (think 4 color theorem proof). But not Cantorian ∞s. Instead their is ∞ analogous to ∞ 🏨 with a top floor and another analogous to ∞ 🏨 without top floor. Cantorian ∞s combine both (w+1 like ∞🏨 no top floor plus a floor on top of it, messing up 'ordinal' math rules, number as set size.) Victor Kosko 01:12, 19 October 2019 (UTC) — Preceding unsigned comment added by Victor Kosko (talk • contribs)

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Reason for reverting edit

Sir, can you please elaborate why you reverted my edit. https://en.m.wikipedia.org/wiki/Special:MobileDiff/930318135 Which assertions do you think are wrong. I'll provide you reliable sources. 2405:204:348F:A538:5494:7BB0:32EC:70DE (talk) 20:44, 11 December 2019 (UTC)

To editor 2405:204:348F:A538:5494:7BB0:32EC:70DE:

• No need to repeat in the lead the first line of section "History", which comes immediately after.
• Omar Khayyam (not Omar khayyam, as you wrote) had no influence on the later developement of the subject of the article. So, his work is not important enough for the lead. Moreover, per WP:NPOV, he must not be more emphasized than other contributors cited in section History.
• It is wrong to credit Descartes of results on the subject of the article
• It is wrong to credit Cardano only the general solution of the cubic equation (see the history section).

D.Lazard (talk) 08:51, 12 December 2019 (UTC)

Revert

[5]? There is no page Division (disambiguation). - CRGreathouse (t | c) 02:53, 13 January 2020 (UTC)

To editor CRGreathouse: Division (disambiguation) exists and is a redirect. WP:INTDAB is perfectly clear, one must not create direct links to disambiguation pages that have not the suffix "(disambiguation)" in their name. Piped links are acceptable, but personally, I think that it is better to inform the reader that the target of the link is a dab page (principle of least astonishment), D.Lazard (talk) 10:12, 13 January 2020 (UTC)

Matrix multiplication reversion

Look at this: https://en.wikipedia.org/enwiki/w/index.php?title=Matrix_multiplication&type=revision&diff=935903747&oldid=935876988 then explain to me why the revert was necessary. thanks Metaquanta (talk) 20:05, 15 January 2020 (UTC)

To editor Metaquanta:: The previous version was its elements (vectors) are uniquely represented by a finite sequence, called coordinate vector, or scalars, which are the coordinates of the vector on the basis. In this sentence, "or" is clearly a typo that must be replaced by "of". Even with the typo corrected, the formulation is correct, but awful. Your edit is its elements (vectors) are each represented by a finite sequence of scalars, called a coordinate vector, which are the coordinates of the vector on the basis. It is worse, as "which" seems to refer to "coordinate vector" (in which case, the plural would be a typo). Otherwise a reader may understand that it refers either to "scalars" or to "elements". "Scalars" is intended but the mathematical meaning would require the restrictive "that", without comma.

The true reason of my revert was that fixing the ambiguities of the sentence seemed easier with the previous formulation. Note also that, after my revert, five edits by me and another user have been needed for gettting something really not confusing (in my opinion). D.Lazard (talk) 21:27, 15 January 2020 (UTC)

Apparently you missed how the diff linked above demonstrates, by your own hand, why you are mistaken. Perhaps you should look again. Actually, considering the contents of your talk page, I think you should probably review Help:Reverting. Metaquanta (talk) 05:29, 16 January 2020 (UTC)